!
!
Sampling!St rategies!for!Representative!
National!CRVS!Verbal!Autopsy!Planning:!
!
A!Guidance!Document!an d!Sample!Size!
Calculator!Tool!
Part A: Principles and Strategy
Version 2.4
July 26, 2018
Review Version
.
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Contents
2
Contents
Part A: Principles and Strategy .......................................................................................................................... 1
Acronyms ......................................................................................................................................................... 6
Preface ............................................................................................................................................................. 7
Acknowledgements .......................................................................................................................................... 9
Executive Summary ........................................................................................................................................ 10
Part A - Principles and Strategy ....................................................................................................................... 13
1. Introduction ............................................................................................................................................... 13
1.1 Pathways to scale for CRVS Verbal Autopsy .............................................................................................. 13
1.2 Rationale for CRVS VA sampling ................................................................................................................ 14
1.3 Rationale for cluster sampling ................................................................................................................... 14
2. Key principles for National CRVS VA Sampling ........................................................................................... 15
2.1 Non-competition with medical certification ............................................................................................. 15
2.2 The need for effective universal death notification and registration ........................................................ 16
2.3 Deaths without medical certification of cause of death ........................................................................... 16
3. Strategic operational considerations for National CRVS VA Sampling ......................................................... 17
3.1 Defining the operational cluster ................................................................................................................ 17
3.2 How many Cause Specific Mortality Fractions? ........................................................................................ 17
3.3 Disaggregation of results ........................................................................................................................... 17
3.3.1 Male-Female disaggregation ................................................................................................................. 18
3.3.2 Age Group disaggregation ..................................................................................................................... 18
3.3.3 Urban-rural disaggregation ................................................................................................................... 18
3.3.4 Sub-national administrative disaggregation ......................................................................................... 19
3.4 De-duplication ........................................................................................................................................... 19
4. Considerations for framing the CRVS VA sample ........................................................................................ 19
4.1 The Sample Frame ..................................................................................................................................... 19
4.2 Inclusions and exclusions .......................................................................................................................... 20
5. Considerations for calculating the CRVS VA sample size ............................................................................. 20
5.1 Statistical approach used in the CRVS VA Sample Size Calculator Tool ..................................................... 20
5.2 Overview of the CRVS VA Sample Size Calculator Tool ............................................................................. 20
5.3 Tool input parameters required ................................................................................................................ 21
5.3.1 Number of clusters ................................................................................................................................ 21
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Contents
3
5.3.2 Maximum acceptable uncertainty range .............................................................................................. 21
5.3.3 Mean cluster population ....................................................................................................................... 21
5.3.4 Crude death rate ................................................................................................................................... 22
5.3.5 Number of years to aggregate for trend ............................................................................................... 22
5.3.6 Percentage of deaths with MCCD ......................................................................................................... 22
5.3.7 Under-notification and non-response rate ........................................................................................... 22
5.3.8 Scenario where population size of eligible clusters is known ............................................................... 23
5.4 Tool output parameters produced ............................................................................................................ 24
5.4.1 Number of clusters required ................................................................................................................. 24
5.4.2 Estimated total population in the sample ............................................................................................. 24
5.4.3 Estimated number of deaths in the sample per year ............................................................................ 24
5.4.4 Estimated number of VAs needed per year .......................................................................................... 24
5.4.5 CSMF uncertainty ranges ...................................................................................................................... 25
6. Considerations for selecting the CRVS VA sample clusters .......................................................................... 25
6.1 Defining the sample selection strategy ..................................................................................................... 25
6.1.1 Stratification .......................................................................................................................................... 25
6.1.2 Simple random sampling ....................................................................................................................... 26
6.1.3 Systematic sampling .............................................................................................................................. 26
6.1.4 Probability Proportional to Size sampling ............................................................................................. 26
6.1.5 Stratified single-stage cluster PPS sampling .......................................................................................... 26
6.2 Documenting the sample method ............................................................................................................. 27
7. Limitations ................................................................................................................................................. 27
8. Scaling up strategy and follow-up period ................................................................................................... 28
9. Conclusions ................................................................................................................................................ 28
Part B: Methods and Tools .............................................................................................................................. 30
Glossary .......................................................................................................................................................... 31
1. Introduction ............................................................................................................................................... 34
2. Preparing the sampling frame .................................................................................................................... 34
3. Calculating the sample size ........................................................................................................................ 35
3.1 Preparatory steps ...................................................................................................................................... 35
3.2 Using the CRVS VA Sample Size Tool ......................................................................................................... 36
4. Selecting the sample clusters ..................................................................................................................... 38
4.1 Stratification .............................................................................................................................................. 38
4.2 Probability Proportional to Size sampling ................................................................................................. 38
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Contents
4
ANNEXES ........................................................................................................................................................ 40
Annex A. Statistical basis of the CRVS VA sample size calculations .................................................................. 41
A.1. Assumptions .............................................................................................................................................. 41
A.2. Power and Significance level ..................................................................................................................... 41
A.3. Individual vs. Cluster design ...................................................................................................................... 41
A.4. Unmatched vs. Matched design ................................................................................................................ 41
A.5. Design related parameters ........................................................................................................................ 42
A.5.1. Coefficient of variation between clusters ......................................................................................... 42
A.5.2. Intra-cluster correlation coefficient .................................................................................................. 42
A.5.3. Design effect ..................................................................................................................................... 42
A.5.4. Coefficient of variation in cluster size ............................................................................................... 43
A.6. Formula for sample size based on proportions ......................................................................................... 43
A.7. Formula for sample size based on rates .................................................................................................... 43
A.8. Cluster size ................................................................................................................................................ 43
A.9. Uncertainty range ...................................................................................................................................... 44
A.10. Further Adjustments ................................................................................................................................. 44
A.10.1. Disaggregation by male and female ................................................................................................. 44
A.10.2. Proportion of deaths having MCCD .................................................................................................. 44
A.10.3. Under-notification and non-response rate ....................................................................................... 44
Annex B. Worked example implementing the Guidance and Tool in one country ............................................ 45
B.1. Preparing to calculate the Cluster Sample Size ......................................................................................... 45
B.1.1. Operational cluster definition ........................................................................................................... 45
B.1.2. Disaggregation level of results .......................................................................................................... 45
B.1.3. Number of years to aggregate for trend .......................................................................................... 45
B.1.4. National level estimates ................................................................................................................... 45
B.2. The sampling frame ................................................................................................................................... 48
B.3. Estimating k ............................................................................................................................................... 49
B.3.1. Options to estimate k ....................................................................................................................... 49
B.4. Estimating MIS ........................................................................................................................................... 53
B.5. Calculating the CRVS VA sample size ......................................................................................................... 54
B.6. Sampling strategy for selecting the CRVS VA sample clusters .................................................................. 58
B.7. Calculating the number of clusters required in order to disaggregate results for male and female ........ 60
B.8. Calculating the number of clusters required separately for areas with different proportions of deaths with
an MCCD ................................................................................................................................................................. 62
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Contents
5
Annex C. Additional Resource Material ........................................................................................................... 64
C.1. National Crude Death Rate estimates for Data for Health Initiative CRVS VA countries .......................... 64
C.2. Method for estimating national level CSMFs ............................................................................................ 65
C.3. Top 20 CSMF estimates for Data for Health Initiative CRVS VA countries ................................................ 67
C.4. Verbal Autopsy Target Cause Lists ............................................................................................................ 76
C.5. Link to CRVS VA Costing Tool for download .............................................................................................. 76
References ...................................................................................................................................................... 78
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Glossary
6
Acronyms,
CDR Crude Death Rate
CRVS Civil Registration and Vital Statistics
CSMF Cause-Specific Mortality Fraction
CSMR Cause-Specific Mortality Rate
CV Coefficient of variation in cluster size
DE Design Effect
DHIS2 District Health Information System 2
GIS Geographic Information System
HDSS Health and Demographic Surveillance System
ICC Intra-cluster Correlation Coefficient
INDEPTH International Network for Demographic Evaluation of Populations and their Health
k Coefficient of variation of the true outcome measure between clusters at one point in time
k
m
Coefficient of variation of the true outcome measure between clusters within the matched pairs
in absence of anything which could change the mortality and/or the CSMFs
MCCD Medical Certification of Cause of Death (sometimes MCCOD)
MIS Maximum possible Inflation in sample Size
PPS Probability Proportional to Size sampling
RS Random Start
SAVVY Sample vital events with verbal autopsy
SCI Symptom-Cause Information
SI Sampling Interval
SMoL Start-up Mortality List for ICD Coding
SRS Sample Registration System
VA Verbal Autopsy
WHO World Health Organization
See Part 2, Methods and Tools, for a Glossary defining these and other terms used throughout this Guidance
Package.
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Preface
7
Preface,
The purpose of this package of a two part Guidance Document and its companion Sample Size Calculator Tool is
to assist countries with scale up and rollout planning for the application of verbal autopsy (VA) as a function of a
national Civil Registration and Vital Statistics (CRVS) system.
Users of the package will include those tasked with designing and managing the CRVS VA system. The package is
intended to be used after pre-testing and pilot phases during which the processes, methods and possibly costing
of the CRVS VA system are perfected and established, and before the scale-up and rollout phase. Every country
will have different implementation circumstances. Therefore, this document is necessarily generic in hopes that
the considerations, options, and methods provided can be adapted and adjusted to the majority of circumstances.
As of 2018, 13 countries participating in the Bloomberg Philanthropies Data for Health Initiative are engaged in a
pre-test or pilot phase implementation of mobile automated VA. Automated VA is intended to be integrated into
their CRVS systems to improve availability of cause of death data for deaths without a medically certified cause,
most of which occur in the community. These initial pre-tests or pilots, usually at district or equivalent scale, have
allowed countries to start to cost out and plan national scale implementation. Although there has been limited
experience with sample vital event “registration” systems with VA (China, India, Indonesia, Tanzania, and Zambia)
these have not been fully integrated with CRVS and do not act to officially register vital events.
In cases where national CRVS authorities wish to take a representative sampling approach to VA implementation,
there remain several open questions and a lack of practical guidance for how to estimate the annual number of
VAs needed to provide valid and representative cause-specific mortality fractions (CSMFs). These data play an
important role in forming health policy and program decisions. There are also questions about the issue of national
and sub-national stratification. Stratification may be needed to address possible disparities due to ethnic, socio-
economic, demographic (e.g. urban/rural) and epidemiologic factors. Therefore, a diverse expert group was
convened to deliberate on these issues and prepare a practical guidance document and tool to assist countries
scaling up from pre-test or pilot phases to national CRVS VA systems. This Technical Guidance Document and
associated tool is the result.
Development of Concepts:
Initial discussions on the concept of CRVS VA sampling strategies were held as part of an International Consultation
Workshop organized and financed by the Bloomberg Philanthropies Data for Health Initiative and convened at the
Swiss Tropical and Public Health Institute CRVS Innovation Hub in Basel Switzerland, August 18-19, 2017.
Participants at this workshop included:
Alan Lopez, Bloomberg Philanthropies Data for Health Initiative, University of Melbourne, Australia.
Daniel Chandramohan, Department of Disease Control, London School of Hygiene & Tropical Medicine, London,
UK.
Daniel Cobos, Bloomberg Philanthropies Data for Health Initiative, CRVS Innovation Hub, Swiss Tropical and Public
Health Institute, University of Basel, Basel, Switzerland.
Deidre McLaughlin, Bloomberg Philanthropies Data for Health Initiative, University of Melbourne, Melbourne,
Australia.
Don de Savigny, Bloomberg Philanthropies Data for Health Initiative, CRVS Innovation Hub, Swiss Tropical and
Public Health Institute, University of Basel, Basel, Switzerland.
Erin Nichols, Bloomberg Philanthropies Data for Health Initiative, NCHS US Centers for Disease Control and
Prevention, National Center for Health Statistics, Hyattsville, Maryland, USA.
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Preface
8
Gregory Kabadi, Bloomberg Philanthropies Data for Health Initiative CRVS Country Coordinator, Dar es Salaam,
Tanzania.
Jordana Leitao, WHO Geneva, Verbal Autopsy Working Group, Geneva, Switzerland.
Magdalena Paczkowski, Bloomberg Philanthropies Data for Health Initiative, Vital Strategies, New York, NY, USA.
Maigen Zhou, China CDC, Shanghai, China.
Margarita Ronderos, Bloomberg Philanthropies Data for Health Initiative CRVS Technical Advisor, Bogota,
Colombia.
Martin Bratschi, Bloomberg Philanthropies Data for Health Initiative, Vital Strategies, Singapore.
Peng Yin, China CDC, Shanghai, China.
Prasanta Mahapatra, Institute of Health Systems, Hyderabad, India.
Sam Clark, Ohio State University, Westerville, Ohio, USA.
Soewarta Kosen, National Institute of Health Research and Development, Jakarta, Indonesia.
Tom Smith, Swiss Tropical and Public Health Institute, Infectious Disease Modeling Unit, University of Basel, Basel,
Switzerland.
Preparation of the CRVS VA Sampling Strategy Guidance Document:
The first drafts of Part A of this guidance document were prepared by Don de Savigny. Sabine Renggli prepared
the first drafts of Part B and all annexes. All others below have contributed significantly to subsequent drafts of
the combined document and final product.
Adam Karpati, Bloomberg Philanthropies Data for Health Initiative, Vital Strategies, New York. USA.
Daniel Cobos, Bloomberg Philanthropies Data for Health Initiative, CRVS Innovation Hub, Swiss Tropical and Public
Health Institute, University of Basel, Basel, Switzerland.
Don de Savigny, Bloomberg Philanthropies Data for Health Initiative, CRVS Innovation Hub, Swiss Tropical and
Public Health Institute, University of Basel, Basel, Switzerland.
Erin Nichols, Bloomberg Philanthropies Data for Health Initiative, US Centers for Disease Control and Prevention,
National Center for Health Statistics, Hyattsville, Maryland, USA.
Martin Bratschi, Bloomberg Philanthropies Data for Health Initiative, Vital Strategies, Singapore.
Philip Setel, Bloomberg Philanthropies Data for Health Initiative, Vital Strategies, New York. USA.
Sabine Renggli, Bloomberg Philanthropies Data for Health Initiative, CRVS Innovation Hub, Swiss Tropical and
Public Health Institute, University of Basel, Basel, Switzerland.
Sam Notzon, Bloomberg Philanthropies Data for Health Initiative, US Centers for Disease Control and Prevention,
National Center for Health Statistics, Hyattsville, Maryland, USA.
Development and testing of the CRVS VA Sample Size Calculator Tool:
This guidance package includes an associated user-friendly CRVS VA Sample Size Calculator Tool in MS Excel. The
following individuals contributed to the conceptualization, design, development and testing of the tool or
contributed to the documentation of the tool.
Christian Schindler, Biostatistics Unit, Swiss Tropical and Public Health Institute, University of Basel, Switzerland.
Daniel Chandramohan, Department of Disease Control, London School of Hygiene & Tropical Medicine, London,
UK.
Daniel Cobos, Bloomberg Philanthropies Data for Health Initiative, CRVS Innovation Hub, Swiss Tropical and Public
Health Institute, University of Basel, Basel, Switzerland.
Don de Savigny, Bloomberg Philanthropies Data for Health, CRVS Innovation Hub, Swiss Tropical and Public Health
Institute, University of Basel, Basel, Switzerland.
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Preface
9
Erin Nichols, Bloomberg Philanthropies Data for Health Initiative, US Centers for Disease Control and Prevention,
National Center for Health Statistics, Hyattsville, Maryland, USA.
Gregory Kabadi, Bloomberg Philanthropies Data for Health Initiative CRVS Country Coordinator, Dar es Salaam,
Tanzania.
Hee-Choon Shin, US Centers for Disease Control and Prevention, National Center for Health Statistics, Hyattsville,
Maryland, USA.
Isaac Lyatuu, Department of Epidemiology and Public Health, Swiss Tropical and Public Health Institute. University
of Basel, Switzerland.
Jon Wakefield, University of Washington, Seattle, WA, USA.
Katherine Fielding, Medical Statistics and Epidemiology, London School of Hygiene & Tropical Medicine, London,
UK.
Lea Multerer, Department of Epidemiology and Public Health, SwissTPH. University of Basel, Switzerland
Philip Setel, Bloomberg Philanthropies Data for Health Initiative, Vital Strategies, Seattle, WA. USA.
Richard Hayes, London School of Hygiene & Tropical Medicine, London, UK.
Sabine Renggli, Bloomberg Philanthropies Data for Health Initiative, CRVS Innovation Hub, Swiss Tropical and
Public Health Institute, University of Basel, Switzerland.
Sam Clark, Ohio State University, Westerville, Ohio, USA.
Yulei He, US Centers for Disease Control and Prevention, National Center for Health Statistics, Hyattsville,
Maryland, USA.
Acknowledgements,
This work was supported financially and technically by the Bloomberg Philanthropies Data for Health Initiative and
partners at the University of Melbourne, Vital Strategies, US Centers for Disease Control and Prevention, National
Center for Health Statistics, and the University of Basel Swiss Tropical and Public Health Institute.
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Preface
10
Executive,Summary,
Many low-income countries are considering introducing verbal autopsy (VA) as an integral part of their civil
registration and vital statistics (CRVS) systems in order to generate population level cause of death statistics in
those parts of the country where there is currently no possibility for medically certified cause of death assignment.
There are presently at least 13 countries
1
implementing VA whereby these countries are establishing their
technical, process and systems integration needs prior to launching national-scale VA implementation.
The primary purpose of VA in CRVS is to provide statistical trend data at population (not individual) level on the
cause-specific mortality fractions for monitoring major health interventions, universal health coverage and
sustainable development goals. Such data do not require a verbal autopsy on every death. A sample of deaths is
sufficient. But how large should the sample of deaths be? And how should those deaths be selected to ensure
results are representative? This strategic guidance document and associated tool are intended to assist such
countries.
What are some of the key principles in this strategy? The most important driving principles behind the VA
Sampling Strategy and Tool are:
1) Verbal autopsy is not a substitute for medically certified cause of death. It is intended for use where there
is no physician, and for generating population level data on proportions and rates of cause-specific
mortality. Therefore this guidance is written for countries where a substantial share of the population
experiences mortality outside of health facilities and in the absence of medical attendance at death. The
tool factors into its calculations the understanding that VAs will be done primarily on community deaths,
i.e. those occurring outside of health facilities, even though some deaths occurring in health facilities may
not receive a medically certified cause.
2) Verbal autopsies do not need to be conducted on all deaths, but only on an appropriately large random
sample of deaths. It is logistically and operationally inefficient to do random VA sampling on individual
deaths. Therefore cluster sampling is recommended whereby the cluster unit needs to be decided. The
principle we propose is that the minimum cluster sample unit should be the catchment area of deaths that
can be reached by a single trained and equipped VA interviewer. Such geographic areas tend to be of a size
in which each interviewer would have a work load of 2 to 4 VAs per month, and tend to be approximately
the size of census or CRVS enumeration areas (e.g. population sizes between 2,000 and 20,000). This is the
minimum cluster unit size. However, some implementation designs may decide on larger cluster units with
larger populations and multiple VA interviewers working across the cluster.
3) Sampling should be driven by careful a priori decisions on the levels of disaggregation that will be applied
in data analysis. At a minimum, the sample size should be adequate to allow analysis of the leading causes
of death separately for males and females, and if possible, for the major age groups of neonates, children
and adults.
4) Strategic consideration must be given to further geographic disaggregation of analyses (urban/rural, and
sub-national (regional/provincial)), especially in countries with decentralized governance of health and
social services.
1
Bangladesh, Colombia, Ghana, Kenya, Morocco, Myanmar, Papua New Guinea, Philippines, Rwanda, Tanzania,
Solomon Islands, Sri Lanka, Zambia.
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Preface
11
5) Statistical representation requires not just the correct minimum sample size in terms of number of clusters
(and VAs) to address the above analyses, but also the drawing of that sample through a random sample of
the cluster units from an appropriately constructed sample frame. This Guidance provides a methodology
for both calculating the size, and doing random cluster sampling. Given it is highly likely that at some point
countries will wish to have disaggregated analyses at least to state, provincial or regional level, we have
designed the calculator to be based on an approach of single-stage stratified random cluster sampling
proportional to population size.
Who should use this guidance and tool? This CRVS VA Sampling Strategies Guide and its associated Sample Size
Calculator Tool are intended primarily for those responsible for providing high quality mortality data in countries
where a decision has been made to use VA as part of the CRVS system. It allows CRVS VA managers in such
countries to determine the number and location of geographic units to be sampled to detect a nationally
representative change in cause specific mortality fractions or rates in populations where medical certification
of cause of death is not yet feasible.
When should the Guidance be applied? The Guidance and the Tool are expected to be of value to countries who
have concluded the pre-test or pilot phases of their VA implementation and who have established the technical,
process, and incremental cost considerations with regard to VA implementation at scale.
What questions does the Guidance address? The Guidance addresses four key issues regarding the
implementation of CRVS VA at national scale:
1) What are the key logistical considerations to make with regard to the definition of an operational CRVS
VA cluster?
2) What are the key strategic considerations to decide with regard to the level of disaggregation at which
analyses will be conducted (sex, age, urban-rural, sub-national administrative, trend period, etc.)?
3) What is the minimum number of sample units (clusters) and number of VAs needed given an acceptable
uncertainty range for detecting significant CSMF changes over time? Or alternatively, what is the
uncertainty range for detecting significant CSMF changes over time given a number of clusters
sampled?
4) How should the required sample clusters be selected from the national sample frame?
How can the Guidance be used? The tool allows CRVS managers to:
1) Determine the required sample size for a national or sub-national system given an acceptable
uncertainty range for detecting significant CSMF changes over time.
2) Determine the uncertainty range for detecting significant CSMF changes over time given the current or
planned deployment of VA.
How does this Guidance help? The relationship between the number of VAs conducted and the resulting
uncertainty range for detecting significant CSMF changes over time of various levels of CSMF is not intuitively easy
to appreciate. For example, a given number of VAs conducted in a relatively small number of very large clusters
will give wider uncertainty ranges compared with those conducted in a larger number of smaller clusters. This has
operational and cost implications. Hence, this tool should be used in concert with the CRVS VA Costing Tool. Using
both tools will be helpful in making key decisions with regard to strategies for scaling up CRVS VA in national
systems.
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Preface
12
The tools are available from the Bloomberg Philanthropies Data for Health Initiative CRVS Knowledge Gateway at
the University of Melbourne (https://crvsgateway.info) and other CRVS resource portals.
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
13
Part,A,-,Principles,and,Strategy,
1. Introduction,
This package of guidance materials (Parts A, B, Annexes and the associated CRVS VA Sample Size Calculator Tool)
is intended to assist countries with their Civil Registration and Vital Statistics (CRVS)-Verbal Autopsy (VA) scale up
and rollout planning. Users will include those tasked with designing and managing the national CRVS VA system,
supported by a governing body such as a National Mortality Committee of the National CRVS Committee.
In addition to discussing strategies and principles, this guidance package proposes approaches to conventional
cluster sampling methods and provides the statistical rationale, logic, mathematical formulations, and a worked
example, for: i) calculating the required number of clusters needed in a VA cluster sample design; and ii) drawing
the needed clusters from a national sampling frame.
Every country will have different implementation circumstances and variations in approach. Therefore, this
document is necessarily generic in hopes that the considerations, options, and methods provided can be adapted
and adjusted to most scenarios where representativeness of VA data is sought.
1.1 Pathways*to*scale*for*CRVS*Verbal*Autopsy*
This guidance package is designed to be used after the pre-test or pilot phases of VA implementation during which
the technical methods, processes, systems integration, and costing of the CRVS VA are established, and before
demonstration and scale-up (See Table 1.1.1).
Table 1.1.1. Pathways to Scale: Phases of CRVS VA Implementation
Phase
Purpose
Example
Scale
Pre-Test
For technical issues
Adapting and testing technologies,
instruments, translations, etc.
~ 100 VAs
Local scale
Pilot
For process issues
Developing training, supervision,
communications, IT processes,
initial costing, and SOPs.
~ 1,000 VAs
District scale
Demonstration
For systems integration
issues
Developing integration with CRVS
and HMIS information systems and
conducting full costing and sampling
strategies.
>1,000 VAs
Regional scale
emulating
proposed national
scenarios
Scaling up
For institutionalization
Rolling out to national or sub-
national implementation
National sample
scale
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
14
1.2 Rationale*for*CRVS*VA*sampling*
In many low-income countries, the majority of deaths occur in areas where there is no medically qualified
professional to legally determine and certify the cause of death. Yet such information is critically necessary for
effective Civil Registration and Vital Statistics (CRVS) systems and for use in policy and planning. In such countries,
there is growing interest to integrate verbal autopsy (VA) into national CRVS systems to cover those deaths
currently unreached by medically qualified death certification (de Savigny, Riley et al. 2017). The purpose of such
innovations in CRVS is to provide more complete estimates of the cause of death patterns at population level, and
not medical certification of individual causes. To achieve this goal, not every death requires a VA; a representative
sample of non-medically certified deaths will suffice.
One rationale for adopting a sampling approach is that VA is a sensitive data collection enterprise that requires a
household visit and rapport with deceased family members. As such, it is a relatively costly and logistically complex
endeavour. Depending upon the numbers of deaths occurring outside of health facilities, costs and complexities
could be prohibitive should a country aim to assign a cause to every such death using VA in the national population.
A sampling approach, in most cases, can provide statistically valid estimates of the main output of a VA system:
Cause-Specific Mortality Fractions (CSMFs).
Therefore, a key question for national CRVS system managers is how many verbal autopsies are needed per
year and from which locations, to give sufficiently precise estimates of the cause-specific mortality fractions
and rates
2
necessary for reliably informing policy and program decisions?
To date most applications of VA have been in longitudinal health observatory settings such as sentinel Health and
Demographic Surveillance Sites (HDSS) or in mortality surveillance systems such as Sample Registration Systems
(SRS) or Sample Vital Events with VA (SAVVY) systems (de Savigny, Renggli et al. 2017). The former HDSS sites
conduct VAs on the total population in their sentinel sites. Hence, sampling is not an issue. National scale SRS and
SAVVY systems are few and each has taken a different approach to establishing their sample size and sampling
frame. These are reviewed and reported separately (See papers being produced by Tanzania, Malawi,
Mozambique, Zambia, Indonesia, India, and China).
The more specific question of how to sample VAs for integration within CRVS systems has never been fully
explored in ways that balance logistical, epidemiological, and statistical considerations related to the specific
purposes and needs of CRVS systems. The factors to consider in providing guidance on how to sample for VA are
numerous. For example, there are questions with regard to the rapidly changing crude death rates and changing
distributions of causes. In highly populous countries, there can be wide geographic and epidemiologic
heterogeneity within the country. In addition, in all countries there is socio-economic heterogeneity. Further,
political and administrative realities frequently intrude and sometimes over-ride technical and scientific criteria in
the sample selection process.
1.3 Rationale*for*cluster*sampling**
Given that a VA is not required for every non-medically certified death for population level CSMF estimates,
combined with the labour and cost-intensiveness of VA means that the logistical and cost considerations of CRVS
VA are most easily addressed by a cluster sampling approach. Cluster sampling brings with it an attendant design
effect on the sample size and subsequent analytic considerations. Most cluster sampling methodologies are
intended for use in sample surveys, case-control studies or randomized controlled trials of interventions in
2
This Guidance focuses on the cause specific mortality fraction since this is the prime purpose of verbal autopsy; however the uncertainty
ranges for detecting significant CSMF changes as predicted by the CRVS VA Sample Size Calculator Tool are very similar for the corresponding
mortality rate of that particular cause of the CSMF.
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
15
comparative population groups. Although there are cluster sample methods for studying intervention exposure
or health behaviours (e.g. Expanding Programme for Immunization, Demographic and Health Surveys), there are
no standard cluster sampling methods for the monitoring of population level cause-specific mortality. This is
essentially the challenge posed by CRVS VA.
Sample designs using cluster sampling to control costs and enhance logistical feasibility encounter a design effect
due to the fact that variance within clusters is less than the variance in a simple random sample of the whole
population. If the design effect is not accounted for, confidence intervals will be incorrectly too narrow and
analysts will risk making type 1 errors of concluding differences to be significant when they are not. This design
effect can be kept as low as possible by following these general principles:
• Using as many clusters as feasible and affordable;
• Using the smallest operational cluster in terms of population as feasible;
• Using a more constant cluster size rather than highly variable size.
In other words, a design using more small clusters is preferable compared to one based on fewer large clusters.
2. Key,principles,for,National,CRVS,VA,Sampling,
There are a number of key principles to consider in embarking on the establishment of a nationally representative
CRVS VA system. These are summarized below.
2.1 Non-competition*with*medical*certification**
VA is an imperfect tool, but it is generally agreed that it is the best available option for understanding mortality
causes in situations where there is no physician in attendance to document the cause of death (D'Ambruoso,
Boerma et al. 2016). As a first principle of this Guidance it cannot be over-emphasized that the implementation of
CRVS VA must never replace medical certification of cause of death (MCCD) or retard improvements in MCCD.
Complete coverage of death registration, death certification, and medical certification of cause for all deaths is
the primary goal of the mortality assessment function of CRVS. VA should only be considered where there is no
doctor and where there is no possibility to obtain a MCCD, or in implementations strategies where physicians are
given the option of using VA to obtain further information to assess the potential cause of death.
The primary mortality objective of CRVS is to produce nationally representative mortality statistics from high
quality cause of death data sources annually, disaggregated by age and sex. CRVS needs ways to incorporate
information from multiple data sources. For some low resource settings or low CRVS performance countries, such
data may only be sourced from VAs for the majority of deaths in the near future. However, the primary aim is to
move countries towards greater production and use of high quality, high coverage MCCD data.
In low-income countries, physician certified MCCD data is mainly available from hospitals. While there are usually
enough facility deaths to calculate CSMFs as well as cause-specific mortality rates, these estimates are highly
confounded by selection biases. CRVS VA from sample systems will never provide as many deaths as seen in
hospitals, but VA sample sizes should be chosen to be of sufficient size to provide representative CSMFs at least
disaggregated by sex. Secondary mortality objectives of CRVS may be to produce nationally representative trend
data on mortality and national and sub-national estimates with further disaggregation, including sex, age,
urban/rural, and other dimensions of interest, based on high quality cause of death data sources as frequently as
is feasible.
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
16
Thus, the availability of CRVS VA will complement the mortality data obtained from hospitals and other health
facilities. This poses challenges concerning the analysis and use of mortality data
3
.
2.2 The*need*for*effective*universal*death*notification*and*registration*
In any CRVS VA implementation, an active, effective, and universal death notification system is essential. Such a
system should notify all deaths in the community to the CRVS system, recording the fact of death with name, date
of death, sex, age and essential identity information sufficient to register the death and contribute to CRVS.
Nevertheless, given that most CRVS systems are still passive, relying on the family to declare the death to some
authority, notification and registration is problematic. Such systems will not ensure that 100% of deaths are
notified and available for VA follow-up. The degree of under-notification will significantly affect the sample size.
This is accommodated in the CRVS VA Sample Size Calculator Tool but does require some assessment of the under-
reporting rate from the pre-test or pilot phases of the implementation.
2.3 Deaths*without*medical*certification*of*cause*of*death*
Based on the above principle, CRVS VA designs focus predominantly on community (out of hospital) deaths where
there is no physician or chance for MCCD. This affects sample size calculations and require decisions on possible
CRVS VA deployment options. These considerations concern whether to do VAs on:
• All deaths in the sampled cluster
• Only community (out of facility) deaths in the sampled cluster
• Only deaths without an MCCD in the sampled cluster
Each country will need to weigh the pros and cons for their particular circumstance, knowing the coverage and
quality of their facility based MCCD implementation and the cost of VA in the scenario. At current quality levels in
many low-income countries, a significant fraction of the MCCD deaths are poorly certified. Even if correctly
certified, MCCD deaths may not be coded to appropriate underlying causes. If it is decided that VA should only be
done on deaths without an MCCD then excluding MCCD deaths will increase the number of clusters needed for
the National CRVS-VA system and increase the cost of VA in countries where a large proportion of deaths have an
MCCD. This is even so in Africa, where usually only 30% of deaths are in a health facility. Countries need to know
what proportion of deaths currently have an MCCD in order to use the CRVS VA Sample Size Calculator Tool. If
that is not known, then they will need to use the proportion of deaths that occur in hospital as a proxy for MCCD
coverage. Additionally, this approach will bias VA results to those who are far from physician services. This adds
extra analytic complexity and requires weighting estimations when combining data analyses from MCCD hospital
enriched data with VA community enriched data.
3
This Guidance does not discuss VA analytic issues that will be the subject of a separate guidance document from the Bloomberg Philanthropies
Data for Health Initiative.
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
17
3. Strategic,operational,considerations,for,National,CRVS,VA,Sampling,
This section of the guide addresses strategic and operational consideration for CRVS VA sampling.
3.1 *Defining*the*operational*cluster**
A major cost driver for VA in CRVS is the training, deployment, and supervision of the VA interviewer. VA
interviewers are deployed at community level such that they can usually reach their assigned or designated
catchment area on foot or on bicycle without the need for higher transport costs. A catchment area like this would
typically contain a population in the range of 3,000 to 15,000 people and can represent a potential operational VA
cluster sample unit. Where crude death rates are in the range of 5 to 10 per thousand per year, such VA
interviewers are likely to live in catchment areas that experience between two to ten deaths per month in
households where routine visitation is feasible. Such a workload should not overwhelm any other duties the
interviewer might have, and is also not so light that VA skills would be lost over time. In rural settings, such areas
are often categorized in censuses at Administration Area Level 3 (e.g. Sub-district or ward)
4
.
It is therefore important when using this VA Sample Size Calculator Tool to choose a cluster unit with an
appropriate size. We suggest setting the cluster unit definition as the catchment population of a single VA
enumerator or interviewer team. Hence, the selection of the cluster unit is driven by the logistical realities of the
CRVS VA implementation. This is the first decision to set when planning the sampling strategy. Ideally, the
geographic boundaries of operational units will correspond with civil registration jurisdictions.
Note the statistical reality that conducting VAs in a small number of clusters with large populations will lead to a
larger uncertainty range for detecting significant CSMF changes over time than conducting the same number of
VAs in a larger number of clusters with smaller populations.
3.2 How*many*Cause*Specific*Mortality*Fractions?*
VA methods available for CRVS are able to distinguish up to 64 distinct target causes of death. However at
population level, CSMFs are usually over dispersed such that the top 20 causes include about 70% of all deaths.
In ranking the top 20 causes from the largest to smallest, the first ranked (largest) cause usually accounts for 10
to 20% of all deaths. The top five causes usually include CSMFs of 5% or higher, the top 10 include causes down
to about 2% CSMF and the top 20 down to about 1% of all deaths. Therefore providing estimates on the top 20
causes specifically in males and females should cover most causes of interest to policy makers. Hence the CRVS
VA Sample Size Calculator Tool allows setting the desired uncertainty range for detecting significant CSMF changes
over time for the 1% CSMF level (approximately the 20
th
ranked cause). The uncertainty range around larger
CSMFs will always be narrower than that for the 1% CSMF.
3.3 Disaggregation*of*results*
The disaggregation of CRVS VA data is another fundamental consideration in the design of a national CRVS VA
system. For example, national authorities will likely wish to have valid estimates for males and females; for deaths
occurring separately in neonates, children and adults; for urban and rural populations; or for sub-national units
such as states, provinces, or regions, or for causes addressed by targeted policies (e.g. road traffic or malaria
deaths). Each type of disaggregation carries with it important implications for sample size and design. A process
4
Administrative Level 0 is the national boundary; Level 1 is the state, region or provincial Boundary; Level 2 is the district boundary; Level 3 is
county, ward or sub-district boundary; Level 4 is the village, town or municipal boundary; Level 5 is the hamlet, neighbourhood boundary or
enumeration area boundary. There is considerable variation among countries in the use of these terms and not all countries use all levels, in
the same way.
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
18
should be established whereby the necessary stakeholders are consulted, and trade-offs in terms of cost and
complexity are assessed under varying scenarios for disaggregation before a final decision is reached.
This CRVS VA Sampling Strategy Guidance and Calculator Tool will calculate the number of clusters that need to
be selected to provide estimates of the CSMFs for the top 20 causes of deaths in a given population. A major driver
of the sample size will be the number of discrete populations for which you require these top 20 causes (e.g.,
disaggregations by sex, age, geographic area, socio-economic status, etc.). It should be borne in mind that the
number clusters directly affects the number of VAs and interviewers required to implement a CRVS VA system
3.3.1 Male-Female+disaggregation+
It is essential in any CRVS system that results are disaggregated by sex. Therefore, if male-female disaggregation
is required the CRVS VA Sample Size Calculator Tool will approximately double the sample size in order to provide
estimates separately for both male and female causes of death (See Annex A.10.1 andB.7). Thus, the user-
configurable settings of the CRVS VA Sample Size Calculator Tool will allow the choice to provide CSMFs for the
top 20 causes in males and females at national level.
3.3.2 Age+Group+disaggregation+
Modern VA questionnaires and diagnostic algorithms are designed to provide age group specific results for
neonates (zero to 27 completed days of age), children (28 completed days to 11 years of age); and adults (12 years
and above). These age groups constitute very different proportions of the denominator population and of course
very different proportions of the total population mortality (see Table 3.3.1)
Table 3.3.1. Approximate VA age group shares in low-income countries.
Verbal Autopsy Age Group
Share of
total
population
Share of total
mortality
Number of VA detectable
target causes
Neonates (0-27 days of age)
~3%
~5%
6 to 7
Children (28 days to 11 years of
age)
~23%
~15%
26 to 57
Adults (12 years and older)
~74%
~80%
26 to 57
The Sample Size Calculator Tool is designed to estimate the needed sample size for the whole male and female
population of all ages. Some countries may want a particular focus on a smaller age group such as neonates or
children. For neonates, who represent a very small proportion of the total population, a larger sample size would
be needed. However there is less need to disaggregate by sex in neonatal mortality analysis, and there are
relatively few causes of neonatal mortality detectable by verbal autopsy. Neonatal causes tend to be more equally
distributed, so that uncertainty ranges can be estimated around 10% CSMF rather than 1%. For a focus on the
child age group by sex, one would need to approximately quadruple the sample size to obtain the same uncertainty
range across the CSMFs as found for the total (male/female) estimation.
3.3.3 Urban-rural+disaggregation+
Another desirable disaggregation may be by urban and rural populations. With the sampling strategy proposed in
this guidance, the urban-rural ratio is self-weighting, and the sampling strategy will allow national estimates of
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
19
CSMFs, accounting for urban rural status. However, if separate estimates of urban and rural CSMFs are needed,
then the Sample Size Calculator Tool can be used to independently calculate and draw sample clusters from urban
and rural clusters separately.
3.3.4 Sub-national+administrative+disaggregation+
Politically, some countries may wish to provide sub-national estimates of CSMFs based on administrative levels,
most likely down to Administrative Level 1 (e.g. Province, Region, or State level). This will increase the sample size
required, along with the costs and scale of CRVS VA. However, if at the sub-national level, estimates with sufficient
statistical power are only required on the top five causes or so, a national-level sample may be adequate.
3.4 De-duplication*
If VA’s are purposely only done on community deaths or on deaths that do not have an MCCD, there will be
instances where VAs will still be done on deaths having had an MCCD. Community key-informants notifying deaths
to the VA system may not know the MCCD status of the death, and indeed the VA respondent at the household
level may not know the status, or understand the difference between a death certificate and a medical certificate
of cause of death or even a burial permit. In such instances, there is a need to avoid the risk of double counting
and double registration through proper system design and the use of unique identifiers. Addressing duplicate
registration should not be solely a Ministry of Health or Civil Registrar’s data management problem but rather
avoided in the design of processes. De-duplication is most efficiently done manually in combination with IT
solutions as part of system design.
4. Considerations,for,framing,the,CRVS,VA,sample,
4.1 The*Sample*Frame*
To calculate the sample size and determine the operational clusters for CRVS VA, a sampling frame needs to be
created. This is a complete inventory of all clusters eligible to be sampled in the country. Part B of this Guidance
Package provides a sample template for such a database (Preparing the sampling frame). Establishing a sample
frame requires the compilation of available administrative and demographic information for each cluster included:
• name of the cluster;
• a unique administrative ID or census code;
• its parent administrative hierarchy of Region and District;
• current estimated population;
• estimated projection of the current crude death rate;
• derived estimate of the number of expected deaths per year.
Potential governmental sources of the above information are suggested in Part B of the manual.
Some additional cluster information might be valuable. This could include:
• urban or rural status;
• area in km
2
;
• derived population density per km
2
;
• the presence of hospitals and health facilities per cluster; or
• the number of lower administrative area units (e.g. number of villages).
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
20
• clusters that might host unusual populations (such as national parks or reserves, refugee camps or
nomadic populations) may also be marked and considered in inclusion/exclusion decisions.
4.2 Inclusions*and*exclusions*
It is useful to open this sample frame database in a Geographic Information System (GIS) or any other GPS
application that hosts the GIS shape or boundary files for the clusters, assuming the clusters have the correct name
or index field. This allows visualizing the size and spatial distribution of the clusters on a national or regional map.
The GIS mapping of the clusters will make evident certain extremes, such as very large area clusters with very
sparse population densities, or very small, densely populated clusters in cities or slums. The presence of refugee
camps, national parks and reserves, and other non-representative populations should also be mapped. You may
wish to exclude such areas, including very low population density clusters from your sample frame. Such maps are
also useful in understanding and communicating how the final sample will be distributed across the country.
5. Considerations,for,calculating,the,CRVS,VA,sample,size,
This section of the Guidance Package gives an overview of the CRVS VA Sample Size Calculator Tool and
summarizes what input parameters it requires, and what outputs it delivers. A Step-by-Step Manual is provided
in Part B of this Guide along with Annexes that provide the details of the statistical calculations it uses. Part B also
provides a real-world worked example of how the Tool can be applied in determining a national CRVS VA sample
size.
This guidance assumes that the national stakeholders have made decisions concerning the operational cluster unit
definition and the required disaggregation level of the results as described in Section 3.
5.1 Statistical*approach*used*in*the*CRVS*VA*Sample*Size*Calculator*Tool*
The statistical approaches used in this CRVS VA Sample Size Calculator Tool are based on the guidance given by
Hayes and Moulton in their book on cluster randomized trials (Hayes and Moulton 2009). Additionally, further
literature was consulted to take into account less trial specific setting as they are present in CRVS VA systems. A
more detailed description of the statistical basis of the CRVS VA sample size calculations and all formulae are
elaborated in Annex A. Here we will focus on the most important parameters a user needs to understand in order
to make use of the Sample Size Calculator Tool.
5.2 Overview*of*the*CRVS*VA*Sample*Size*Calculator*Tool*
The CRVS VA Sample Size Calculator Tool is a complex statistical calculator currently in MS Excel, but with a very
simple user interface. User defined inputs are entered into yellow shaded cells. At start up, the user selects the
country name from a drop-down list and enters the year on which the input data is based on. There is an option
to indicate if the sample is for a subnational stratum such as a Region.
The tool works in two modes:
1) Mode 1 calculates the required sample size (number of clusters) for a pre-determined acceptable uncertainty
range for detecting significant CSMF changes over time for the CSMF of 1% which must be entered in a
designated cell.
Or
2) Mode 2 calculates the uncertainty ranges for detecting significant CSMF changes over time for a given number
of clusters which must be entered in a designated cell.
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
21
Finally the analyst indicates (a) whether or not there is an intention to disaggregate results by sex with selecting
yes or no and (b) if the population size of each eligible cluster is available. (See Figure 5.2.1)
Figure 5.2.1 Example of the start-up screen from the CRVS VA Sample Size Calculator Tool
5.3 Tool*input*parameters*required*
If the population size of each eligible cluster is not known the tool requires one mode specific input (5.3.1 or 5.3.2)
and five general inputs to calculate the above described scenarios (5.3.3-5.3.7) (See Figure 5.3.1). For the scenario
where the population size of each eligible cluster is known, see 5.3.8.
5.3.1 Number+of+clusters++
To estimate the uncertainty ranges for detecting significant CSMF changes over time based on a given number of
clusters, you will need to enter the number of clusters you are expecting to sample.
5.3.2 Maximum+acceptable+uncertainty+range++
The uncertainty range is the range within which changes in CSMFs over time will not be detectable with sufficient
statistical power. Note: the range is given in percentage change, which is not to be mistaken with percentage point
change. We have indexed the Calculator to allow you to specify the acceptable uncertainty range for detecting
significant CSMF changes for the smallest CSMF of interest (causes in the range of 1% of total deaths) as for this
cause the range will be the widest. Uncertainty ranges at all higher CSMFs will always be narrower. Thus, the
value to be entered is the uncertainty range (percentage change) of the 1% CSMF that is acceptable. For example,
setting the acceptable uncertainty at 50% (as in Figure 5.2.1) means that the tool will calculate a sample size
capable to detect a change in CSMF over time of 50% or more, meaning for the 1% CSMF an increase to 1.5% or a
decrease to 0.5% in the next time period.
5.3.3 Mean+cluster+population+
The Calculator needs to know the mean cluster population in order to estimate the numbers of deaths, and hence
VAs needed. Ideally the cluster definition should be chosen such that the range of cluster populations is not too
large.
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
22
5.3.4 Crude+death+rate+
The annual crude death rate (CDR) per 1,000 is a key input parameter that affects CRVS VA sample size. You will
need a national estimate. This might be available from a recent census, but note that in many low-income
countries, CDR changes measurably from year to year. In most low-income countries, the CDR is presently falling.
Thus, for the purposes of estimating the sample size for a national CRVS VA system it is better to be conservative
and choose a lower expected value for CDR. Using a lower CDR increases the likelihood that enough clusters are
sampled to produce the desired estimates. CDRs can be found online from a number of sources that model and
forecast CDR trends for each country (See Part B and Annex C.1).
5.3.5 Number+of+years+to+aggregate+for+trend+
The Calculator will need to know how many years you aim to aggregate for the trend analysis. As a default it
adjusts for a three-year follow up period. This means that it is assumed that deaths occurring within the three
years will be aggregated and CSMFs from the first three years will be compared with CSMFs of the second three
years. We make the assumption that there is no re-selection of clusters after the first three years. The calculator
estimates the number of clusters needed to detect a significant change in one CSMF between the first and the
second three years given a pre-determined uncertainty range for detecting significant CSMF changes.
5.3.6 Percentage+of+deaths+with+MCCD+
Assuming a strategic design decision has been made that VA will be conducted only on deaths that occur outside
of health facilities or for deaths without a MCCD (see Section 2.2) a national estimate of the proportion of deaths
in health facilities or with an MCCD will be required, respectively.
5.3.7 Under-notification+and+non-response+rate+
It is very likely that it will not be possible to conduct a VA on every eligible death in the cluster. One problem could
be that deaths for which VA should be done are not notified. This is particularly of concern with neonatal deaths.
It could also be that the death is notified, but due to implementation challenges (e.g. household not reachable,
family moved away) the VA interview is not conducted. Further, there is the possibility that the family of the
deceased refuses to consent to the interview. This is what we call the “Under-notification and Non-response Rate”
in the tool. An estimate of the proportion of such missed deaths must be made as this rate strongly influences the
sample size. It is crucial to be conservative in this estimate. If this rate is under estimated, the sample size might
be too small to draw conclusions with acceptable uncertainty ranges. From experience so far using VA in CRVS,
the under-notification and non-response rate has been as high as 40%. Even with solving most implementation
problems, under-reporting will likely not be less than 10%. A careful analysis of results from the pre-test or pilot
phases should be conducted to estimate this CRVS VA performance parameter realistically (See Table 1.1.1).
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
23
Figure 5.3.1. Example of the input parameters screen from the CRVS VA Sample Size Calculator Tool if population
size of eligible clusters is not known
5.3.8 Scenario+where+population+size+of+eligible+clusters+is+known+
If the population size of each eligible cluster is known the tool requires the analyst to list all clusters with their
population sizes as well as cluster specific CDRs (Figure 5.3.2). In case the latter is not available the national CDR
(5.3.4) can be listed for all clusters. Note: Eligible cluster are all clusters in your final sampling frame after having
excluded not eligible clusters. The tool will calculate the expected annual number of deaths in each cluster and
the annual mean number of deaths per cluster (using the harmonic mean). The inputs for “Mean cluster
population” (5.3.3) and “Crude Death Rate” (5.3.4) will subsequently not be needed anymore (Figure 5.3.3).
Figure 5.3.2 Example of the list with all eligible clusters and their corresponding population size and CDR
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
24
Figure 5.3.3 Example of the input parameters screen from the CRVS VA Sample Size Calculator Tool if population
size of eligible clusters is known
See Part B and the Annex A for the explanation of the pre-set values for power, significance level and design related
parameters (k, MIS), and how to change these if desired.
5.4 Tool*output*parameters*produced*
The CRVS VA Sample Size Tool produces five outputs instantly once the inputs are entered (See Figure 5.4.1).
5.4.1 Number+of+clusters+required+
The main output of the Calculator is the number of clusters required for the scenario inputs. This determines all
other outputs listed, and provides the basis for costing the scenarios.
5.4.2 Estimated+total+population+in+the+sample+
It may be of interest to know the sampled population size in aggregate across the sampled clusters in order to
understand what percent of the total national or stratum population is under VA surveillance.
5.4.3 Estimated+number+of+deaths+in+the+sample+per+year+
This output is the number of expected deaths per year in the total sample of clusters. It should not be confused
with the total number of VAs required since this will also include deaths with a MCCD, occurring inside the health
facility, or missed due to under-notification and non-response.
5.4.4 Estimated+number+of+VAs+needed+per+year+
This is the number of VAs needed per year and a useful output if the incremental cost of each VA is known.
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
25
5.4.5 CSMF+uncertainty+ranges+
Finally a table of CSMF uncertainty ranges (Uncertainty as % of CSMF, Lower and Upper bound of uncertainty
range) for detecting significant CSMFs changes for ten major levels of CSMF from 1% to 25% is given. In other
words the lower and upper bound indicate the lowest detectable difference between the CSMFs from the first
three years and the second three years. This means the CSMF of the second three years must be equal or outside
these boundaries in order for the change to be statistically significant. The CSMF levels span the full range of
CSMFs expected for the causes of major public health importance. The range indicated for the 1% CSMF should
equal the range entered in the input parameters. The uncertainty range at higher CSMFs will all be narrower. It
does not matter what the specific cause is for any given CSMF, the uncertainty range is relative to the CSMF level.
See Figure 5.4.1 for all outputs specified by the inputs in Figure 5.3.1.
Figure 5.4.1. Example of the output parameters screen from the CRVS VA Sample Size Calculator Tool
6. Considerations,for,selecting,the,CRVS,VA,sample,clusters,
This section of Part A outlines key operational considerations for the selection of the required number of clusters
once the sample size is calculated as above. A manual of the full step-by-step details for how to draw the sample
is provided in Part B section 4.
The key principles of the sample selection applied in this guidance package include:
• Using a suitable sample size
• Using a sampling frame which is a complete list of all cluster units eligible to be sampled
• Using the most simple sample selection strategy possible
• Drawing and implementing the sample exactly as designed
• Providing good sampling method documentation
6.1 Defining*the*sample*selection*strategy*
This section describes the selection strategy of the CRVS VA sample from the sampling frame once the cluster
sample size is known and the sample frame of eligible clusters has been prepared. To foreshadow the intention,
we recommend “stratified single-stage proportional to population size cluster sampling” and summarize the
background and logic for this below.
6.1.1 Stratification+
Simple random sampling is one option to select the required number of clusters from the sampling frame.
However this can cause problems; the resulting sample may not adequately reflect characteristics of the country.
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
26
For example, in a simple random sample, clusters from rural areas could be under-represented or over-
represented compared to the proportion of the population living in such areas. Stratified sampling tries to address
this problem by using information about cluster characteristics to choose a more representative sample.
Therefore, it is recommended to stratify your sample, if possible. For example, it might be desirable to ensure that
clusters are representative for the populations within each major administrative zone (e.g. Level 1, Region, State,
or Province). This is the most common sub-national level of disaggregation that countries are interested in, both
politically and epidemiologically.
Independent of the decision to stratify or not, each sample cluster will need to be randomly selected from the
sampling frame. Here we present three options for doing this. For further details on this, also see Part B, section
4.1 and the worked example in Annex B.
6.1.2 Simple+random+sampling+
In simple random sampling, all potential sampling units (clusters) are known and can be listed, and each unit
(cluster) within the sampling frame has an equal probability of being selected. The selection would be done by
creating random numbers between 1 and the number of clusters in the sampling frame. The number of random
numbers to be created is given by the number of required clusters.
6.1.3 Systematic+sampling++
In systematic sampling, the sampling frame is sorted according a selected variable (e.g. alphabetic order of
administration level 1 names). In a next step, the number of clusters in the sampling frame (or, in the case of
stratified sampling, in the stratum) is divided by the number of clusters to be sampled (Bierrenbach 2008). This
reveals the sampling interval. Thirdly, a random number between 1 and the sampling interval is chosen as the
random starting point in the sampling frame. The cluster at the position of the random starting point in the sorted
sampling frame is the first cluster to be selected. The other clusters are then selected at regular intervals according
to the size of the sampling interval.
6.1.4 Probability+Proportional+to+Size+sampling+
The main problem of the two options described above is that the sampling does not result in the most
representative selection of clusters. For example, you might end up selecting clusters with low populations. To
overcome this problem, we can use Probability Proportional to Size (PPS) sampling.
PPS sampling is a sampling procedure under which the probability of a cluster being selected is proportional to
the population size of that cluster. Given that the number of deaths will be generally correlated with the
population size, the sample will be self-weighting.
6.1.5 Stratified+single-stage+cluster+PPS+sampling+
To address the above concerns we propose stratified single-stage cluster PPS sampling. Note however that
sampling can be done in one stage (single-stage) or in multiple stages (multi-stage). In single-stage sampling, we
sample only once although you could use several different sampling strategies in combination. For example, you
could stratify your sample first by regions and then sample clusters from many within a stratum (actual sampling
by simple random sampling or PPS sampling). On balance, we recommend using a “stratified single-stage PPS
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
27
cluster sampling” approach for VA implementation if possible. The associated CRVS Sample Size Calculator Tool is
designed for such kind of sampling approach
5
. See Part B Section 4.2 for details on how to apply this approach.
6.2 Documenting*the*sample*method*
In preparing this guidance package and consulting a number of countries that operated sample registration
systems we found that corporate memory on how the sample size was calculated and drawn had been lost over
the years. Based on the CRVS Sample Size Calculator Tool inputs, one function of the Tool that we have added is a
function to produce not only tabular outputs as shown in Figure 5.4.1 but also a narrative text that can be saved
and used in documentation, reports or publications to summarize the essential information needed to
communicate and archive the sample calculations. Below is an example of the sample documentation script. The
tool automatically adds the input and output values indicated into the script output.
This CRVS VA sample size was calculated assuming an under-notification and non-response rate of a%, a
MCCD/health facility death coverage of b%, an annual crude death rate of c per 1,000, and a mean population
per cluster of d. The sample size was designed to give e% power of obtaining a significant difference (p<f) for a
change of g% in the cause specific mortality fraction of 1% when monitored over h years. Design related
parameters were assumed to be k
m
= i and MIS = j. The sample size was doubled in order to have disaggregated
results for male and female. Based on these inputs, the estimated sample size required was k clusters (and l
verbal autopsies per year). The estimate is based on the cluster sample size formula for proportions from Hayes
and Bennett for matched studies (Hayes and Bennett 1999). The sample is intended to be drawn based on
stratified single-stage cluster proportional to population size sampling.
In case the population size of each eligible cluster is known the first sentence would be modified to:
This CRVS VA sample size was calculated assuming an under-notification and non-response rate of a%, a
MCCD/health facility death coverage of b%, and an expected annual mean (harmonic mean) number of deaths
per cluster of d.
7. Limitations,
There are certain limitations of the sample size calculations and the sample selection strategy, some of which are
discussed here.
For the sample size calculations, we considered all input parameters (see section 5.3) to be relatively constant
over time. If they were to change significantly over time this could affect the sample size calculations:
• CDR: This could be a problem if the CDR decreases significantly because then the number of required
clusters would be underestimated. Thus, we recommend in section 5.3.4to choose a lower expected CDR
value in order for the sample size calculation to be conservative.
5
An alternative to single-stage sampling would be to do multi-stage sampling. This would entail sampling a few regions from many (first stage
sampling), and then selecting a pre-determined number of clusters within the regions sampled from the first stage (second stage sampling).
However, such a sampling strategy will have implications on the sample size calculations. It is likely to increase the design effect
5
and thus lead
to a larger required number of clusters to preserve the level of statistical power desired. Alternatively, if the number of clusters is fixed, the
uncertainty ranges for detecting significant CSMF changes will increase.
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
28
• Cluster size: Assuming a constant k, an increase in cluster size would reduce the number of clusters
needed and a decrease in cluster size would increase the number of clusters needed.
For the sample selection strategy, we have not discussed a situation where some clusters would be purposively
sampled based, for example, on political considerations. Nor have we treated capital or large cities any differently
in terms of sampling and the number of clusters selected. Depending on circumstances, however, such non-
statistical sampling of some clusters may be a practical necessity.
8. Scaling,up,strategy,and,follow-up,period,
Moving from the pre-test, through the pilot and demonstration phases (Table 1.1.1) whereby the methods,
processes, systems integration and costing of CRVS VA are established, it is likely that reaching the minimum
sample size needed for the national level male and female CSMFs will take a year or more. It will then take some
years to begin to see detectable trends – particularly for less common causes. The Sample Size Calculator Tool
addresses this problem by allowing to aggregate deaths across a user specified number of consecutive years (see
section 5.3.5). We make the assumption that there is no re-selection of clusters after the first set of consecutive
years of follow up, and that the CRVS VA will continue for some years in the same clusters, given the logistical and
cost implications of equipping training and supervising VA activities. As the outcome measure is mortality, we do
not expect any detectable Hawthorne effect of long-term monitoring of mortality in the same clusters (Ref from
INDEPTH, Matlab, etc.). During the initial scaling up to national level, it is unlikely that countries will achieve the
sample size sufficient for sub-national analysis although for example disaggregating by urban and rural could be
feasible. Scaling up over time to permit sub-national or other sub-group analyses would involve adding more
clusters, rather than selecting different clusters.
9. Conclusions,
Who is this Guidance for? This CRVS VA Sampling Strategies Guide and its associated Calculator Tool are intended
primarily for those responsible for providing high quality mortality data in countries where a decision has been
made to use VA as part of the CRVS system. It allows CRVS VA managers in such countries to determine the number
and location of geographic units to be sampled to detect a nationally representative change in CSMFs or rates
in populations where medical certification of cause of death is not yet feasible.
When should it be applied? The Guidance and the Tool are expected to be of value to countries who have
concluded the pre-test or pilot phases of their VA implementation and who have established the technical,
process, and incremental cost considerations with regard to VA implementation at scale.
What questions does it answer? The Guidance addresses three key issues regarding the implementation of CRVS
VA at national scale:
1) What are the key logistical considerations to make with regard to the definition of an operational CRVS
VA cluster?
2) What are the key strategic considerations to decide with regard to the level of disaggregation at which
analyses will be conducted (sex, age, urban-rural, sub-national administrative, trend period, etc.)?
3) What is the necessary number of sample units (clusters) and number of VAs needed given an
acceptable uncertainty range for detecting significant CSMF changes over time? Or alternatively, what
is the uncertainty range for detecting significant CSMF changes over time given a number of clusters
sampled?
4) How should the required sample clusters be selected from the national sample frame?
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
29
How can it be used? The tool allows CRVS managers to:
1) Determine the required sample size for a national or sub-national system given an acceptable
uncertainty range for detecting significant CSMF changes over time.
2) Determine the uncertainty range for detecting significant CSMF changes over time given the current or
planned deployment of VA.
How does this help? The relationship between the number of VAs conducted and the resulting uncertainty range
of various levels of CSMF is not intuitively easy to appreciate. For example, a given number of VAs conducted in a
relatively small number of very large clusters will give wider uncertainty ranges for detecting significant CSMFs
change over time compared with those conducted in a larger number of smaller clusters. This has operational and
cost implications. Hence, this tool should be used in concert with the CRVS VA Costing Tool. Using both tools will
be helpful in making key decisions with regard to scaling up CRVS VA in national systems. The tools are available
from the Bloomberg Philanthropies Data for Health Initiative CRVS Knowledge Gateway at the University of
Melbourne (https://crvsgateway.info) and other CRVS resource portals.
, ,
CRVS-Verbal Autopsy Sampling Strategies for Part A. Principles and Strategy
Representative VA Implementation: A Practical Guide
30
!
!
Sampling!Strategies!for!National!Scale!
CRVS!Verbal!Autopsy!Planning:!
!
A!Guidance!Document!and!Sample!Size!
Calculator!Tool!
Part B: Methods and Tools
Version 2.4
July 26, 2018
Review Version
CRVS-Verbal Autopsy Sampling Strategies for Part B
Representative VA Implementation: A Practical Guide Methods and Tools
31
Glossary,
Cause-specific mortality fraction: The proportion of deaths caused by a specified cause of death relative to the
total number of deaths occurring in a given period of time.
Cause-specific mortality rate: A mortality rate that specifies deaths according to their cause (International
Epidemiological Association 2014) expressed as the number of people dying due to a specified cause of death
relative to the total number of population for a given period, usually denominated by 100,000 population per year.
Cluster sampling: A method of sampling in which the members of a population are arranged in groups (the
‘clusters’) based on defined cluster units, and a number of clusters are selected at random within which all
population members are included.
Cluster sample design: refers to the use of clusters in sample surveys as opposed to simple random sampling.
Cluster size: Is the number of individuals in a single cluster contributing to the denominator of the outcome to be
measured across clusters.
Cluster unit: The sampling unit is “the unit into which a sampled population is divided for purposes of selection
for study” (International Epidemiological Association 2014). In cluster sampling, these units may be geographic or
administrative regions, communities, households, or other aggregates or entities.
Coefficient of variation between clusters: “The ratio of the standard deviation to the mean” (International
Epidemiological Association 2014). The coefficient of variation between clusters measures the variation of the true
outcome measure between clusters.
Coefficient of variation in cluster size: “The ratio of the standard deviation to the mean” (International
Epidemiological Association 2014). The coefficient of variation in cluster size measures the variation of cluster size
between clusters.
Complex sampling: In contrast to simple random sampling, sampling which includes stratification, multistage
clustering or over sampling.
Crude death rate: “An estimate of the portion of a population that dies during a specified period unadjusted by
age. The numerator is the number of persons dying during the period; the denominator is the number in the
population, usually estimated as the midyear population” or person-years lived in the year. (International
Epidemiological Association 2014) If not stated otherwise within this document the specified period is one year
and rates are given per 1,000 population.
Design Effect: An effect of a study design feature on the performance or outcome of a statistical procedure. A
specific form is the effect attributable to intra-class correlation in cluster sampling. The design effect (deff) for a
cluster design is the ratio of the variance for that design to the variance calculated from a simple random sample
of the same size. (International Epidemiological Association 2014).
Implicit stratification: A means of stratifying through geographic sorting of the sample frame, coupled with
systematic proportional to size sampling (PPS).
Intra-cluster Correlation Coefficient: “Intra-class correlation in surveys and group-randomized studies is the
extent to which members of a group (cluster) resemble each other more than they resemble members of other
groups (clusters).” (International Epidemiological Association 2014).
Matched design: Two groups of observations are compared, which originate from matched pairs. Matched pairs
is a term used for observations arising from either two individuals or clusters that are individually matched on a
CRVS-Verbal Autopsy Sampling Strategies for Part B
Representative VA Implementation: A Practical Guide Methods and Tools
32
number of variables, for example, age, sex, etc., or where two observations are taken on the same individuals or
clusters on two separate occasions (Everitt and Skrondal 2010).
Maximum possible Inflation in sample Size: The additional amount by which the sample size required for a cluster
design needs to be multiplied to obtain the size required when cluster sizes are variable rather than equal.
Multistage cluster sampling: First sampling subnational geographic areas, and then sampling clusters.
Uncertainty range: The range within which changes in the outcome measure from one time period to the
subsequent time period will not be detectable with sufficient statistical power. The range is given in percentage
change.
Medical certification of cause of death: The situation where a licensed physician or another designated health
professional determined the causes of death and these causes were documented on a medical certificate of cause
of death form (International Epidemiological Association 2014).
Person-years of follow up: “A measurement combining persons and time as the denominator in incidence and
mortality rates when, for varying periods, individual subjects are at risk of developing disease or dying. It is the
sum of the periods of time at risk for each of the subjects. The most widely used measure is person-years. With
this approach, each subject contributes only as many years of observation to the population at risk as the period
over which that subject has been observed to be at risk of the disease; a subject observed over 1 year contributes
1 person-year, a subject observed over a 10-year period contributes 10 person-years.” (International
Epidemiological Association 2014).
Power: “Roughly, the ability of a study to demonstrate an association or effect if one exists. The probability that
the test hypothesis will be rejected if it is false; it is equal to 1- b, where b is the probability of type ii error (failing
to reject a false null hypothesis).” (International Epidemiological Association 2014).
Primary sampling unit: Geographically-defined administrative unit selected at the first stage of sampling.
Probability sampling: Selection methodology where by each population unit (person, household, cluster, etc.) has
a known, non-zero chance of inclusion in the sample.
Probability Proportional to Size Sampling: A sampling procedure under which the probability of a unit (e.g. a
cluster) being selected is proportional to the size of the unit.
Sampling frame: “A list of members of the population of interest is called the sampling frame.” (Upton and Cook
2014) In cluster sampling this is a list of all clusters eligible to be sampled.
Sample Registration System: A Sample Registration System is one in which the fact of vital events, such as births
and deaths, are recorded or registered but without cause of death documentation.
Sample vital events with Verbal Autopsy: An SRS system that includes active follow-up of deaths in the community
to determine their likely cause of death is called “Sample Vital Events with Verbal Autopsy (SAVVY).”
Significance level: A pre-specified cut-off or alpha level for declaring a result “statistically significant”, typically
0.05 (International Epidemiological Association 2014).
Stratification: “The process of or result of separating a sample into several subsamples according to specified
criteria, such as age groups, socioeconomic status, etc.” (International Epidemiological Association 2014). In
stratified sampling the population is divided into subsets (called strata), usually mutually exclusive subnational
geographic areas, within each of which an independent sample is selected.
Systematic sampling: Selection from a list, using a random start and predetermined selection interval, successively
applied.
CRVS-Verbal Autopsy Sampling Strategies for Part B
Representative VA Implementation: A Practical Guide Methods and Tools
33
Unmatched design: Two groups of observations are compared, which originate from a completely different set of
individuals or clusters.
VA cluster unit definition: The catchment population of a single VA enumerator or interviewer team.
VA target causes: A cause of death which can be identified using a particular VA questionnaire and algorithm
combination.
!
CRVS-Verbal Autopsy Sampling Strategies for Part B
Representative VA Implementation: A Practical Guide Methods and Tools
34
1. Introduction,
Part A of the guidance packages described the principles and strategies for national scale CRVS VA sampling,
including strategic operational considerations as well as considerations for framing the sample, calculating the
sample size and selecting the actual CRVS VA sample clusters. Part B of this guidance package provides a step-by-
step manual for how to implement the principles and strategies outlined in part A:
1. how to prepare the national sample frame of all eligible CRVS VA clusters;
2. how to use the CRVS VA Sample Size Calculator Tool to determine the number of clusters to sample for
CRVS VA; and
3. how to draw the required number of clusters from the sampling frame.
The Annexes include the statistical basis of the CRVS VA sample size calculations, a worked example of the entire
process as well as a number of useful resources.
2. Preparing,the,sampling,frame,
To calculate the sample size and determine how to select the number of operational clusters for CRVS VA a
sampling frame needs to be created. To do so we start with a complete inventory of all possible clusters in the
country entered into a spreadsheet or database. Available demographic information on each cluster should be
included in the inventory. This may include the current population of each cluster, its area in km
2
, the population
density, and urban or rural status and estimated projection of the current crude death rate. This is most easily
done by preparing a flat MS Excel table listing all of the cluster units by name or administrative or census code.
Each cluster unit listed should be associated with its administrative hierarchy of Region, District, etc. in which it
resides and assigned a unique ID. The necessary attributes (listed below) for each cluster in the frame can then be
entered as shown in Figure 6.2.1.
Figure 6.2.1 Example of a sampling frame database
Estimated population size
Estimated population sizes for the target year down to Administrative Level 4 should be available from the national
bureau of statistics. However if this is not the case, the national bureau of statistics normally provides decadal
census data down to Administrative Level 4, with inter-censal growth rates to Administrative Level 1. Use the
census population from the census year for each cluster in the sampling frame database. Then add a column to
enter the inter-censal growth rate per annum from the Administration Level 1 in which the cluster resides (or any
lower Administration Level if available). In a last step estimate the size of the population in the target year using
the following formula:
CRVS-Verbal Autopsy Sampling Strategies for Part B
Representative VA Implementation: A Practical Guide Methods and Tools
35
!"#$%# & $%#
!"#$%$&'"()
' (
*
!
"##
+,
-
Where r is the inter-censal growth rate per annum and t the number of years between the census year and the
year for which the population size ought to be calculated.
Estimated crude death rate
The next column records the estimated CDR for the cluster. To calculate the estimated CDR you will need the
national CDR of the target year (see Part A 5.3.4) and the national CDR from the last census, where also CDR rates
for subnational levels are available. Pick the lowest administrative level for which CDRs were reported. Finally,
calculate the ratio of the subnational CDRs to the national CDR for the year of the census and then apply this ratio
to the national CDR of the target year.
Estimated expected number of deaths
Multiplying the cluster CDR times the cluster population divided by 1,000 will provide the expected number of
deaths per cluster per year.
Area and population density (optional)
The next column in the database could be the area of the cluster in km
2
. This should be available from any national
digital cartography office or could be calculated using a Geographic Information System (GIS) and shape files (see
below “Visualization of clusters in maps using GIS”). The next column is for the calculated value of the population
density in population per km
2
. This is useful in understanding potential clusters to exclude. Particularly sparsely
populated clusters may pose insuperable logistical and cost challenges which may justify their exclusion from the
sample frame.
Urban-Rural status (optional)
The last column in this example of a sampling frame indicates whether a given cluster is predominantly urban or
rural.
Additional information
Some additional cluster information might be relevant as well. This could be the presence of hospitals and health
facilities per cluster or the number of lower administrative area units (e.g. number of villages). Clusters that might
host unusual populations (such as refugee camps or nomadic populations) may also be considered in
selection/exclusion decisions.
3. Calculating,the,sample,size,,
This section of the Guide deals with information that will be needed in order to use the CRVS VA Sample Size
Calculator Tool and gives step-by-step instructions on how to actually use the Tool. It assumes that primary
stakeholders have made the key decisions concerning the operational cluster unit definition and the required
disaggregation level of the results as described in Part A, Section 3.
3.1 Preparatory*steps*
In order to calculate the needed number of clusters for CRVS VA implementation at national scale or at the
selected level for disaggregation, we need to have certain input parameters at hand. The following is a checklist
of sequential steps to follow to prepare these input parameters. .
1. Define the VA operational clusters units (see Part A, section 3.1).
CRVS-Verbal Autopsy Sampling Strategies for Part B
Representative VA Implementation: A Practical Guide Methods and Tools
36
2. Decide on the level of result disaggregation (see Part A, section 3.3)
3. Decide on the number of years to be aggregated for trend analysis (see Part, section A 5.3.5)
4. Identify the best source of national estimates for the top 20 proportionate causes of deaths (e.g. from a
local source or IHME GBD Compare) (See Annexes C.2 and C.3).
5. Identify from these estimates, the top 20.
6. Check if the identified causes are included in the VA target cause list; if not continue down the list until 20
target causes are identified.
7. Note the range of CSMFs between the 1st and 20
th
cause.
8. Determine the best estimate of national annual CDR for the current year and get the same disaggregated
by sex (see Part A, section 5.3.4 and Annex C.1).
9. Get national estimates for the proportion of total deaths with a MCCD or occurring within a health facility
depending on your decision (see Part A, section 2.2 and 5.3.6).
10. Get an estimate from the pilot for the proportion of deaths for which a VA should be conducted, but is not.
This is the under-notification and non-response rate (see Part A, section Error! Reference source not found.
and 5.3.7).
11. Prepare a sampling frame database of the operational clusters as explained above (Part B, section 2).
12. As an optional step you could at this stage map the clusters using a GIS to identify eligible clusters based on
population density thresholds for the final sampling frame by excluding outlier clusters at the extreme
ranges of the population density (e.g. national parks with extremely low population density or refugee
camps with extremely high population density). This will result in the final sampling frame with all eligible
clusters (see Part A, section 4.2).
13. Calculate the mean cluster population for the remaining clusters in the sampling frame.
14. If possible, estimate the coefficient of variation of the true proportions between clusters, k (see Annex B.2).
15. If possible, estimate the Maximum possible Inflation in sample Size. MIS (see Annex B.4).
16. Enter required parameters into the CRVS VA Sample Size Calculator Tool to determine the number of
clusters to be sampled for various scenarios of interest.
3.2 Using*the*CRVS*VA*Sample*Size*Tool*
Once all preparatory steps are completed you can start using the CRVS VA Sample Size Tool to calculate the sample
size required. To do so, follow the steps described here:
1. Open the CRVS VA Sample Size Calculator Tool in MS Excel version 2010 or later:
2. Enter the name of your country and the year.
3. Define whether you want to use the tool in Mode 1 or 2 and enter the required parameters.
a. Mode 1: Calculate the required sample size for a pre-determined maximum acceptable uncertainty
range for detecting significant CSMF changes over time (Part A, section 5.3.2): The uncertainty
range is the range within which changes in CSMFs over time will not be detectable with sufficient
statistical power. Note: the range is given in percentage change, which is not to be mistaken with
percentage point change. We have indexed the Calculator to allow you to specify the acceptable
uncertainty range for detecting significant CSMF changes for the smallest CSMF of interest (causes
in the range of 1% of total deaths) as for this cause the range will be the widest. Uncertainty ranges
at all higher CSMFs will always be narrower. Thus, the value to be entered is the uncertainty range
(percentage change) of the 1% CSMF that is acceptable. For example, setting the acceptable
uncertainty at 50% means that the tool will calculate a sample size capable to detect a change in
CSMF over time of 50% or more, meaning for the 1% CSMF an increase to 1.5% or a decrease to
0.5% in the next time period.
CRVS-Verbal Autopsy Sampling Strategies for Part B
Representative VA Implementation: A Practical Guide Methods and Tools
37
b. Mode 2: Calculate the uncertainty range for detecting significant CSMF changes over time for a
given number of clusters (Part A, section 5.3.1): For this, you will need to enter the number of
clusters you are expecting to sample.
4. Decide if you want to calculate your sample size in order to be able to disaggregate your results by male
and female. Choose “Yes” or “No”.
5. Select whether or not you know the population size of each eligible clusters. If you already prepared your
final sampling frame (Part B, section 3.1), then this answer is yes.
6. If you know the population size of each eligible cluster, enter their names, population size and crude death
rate (best to copy from your sampling frame). If you do not know the cluster specific crude death rate, use
the best proxy, which might be the crude death rate from any administration level above the cluster level
or simply the national crude death rate.
7. Enter your input parameters (Part A, section 5.3):
a. Power (set to default 0.8 = 80%).
b. Significance level (set to default 0.05 = 5%).
c. Mean population per cluster (only if you do not know the population size of each eligible cluster).
d. Mean crude death rate per 1,000 (only if you do not know the CDR of each eligible cluster).
e. Estimation for the coefficient of variation in the true proportions between clusters, k (set to default
0.25).
f. Estimation for the Maximum possible Inflation in sample Size, MIS (default 1.5 if population size of
each eligible cluster is not known, otherwise 1).
g. Number of years to aggregate for trend analysis.
h. Adjustment for proportion of deaths having MCCD or occurring with a health facility.
i. Adjustment for under-notification and non-response (%).
8. In the results section you will see the following output parameters (Part A, section 5.4):
a. Number of clusters required.
b. Estimated total population in the sample.
c. Estimated number of deaths in the sample per year.
d. Estimated number of VAs needed per year.
e. Table of estimated uncertainty ranges for pre-set CSMFs levels (25%, 20%, 15%, 12.5%, 10%, 7.5%,
5%, 3%, 2%, and 1%).
Note: CSMF levels are pre-set and you will need to remember what CSMFs levels are relevant for
your context and only consider those.
Note: You will need to make a decision about the number of clusters to be sampled based on the
acceptable uncertainty range for detecting significant CSMF changes of ONE specific CSMF level
(cause of death). For all other CSMF levels (causes of death) the uncertainty range will be given by
the calculated number of sampled clusters.
9. You can now play with the uncertainty range or the number of clusters in a “what if” manner, depending
on what you selected in step 3. This will allow you to observe how your input affects the number of clusters
required and the uncertainty ranges of the CSMF levels.
10.
Note: In case you are also interested in mortality rates, the uncertainty ranges for detecting significant CSMF
changes over time is very similar to the uncertainty range in rates assuming all other parameters being constant.
CRVS-Verbal Autopsy Sampling Strategies for Part B
Representative VA Implementation: A Practical Guide Methods and Tools
38
4. Selecting,the,sample,clusters,
Having determined the sample size in terms of the number of clusters needed, the sampling strategy now needs
to specify how to select the sample clusters to be included in the CRVS VA system from the sampling frame. Recall
the cluster unit is the defined catchment area of the VA interviewer or interviewer team. Within a cluster, VAs
would need to be done for all deaths eligible for VA within the resident population of the cluster unit. The final
sampling frame from which outlier clusters have been excluded (Part B, section 2) will be required. There are
various types of sampling strategies. Here we will describe the procedures for the in Part A recommended
“stratified single-stage proportional to size cluster sampling” (Part A, section 6.1).
4.1 Stratification*
Depending on the circumstances in your country, it might be desirable to make sure that clusters are
representative for the number of deaths occurring within each major Administrative Level 1 (e.g. Level 1, Region,
State, and Province) and within urban and rural areas.
To do the above suggested stratification, follow the steps listed here:
1. Group the clusters in the sampling frame by administrative level 1 (region) and by urban/rural areas to
create so-called ‘strata’. For instance, urban clusters from region 1 fall into one stratum (stratum 1), rural
clusters from region 1 into another (stratum 2) and so on.
2. Distribute the total number of required clusters across all the strata proportional to the population in
each stratum. For instance, if all people from urban clusters in region 1 (stratum 1) make up 5% of the
total population in the country, 0.05 times the total number of required clusters would be assigned to
this stratum.
3. Select the required number of clusters within each stratum based on the below explained Probability
Proportional to Size sampling processes.
4.2 Probability*Proportional*to*Size*sampling*
To implement Probability Proportional to Size (PPS) sampling, do the following (Bierrenbach 2008):
1. List all clusters within a stratum with their name, unique ID and the number of estimated population in
the cluster
2. In a new column, calculate the cumulative sum of the cluster population (the total population in the
stratum should be the last figure in this column)
3. Obtain the number of clusters to be sampled (d) in each stratum (from the Sample Size Calculator Tool).
4. Divide the total population in the stratum by the number of required clusters (d) in the stratum, leading
to the sampling interval, SI
5. Choose a random number between 1 and the sampling interval to get the random start, RS
6. Calculate the following series: RS; RS+SI; RS+2*SI; … RS+(d-1)*SI
7. The clusters selected are those for which the cumulative sum contains one of the serial numbers
calculated in 6).
CRVS-Verbal Autopsy Sampling Strategies for Part B
Representative VA Implementation: A Practical Guide Methods and Tools
39
!
CRVS-Verbal Autopsy Sampling Strategies for Part B
Representative VA Implementation: A Practical Guide Methods and Tools
40
ANNEXES,
CRVS-Verbal Autopsy Sampling Strategies for Annex A. Statistical basis of the
Representative VA Implementation: A Practical Guide the CRVS VA sample size calculations
41
Annex,A.,Statistical,basis,of,the,CRVS,VA,sample,size,calculations,
A.1. Assumptions*
Sample size estimates are driven by the sampling strategy. Here we assume a sampling strategy which uses a
single-stage random cluster sampling design (see Part A, Section 6.1). The cluster unit is assumed to be the
defined catchment area of the VA interviewer or interviewer team as suggested in Part A, Section 3.1. Further,
we expect at a minimum, that results must be representative for the national level and disaggregated by sex.
We also set the number of years to aggregate for a trend analysis to three. The clusters selected for the first
three years, will be the same in the second three years. This means for the sample size calculations you need
to calculate the number of clusters needed to detect a significant change in one CSMF between the first and
the second three year periods. All input parameters are assumed constant over time.
A.2. Power*and*Significance*level*
In a first step, you need to define to what extent you can accept statistical errors in such a trend analysis. There
are two types of statistical errors. The first would be that you conclude a change in one CSMF between the
first and the second three year periods, although there is no such change in reality. By defining the significance
level (referred to as
a)
, you decide on an acceptable probability of making this kind of error. This value is also
known as the p-value and is often set to 0.05 (5%).
The second error would be that you conclude no change in one CSMF between the first and the second three
years, although there is such a change in reality. An acceptable probability of doing this error is generally seen
to be 0.2 (20%) (referred to as
b)
. The power of a statistical test is consequently the probability of not making
this error and therefore is often set to 0.8 (80%).
This means you assume that the sample size is designed to give 80% power of obtaining a significant difference
(p<0.05) for a given change in CSMF.
A.3. Individual*vs.*Cluster*design*
In an individual design, you would randomly select deaths (individuals) from an area, in this case the country,
to analyze the CSMFs. To do so you would need to know how many deaths (individuals) you would need to
analyze in order to detect a significant change in one CSMF between the first and the second three years. This
is logistically infeasible and therefore you will need to select a number of clusters within which you analyze all
deaths (cluster design). Thus, instead of calculating the number of deaths (individuals) to be sampled, you
need to calculate the number of clusters to be sampled from the sampling frame.
A.4. Unmatched*vs.*Matched*design*
In an unmatched design two groups of observations are compared, which originate from a completely
different set of individuals or clusters. This would for example be the case if you randomly selected a first group
of clusters for the first three years and another group of clusters for the second three years and then compared
the CSMFs of the two different groups of clusters.
In a matched design two groups of observations are compared, which are paired, meaning they originate from
the same or similar set of individuals or clusters. Matching should lead to greater comparability between the
two groups of observations (Hayes and Bennett 1999). This is the case in your scenario where the clusters
selected for the first three years will be the same in the second three years. Thus, observations from the first
three years are matched with observations of the second three years. This assumes that the clusters in the
second three years are still representative.
CRVS-Verbal Autopsy Sampling Strategies for Annex A. Statistical basis of the
Representative VA Implementation: A Practical Guide the CRVS VA sample size calculations
42
A.5. Design*related*parameters**
The fact that the design is clustered and these clusters are paired and of unequal size requires you to take into
account some additional parameters when calculating the sample size.
A.5.1. Coefficient+of+variation+between+clusters+
In an unmatched design, you would need to take into account that there is some variation in CSMFs between
clusters. This variation is given by k, the coefficient of variation of true proportions (or rates) between clusters
at each time point (in the first three years or second three years) (Hayes and Bennett 1999). k is defined as the
standard deviation of true proportions (or rates) divided by the mean proportion (rate) (Hayes and Bennett
1999). If there is no variation in one CSMF between clusters then k would be 0 (Hayes and Bennett 1999). As a
rough guideline, Hayes and Bennett state that experience suggests that k is often
)
0.25, and seldom exceeds
0.5 for most health outcomes (Hayes and Bennett 1999). Options for how to estimate k are given in Annex B.3.
In a matched design, k is replaced by km. k
m
is the coefficient of variation of true proportions (or rates) between
clusters within the matched pairs in absence of anything which could change the mortality and/or the CSMFs
(Hayes and Bennett 1999). This means that k
m
is the coefficient of variation in one CSMF between the first
three years and the second three years within a cluster in absence of anything which could change the
mortality and/or the CSMF. This might for example only include in- and out-migration and ultimately lead to
the question how similar the populations are in the second three years compared to the population in the first
three years. It is impossible to obtain empirical estimates of k
m
in practice and thus we propose the
conservative assumption of k (= 0.25) being the upper limit for k
m
6
as recommended by Hayes and Bennett
(Hayes and Bennett 1999). Options to estimate k
m
based on non-empirical estimates are given in Annex B.3.
A.5.2. Intra-cluster+correlation+coefficient+
In a cluster design there are two types of variances – the variance of observation within the same cluster and
the variance of true cluster means (Kerry and Bland 1998). One way of summarizing the relationship between
these two components is the Intra-cluster Correlation Coefficient (ICC) (Kerry and Bland 1998). The ICC is
defined as the ratio of the between-cluster variance to the total variance (both between and within clusters)
(Pagel, Prost et al. 2011). Thus, it quantifies how much more similar outcomes are for individuals within clusters
than for those in different clusters (Kerry and Bland 1998, Killip, Mahfoud et al. 2004, Pagel, Prost et al. 2011).
It has a value between 0 and 1 (Pagel, Prost et al. 2011). An ICC of 0 means that observations within clusters
are no more similar to each other than observations from different clusters (there is no between-cluster
variability) (Pagel, Prost et al. 2011). In contrast, an ICC of 1 indicates that observations within the same cluster
all have identical outcomes (there is no within-cluster variability) (Pagel, Prost et al. 2011). For binary
outcomes, the relationship between the ICC and k has been defined as follows:
*++ & ,
.
-
.
/ 0 .
1
whereas p in your case would be the probability of dying of one specific cause (the CSMF for one specific cause)
(Preisser, Reboussin et al. 2007, Pagel, Prost et al. 2011).
A.5.3. Design+effect+
According to Eldridge et al. the design effect, DE, represents the amount by which the sample size required for
a non-cluster design (individual design) needs to be multiplied to obtain the size required for a more complex
design such as a cluster design (Eldridge, Ashby et al. 2006). Pragmatically, the DE is the number of deaths
(individuals) needed in a cluster design (n2) divided by the numbers of deaths (individuals) needed in a non-
cluster design (n1). The DE can also be formulated using the ICC, whereas the commonly used DE estimate for
equal cluster sizes is given by:
6
Alternatively, a less conservative assumption would be to use k=0.15.
CRVS-Verbal Autopsy Sampling Strategies for Annex A. Statistical basis of the
Representative VA Implementation: A Practical Guide the CRVS VA sample size calculations
43
2! & / 3
4
5 0/
6
*++
with m being the average size of the cluster (number of deaths for CSMFs) (Hayes, Alexander et al. 2000,
Eldridge, Ashby et al. 2006, Pagel, Prost et al. 2011).
A.5.4. Coefficient+of+variation+in+cluster+size+
Variation in cluster size needs to be taken into account in addition to the variation of outcomes between
clusters (k or km) (Eldridge, Ashby et al. 2006). To do so you need to know the coefficient of variation of cluster
size, cv, which is defined as the ratio of the standard deviation of cluster sizes to the mean cluster size (Eldridge,
Ashby et al. 2006). Together with the ICC, you can then calculate the Maximum possible Inflation in sample
Size (MIS) required when cluster sizes are variable rather than equal.
7*8 &9
/ 3
:4
/ 3 ;<
.
6
5 0/
=
*++
/ 3
4
5 0/
6
*++
An alternative to the MIS would be to use the harmonic mean of the cluster size instead of the arithmetic mean
m and y in the formula in A.6 and A.7 (Hayes and Moulton 2009). Yet, for this you need to know at least the
population size of each eligible cluster. If you do, select the corresponding option in the Sample Size Calculator
Tool and the tool will consider the harmonic mean. In this case the MIS will be automatically set to 1, otherwise
the MIS is set to 1.5. An MIS of 1.5 was chosen because this revealed a similar number of clusters required as
if the harmonic mean was used all other parameters being constant.
A.6. Formula*for*sample*size*based*on*proportions*
CSMFs represent proportions of one specific cause of death compared to all deaths. According to Hayes and
Bennett (Hayes and Bennett 1999) the sample size formula for proportion (CSMFs) in matched designs is as
follows:
; & > 3 4?
/0 .
3 ?
1
6
.
@
2
4/ 0 .
2
6A5 3 @
3
4/ 0 .
3
6A5 3 ,
4
.
4.
2
.
3 .
3
.
6
4.
2
0 .
3
6
.
c is the number of clusters required. z
a
/2
and z
b
are standard normal distribution values corresponding to a/2
and b respectively (see Annex A.2) (Hayes and Bennett 1999). p
0
is the true mean population proportion for a
specific cause in the first three years and p
1
is the true mean population proportion of a specific cause in the
second three years. m is the number of individuals, in your case deaths, sampled in each cluster (average size
of the cluster using the arithmetic mean). As discussed above k
m
will need to be replaced by k (Annex A.5.1).
A.7. Formula*for*sample*size*based*on*rates*
Based on Hayes and Bennett (Hayes and Bennett 1999) the sample size formula for rates, in your case mortality
rates, in matched designs is as follows:
; & > 3 4?
/0 .
3 ?
1
6
.
4B
2
3 C
3
6AD 3 ,
4
.
4C
2
.
3 C
3
.
6
4C
2
0 C
3
6
.
l
0
is the true mean population rate for a specific cause in the first three years and l
1
is the true mean
population rate of a specific cause in the second three years. y is the number of person-years of follow-up in
each cluster (average size of the cluster using the arithmetic mean).
A.8. Cluster*size*
CSMFs represent the proportion of one cause of death in all deaths occurring. Thus, the denominator is all
deaths. For mortality rates, you look at the number of deaths of one cause occurring in a population, which is
often expressed as x deaths per 100,000 person-years. In this case the denominator is person-years. This
differentiation is also important for the above formulas.
CRVS-Verbal Autopsy Sampling Strategies for Annex A. Statistical basis of the
Representative VA Implementation: A Practical Guide the CRVS VA sample size calculations
44
The cluster size m in the formula for proportions is the number of deaths in each cluster for the period under
investigation. This means to calculate the cluster size m you have to multiply the average number of deaths
per year and cluster by the number of years, which you will aggregate for a trend analysis.
In contrast, the cluster size y in the formula for rates is the number of person-years of follow up in each cluster
for the period under investigation. To calculate the cluster size y you would therefore need to multiply the
average number of individuals per cluster (number of person-years of follow up per year) by the number of
years, which you will aggregate for a trend analysis.
A.9. Uncertainty*range**
Both the formulas for proportions and rates in A.6 and A.7 require you to know the true proportion or rate of
a specific cause in the second three years. For this, you would at least need to know the expected change from
the first three years to the second three years. Because this is not possible, the Sample Size Calculator Tool will
require you to put in an acceptable uncertainty range. The uncertainty range is the range within which changes
in CSMFs over time will not be detectable with sufficient statistical power. The range is given in percentage
change, which is not to be mistaken with percentage point change. The Sample Size Calculator Tool also allows
you to play with this uncertainty range, meaning the minimal percentage change you would like to be able to
detect, in a “what if” manner and observe how it affects the number of clusters needed.
A.10. Further*Adjustments*
Once you calculated the c (number of required clusters) in the above formulas (A.6 and A.7), there are still a
couple of adjustments needed to account for additional factors influencing the sample size.
A.10.1. Disaggregation+by+male+and+female+
In order to have disaggregated results for male and female, you will need roughly to double the calculated
number of clusters required. In theory, this estimation only holds true if the CDRs for female and male are
somewhat similar. If you wish to know if this is the case in your situation, you would need to calculate the
required number of clusters for the sub-population of the sex with the lower CDR (often female). An example
of how this is ought to be done is attached in Annex B.7.
A.10.2. Proportion+of+deaths+having+MCCD++
If the CRVS VA strategic design decision is to conduct VA only on deaths which had not had a MCCD or do not
occur within a health facility, the number of deaths that can be analysed in each cluster will be smaller. Thus,
the cluster size m in the formula for proportions or y in the formula for rates will be smaller. This will increase
the numbers of clusters needed. The factor by which the cluster size has to be adjusted is given by
EF;G%H
5!!6
& 4/ 0#
5!!6
6
where p
MCCD
is the proportion of deaths for which a MCCD is available or the proportion of deaths which occur
in a health facility.
Again, this calculation only holds true if the proportion of deaths with an MCCD or occurring in a health facility
is similar across the country. If this is not the case (e.g. if in urban areas the proportion of deaths with an MCCD
is much higher than in rural areas), then you will need to calculate the number of clusters required in urban
and rural areas separately. An example of how to do this is given in Annex B.8.
A.10.3. Under-notification+and+non-respon s e+rate+
As introduced in Part A, section 5.3.7, the proportions of deaths for which VA should be conducted, but is not,
is the so-called under-notification and non-response rate. Again, the factor by which the cluster size has to be
adjusted is given by
EF;G%H
7898:
& 4/ 0#
7898:
6
where p
UN&NR
is the under-notification and non-response rate.
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
45
Annex, B., Worked, example, implem e nting, the, Guidance, and, Tool, in,
one,country,
For illustrative purpose of this guidance document, Tanzania was selected to provide a worked example of how
to calculate and draw the CRVS VA sample in practice. For this, we will follow the steps outlined in Part B.
B.1. Preparing*to*calculate*the*Cluster*Sample*Size*
B.1.1. +Operational+cluster+definition+
VA implementation will take place in Tanzania Mainland only (excluding Zanzibar). The administration level 1
in Tanzania Mainland is the region, level 2 the district, level 3 the division, and level 4 the ward. The catchment
area of a VA interviewer team in Tanzania, which consists of two VA interviewers, is the ward (Administration
area level 4). Thus, we decide the cluster unit to be defined as the ward. According to the census 2012, there
are 3,312 wards in Tanzania Mainland with an expected total population of 50,366,198 in 2017 (extrapolated
based on inter-censal administration level 2 growth rates from the 2012 census; see B.2) (National Bureau of
Statistics and Ministry of Finance 2013). The wards vary widely in area from 0.1 to 11,503 km
2
. Also, ward
population sizes vary considerably from 753 to 148,017 people. Given an annual national CDR of 6.351/1,000
for 2017, there are on average 97 deaths per ward per year. (You do not need all this information at this point,
but it is provided here to give you a brief overview of the situation if you are not familiar with Tanzania)
B.1.2. Disaggregation+level+of+results+
For the disaggregation level of results, it is decided that the results ought to be representative for males and
females at national level.
B.1.3. Number+of+years+to+aggregate+for+trend++
In Tanzania a step-wise up-scaling is planned and full scale sample VA operations are expected to be reached
only after a couple of years. We will allow for a three year follow-up period for national trends. This means
that data will be gathered over three years and then compiled to one data set. In long-term, it is aimed to
compare a three year period with the subsequent three years.
B.1.4. National+level+estimates+
To get the estimated CSMFs for Tanzania download the CSMFs data from https://vizhub.healthdata.org/gbd-
compare/ and prepare a frequency distribution as described in Annex C.2. As Tanzania uses the WHO 2016 VA
cause list we will drop “Alzheimer disease and other dementias”, which is ranked as the 18
th
cause. Instead we
add the 21
st
cause, which is “Interpersonal violence”.
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
46
We note that the CSMFs range between 11% and 1.1%.
To get the annual national overall CDR, we conduct an online search, which reveals:
CDR
[per 1'000]
Year
Source
Link
6.351
2017
World Population
Review
7
http://worldpopulationreview.com/countries/tanzania-
population/crude-death-rate/
6.351
2015
-
2020
UN/population
division
8
https://esa.un.org/unpd/wpp/Download/Standard/Mortality/
6.49
2017
Knoema
https://knoema.com/atlas/United-Republic-of-
Tanzania/topics/Demographics/Mortality/Crude-death-rate
6.68
2015
Index Mundi
http://www.indexmundi.com/facts/tanzania/indicator/SP.DYN.CDRT.
IN
6.68
2015
Country Economy
https://countryeconomy.com/demography/mortality/tanzania
7.015
2015
World Bank
9
https://data.worldbank.org/indicator/SP.DYN.CDRT.IN?locations=TZ&
view=chart
7
http://worldpopulationreview.com/countries/xxx-population/crude-death-rate/ (xxx has to be replaced by the country’s name).
8
UN: https://esa.un.org/unpd/wpp/Download/Standard/Mortality/
9
https://data.worldbank.org/indicator/SP.DYN.CDRT.IN?locations=XX (xxx has to be replaced by the country’s name)
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
47
7.6
2017
CIA
https://www.cia.gov/library/publications/the-world-
factbook/geos/tz.html
7.79
2015
Open Data For
Africa
http://tanzania.opendataforafrica.org/UNWPP2012R/world-
population-prospects-the-2012-revision-updated-13-june-2013
7.8
2013
WHO
http://apps.who.int/iris/bitstream/10665/170250/1/9789240694439
_eng.pdf
8.8
2012
UNICEF
https://www.unicef.org/infobycountry/tanzania_statistics.html
9.4
2012
NBS/Census
http://www.nbs.go.tz/nbs/takwimu/census2012/Mortality_and_Heal
th_Monograph.pdf
Here is one example from World Population Review: Modeled trend in crude death rate for Tanzania, 1950 to
2100
Given that we expect a further decrease in the CDR in the coming years, we select the lowest CDR of 6.351.
For CDRs disaggregated by sex, data from the 2012 census for Mainland Tanzania is available. Assuming that
the ratio of the overall CDR to the male and female CDR remained the same, we can calculate the expected
CDRs for male and female in 2017 as follows:
Year
Overall CDR
Male CDR
Female CDR
2012
9.4
10.1
8.6
2017
6.351 (from above)
=10.1/9.4*6.351=7.43
=8.6/9.4*6.351=5.81
Here we assume that in Tanzania the CRVS VA strategic design decision is to conduct VA only on deaths, which
had not had a MCCD. Thus, we need an estimate of the percentage of total deaths with a MCCD. We know
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
48
from DHIS2 that in 2016 34,189 deaths had a MCCD. Additionally, the population projection from the National
Bureau of Statistics estimated a total of 48,676,699 people on Tanzania Mainland in 2016. With this and an
expected CDR of 6.502 (Source: World Population Review) for 2016, we would expect 316,495 deaths in 2016.
Comparing the expected number of deaths for 2016 and the deaths with a MCCD in 2016, reveals that only
11% of all deaths have a MCCD. Thus, we will use this estimate for further calculations later on.
Regarding the under-notification and non-response rate, we here assume to have a notification achievement
level of 90% and a response rate close to 100%. This will lead to an under-notification and non-response rate
of 0.1 (10%), which is rather optimistic. If possible, this rate should be carefully analyzed using results from the
areas to set this parameter correctly.
B.2. The*sampling*frame*
To prepare the sampling frame of the format given in Part B, section 2, for Tanzania Mainland, we use shape
files and additional data from the census 2012.
The estimated population size for 2017, (EstPop2017), is calculated with the following formula:
!IG$%#>J/K & $%#>J/> ' (
*
)
322
+,
-
whereas Pop2012 is the population size in 2012, r the inter-censal growth rate per annum of a corresponding
district and t the number of years between 2012 and 2017 (in this case t=5).
The area we calculate using the QGIS function $area/1,000,000.
In the 2012 census the CDR was available down to regional level. Similar to calculating the sex specific CDR, we
calculate the estimated regional CDR for 2017 based on the ratio of the regional CDR 2012 to the national CDR
2012 and multiplying this ratio by the 2017 CDR.
The estimated expected number of deaths in 2017 is then the estimated population in 2017 times the
estimated regional CDR for 2017 divided by 1,000.
As a next step we visualize the 3,321 wards of Tanzania Mainland using QGIS to look at population density (left
map) and in particular to find a reasonable population density threshold until which VA implementation is still
feasible.
For example using 15 people/km
2
as a cut off would drop 236 of the 3,312 wards, whereas within those there
are 80 of the 83 biggest wards in terms of area (right map). This makes sense regarding feasibility as in wards
with a big area VA implementation will be challenging.
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
49
Dropping these 236 leads to the fact that we drop 4.4% of total population. The following table summarizes
the characteristics of the sampling frame with and without the wards with a population density lower than
15/km
2
.
Relevant characteristics
All wards in Tanzania Mainland
Excluding wards with a population
density <15/km2
Number of wards
3,312
3,076
Area [km
2
]
mean=270km
2
; median=112 km
2
;
min=0.1 km
2
; max=11,503 km
2
mean=160 km
2
; median=103 km
2
;
min=0.1 km
2
; max=1,728 km
2
Total estimated population in 2017
50,366,198
48,140,318 (95.6%)
Estimated population per ward in 2017
mean=15,207; median=11,825;
min=753; max=148,017
mean=15,650; median=12,185;
min=1,137; max=148,018
Estimated expected death per ward in
2017
95.96749 (arithmetic mean)
98.70358 (arithmetic mean)
64.97327 (harmonic mean)
Average number of villages per ward
4.6
4.7
We decide that the sampling frame without the low population density wards, will be our final sampling frame.
In B.5 we will need the mean population per ward, which is 15,650 and the mean number of deaths per ward
in 2017, which is 98.7 (based on the arithmetic mean) or 65.0 (based on the harmonic mean).
B.3. Estimating*k*
As elaborated in A.5.1 k is the coefficient of variation in the outcome measure between clusters at one time
point. Here, we will give you some options how to estimate the k based on existing data.
B.3.1. Options+to+estimate+k+
Option 1: In Tanzania we know the CDR at regional level, which is three administration levels above our cluster
level (the ward). However, we will here calculate the coefficient of variation in CDRs between regions, k
REGION
.
Assuming that variation between clusters increases the smaller the clusters are and that cause specific
mortalities vary at least as much as the overall CDR, this estimated k
REGION
will give us some idea of the k
CLUSTER’s
minimal value.
According to Hayes and Moulton k is defined as follows (Hayes and Moulton 2009):
, &
L
;
.
2
9%H9, &
L
;
C
2
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
50
Whereas the s
B
is the between-cluster standard deviation and the p
0
or l
0
is the mean population proportion
and rate, respectively. In our case the k is k
REGION
, s
B
is the between-region standard deviation, and l
0
is the
mean population rate.
You will need to fill cells highlighted in yellow based on your input data.
If you had CDRs for all of your clusters, you could do the same calculations as done here for regions and get
your true k
CLUSTER
fro the overall CDR.
Option 2: If the true cluster proportions or rates are approximately normally distributed, 95% will lie within
two standard deviations of the population mean (Hayes and Bennett 1999). For a given k this would imply that
the rates (or the proportions) in the clusters would vary roughly between (Hayes and Bennett 1999):
C
2
' 4/ M> ' ,
!<7=>?:
6
where l
0
is the mean population rate (for proportions l
0
would need to be replaced by p
0
). This means we
need to choose k
CLUSTER
big enough so that the above term captures at the minimum the ranges we see in
reality. The IHME data downloaded under B.1.4 give us a rough idea what the “Lower Bound” and “Upper
Bound” could be. Thus, we now use these bounds to estimate the required k. Ultimately, the following would
need to be true:
C
2
'
4
/ 0 >' ,
!<7=>?:
6
N O%P(H9Q%RST
@A5?
C
2
'
4
/ 3 >' ,
!<7=>?:
6
U V##(H9Q%RST
@A5?
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
51
You will need to fill cells highlighted in yellow based on the downloaded IHME data. Columns J and R will notify you with “false” if the lower bound of the IHME data is lower
than what is captured by your selected k or if the upper bound of the IHME data is bigger than what is captured by your selected k. You can now increase or decrease k in order
to see what value for k captures most of the ranges given by the IHME data. Here we decide to select k = 0.25.
With “Conditional Formatting” in the “Home” tab of Excel, you can also highlight cells containing “false” and whether the lower, upper or both bounds lead to the “false”
statement. To do so do the following:
Home > Conditional Formatting > New Rule > Format only cells that contain > select “Cell Value” & “greater than” (for Column H and P)/ “Cell Value” & “less than” (for Column
I and Q)/“Specific Text” & ”containing” (for column J and R) > type “F2” (for column H), “G2” (for column I), “false” (for column J), “N2” (for column P), “O2” (for column Q),
“false” (for column R) > click on “Format” > select the tab “Fill” > select the red color
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
52
Option 3: If you had the overall CDR or cause-specific mortality rates for a given number of clusters (here referred
to as sample clusters) from a pilot or a similar intervention (e.g. SAVVY) you could use this data to get an idea of
the k in all your clusters.
According to Hayes and Moulton (Hayes and Moulton 2009) the following holds true:
!
!
"
" #
"
$
%
&
'
#
()*+(, "
!
!
%
where
!
!
is the between-cluster standard deviation from all your clusters, s the standard deviation of the
observed rates across your sample clusters, r is the overall rate of your sample clusters, and
&
'
#
the harmonic mean
of the person-years in the sample cluster.
We did not have such data for Tanzania, but given this could be the case for other countries, we provide here an
“artificial” example.
You need to fill cells highlighted in yellow based on your data from the sample clusters. You will only need the
population size (column B) and either the annual deaths (column C) or the CDR (column D).
10
If you were to do the calculation for cause-specific mortality rates, you select one specific cause and then put in
the cause-specific mortality rate instead of the CDR.
For proportions, meaning CSMFs, the above formula would be (Hayes and Moulton 2009):
!
!
"
" #
"
$
-./ $ -0
1
2
#
()*+(, "
!
!
-
where p is the overall proportion of your sample clusters (computed from all sample clusters combined) and
1
2
#
is the harmonic mean of the number of deaths in the sample clusters.
10
Population sizes of Ward 1 to 10 in the example originate from 10 randomly picked wards in Tanzania and CDRs
come from estimated regional CDRs in 2017 for Tanzania. Annual deaths were calculated correspondingly.
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
53
In conclusion, given the results from option 1 and 2 and the fact that k is often
3
0.25, we perceive k=0.25 as
appropriate, although potentially rather conservative. Overall, if available data is insufficient to calculate k, it is
better to overestimate k than underestimate it.
B.4. Estimating,MIS,
Here we provide an option on how to estimate the MIS. However, for sample size calculations we will use the
harmonic mean of the cluster size instead of the arithmetic mean m and y in the formula in A.6 and A.7 (Annex A,
Section A.5.4) (Hayes and Moulton 2009). We will base our calculations of the MIS on CSMFs. To calculate the MIS
we need the ICC, the coefficient of variation in cluster size, cv, and the mean cluster size. The mean cluster size is
the mean number of deaths in a cluster and known to be 98.7 (see section B.2).
First we calculate the ICC based on the CSMFs for Tanzania and k=0.25. For each cause we will have another ICC.
Yet, for the calculations of the MIS, we would need a single ICC, which is appropriate for most causes.
You will need to fill the cells highlighted in yellow based on your CSMFs and the selected k. The formula used to
calculate the ICC is given in A.5.2. In the cell B24 you can play around with a possible overall ICC to use in the MIS
calculations. Column D will notify you with “false” if the calculated ICC in column C is bigger than the overall ICC.
In our case we will decide for an overall ICC of 0.005 as this covers almost all causes except for the first two. For
the first two causes this mean, that selecting an ICC of 0.005 could potentially increase the minimal percentage
change you would like to be able to detect (uncertainty range) from the first to the second three years. However,
as you will see later on in B.5 the uncertainty range for detecting significant CSMF changes for the top two causes
will be the smallest and thus being able to potentially measure only a slightly bigger change is not such a problem.
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
54
For calculating the coefficient of variation in cluster size, cv, you will now need your sampling frame. The cluster
size in the case of CSMFs is the number of deaths per cluster. Thus, we are interested the variable “Estimated
expected number of deaths in 2017”. For this variable you will need to calculate its mean and the standard
deviation. As reference it is also a good idea to look at the highest and the lowest value. Based on this we then
calculate the cv and the MIS using an ICC of 0.005.
In the case of Tanzania this results in a cv of 0.89 and a MIS of 1.26. As you will see later on (B.5), an MIS of 1.5
would be needed to come up with a similar number of clusters required as if the harmonic mean was used all
other parameters being constant.
B.5. Calculating,the,CRVS,VA,sample,size,
For calculating the sample size (required number of clusters) we will us the Sample Size Calculator Tool and the
instructions given in Part B, section 3.2.
We will choose the option to estimate the number of clusters based on an acceptable uncertainty range for
detecting significant CSMF changes. Therefore, we will need to enter the uncertainty range for detecting
significant CSMF changes acceptable for us for the cause of death, which is closest to 1% CSMF in the top 20 list.
In our case this is the 20
th
cause, which is “Interpersonal violence” with a CSMF of 1.2% (see section B.1.4). We
will need to give an estimate what percentage change we would like to be able to detect for the CSMF of
“Interpersonal violence” between the first three years and the second three years. For the moment, we will
assume that 50% is acceptable for us. This means we think that for the CSMF of “Interpersonal violence” we would
like to detect a decrease to 0.6% or less or an increase to 2.4% or more.
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
55
In the next step we will select “Yes”, meaning we want our sample size to be calculated in a way that we can
disaggregate our results by male and female. Also, given we prepared our sampling frame we will say “Yes” for
the question whether we know the population size of each eligible cluster.
In a next step we will copy and paste the name, population size and crude death rate of each eligible cluster from
the sampling frame into the provided table in the tool.
This will automatically compute the expected annual number of deaths in each cluster from which the tool will
subsequently calculate the expected annual mean number of deaths per cluster using the harmonic mean. To
cross check the calculations, the automatically calculated expected annual mean number of deaths per cluster
should be the same as calculated above from our sampling frame using the harmonic mean (B.2;64.97327).
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
56
Finally, based on our work in B.1 to B.3, our input parameters are as follows. For the power and significance level
we assume the default values (Power = 0.08 and significance level = 0.05).
The results reveal the following:
For Tanzania, we know that the CSMFs range from 11% to 1%. Thus, we are in particular interested in the
uncertainty ranges of CSMFs between 10% and 1%. For example, looking at our CSMF frequency distribution
(section B.1.4), we see that “Lower respiratory infections” make up 10% of total deaths. This means that if between
the first and the second three years the CSMF for “Lower respiratory infections” were to change to 7.8% or less or
to 12.2% or more (plus/minus 22% or more), we would be able to detect this difference with for us acceptable
statistical errors (power and significance level, also see A.2).
Note: The uncertainty range for detecting significant CSMF changes for the cause of death at the 1% CSMF level
will always be larger than the uncertainty range in any other cause.
We can now play around with the uncertainty range of the cause of death closest to 1% (“Interpersonal violence”)
and see how this affects the number of clusters to be sampled and the uncertainty ranges for all other causes.
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
57
In the case of Tanzania, we decide that conducting VA in 100 clusters is on one hand feasible, (keeping in mind
logistical and financial considerations), but also leads to a minimal detectable difference (uncertainty range) in the
CSMF for the 20
th
cause (cause of death closest to 1%) of 42.3%, which is satisfactory and acceptable for us. The
final input parameters are the following:
Note: You could now also select “No” for the question whether you know the population size of each eligible
cluster and enter mean population per cluster (15,650) and the crude death rate (6.351) based on the inputs from
B.2. With an MIS of 1.5 you would then end up with a similar number of clusters required (104) as if the harmonic
mean was used all other parameters being constant.
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
58
B.6. Sampling,strategy,for,selecting,the,CRVS,VA,sample,clusters,
Based on the calculations done in B.5 we now need to sample 100 wards from our sampling frame. Given that we
want our sample to reflect characteristics of the whole country, we decide to stratify by region and urban/rural
status. To do so we follow the instructions given in Part B, section 4.1 and obtain the number of wards (clusters)
we need to sample per strata:
Cells highlighted in yellow require input from your sampling frame or the above sample size calculations.
To now pick the number of required wards from each stratum, we will use PPS sampling (see Part B, section 4.2).
For this, we will need a list of all eligible wards per stratum. Here, we will work out the example of Arusha urban,
where we pick one ward from 19 wards. You would need to do this for each individual stratum.
To implement PPS sampling we will follow the steps in Part B, section 4.2 and add a couple of Excel specific features
to facilitate the work.
1) In column A to F we list characteristics of all clusters in the stratum Arusha urban. This information comes
from the sampling frame.
2) In column G we calculate the cumulative sum of the stratum population. This means row 2 equals F2, row
3 equals G2 + F3 and this formula will then need to be dragged down for all subsequent rows. G20 is the
total population size in the stratum (also in E22).
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
59
3) In E24 we calculate the sampling interval by dividing the total population in the stratum by the number of
required clusters in the stratum. The number of clusters to be sampled in the stratum comes from above
and is 1 in the case of Arusha urban.
4) In E25 we choose a random number between 0 and 1. The random start shown in E26 is then given by this
number multiplied by the sampling interval (E24).
5) To automate the calculation of the series: RS; RS+SI; RS+2*SI; … RS+(d-1)*SI, we will use some intermediate
steps in Excel:
a. In column H and I we define the lower and the upper bound of the cumulative population in each
cluster. In row 2 this is 0 (column H) to G2 (column I) and in row 3 this is I2 (column H) to G3
(column I). The formulas from row 3 you will then need to drag down till the end of your list.
b. In column J we define the target which is the value of the series, meaning the random start plus
the sampling interval times column L (number of wards already selected). Again the formula in row
2 is different from the rest and the formula given for row 3 will need to be dragged down to the
last cluster in the list.
c. Column K indicates with 1 if a ward is selected and with 0 if the ward is not selected. Here the
formula for row 2 can be entered and then dragged down to the last cluster.
d. Column L sums up how many wards were already selected and is primarily needed to calculate the
target in column J. Again, the formula in row 2 is different from the rest and the formula given for
row 3 will need to be dragged down to the last cluster in the list.
6) The clusters selected are those with a 1 in column K. In our case this would be the ward called “Sombetini”.
Note: Every time you refresh the Excel file, the random number in E25 will be different and therewith the clusters
selected will be different.
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
60
B.7. Calculating, the, number, of, clusters, required, in, o rder, to, disaggregate,
results,for,male,and,female,
As explained in A10.1 the Sample Size Calculator Tool doubles the calculated number of clusters required in order
to have disaggregated results for male and female. It is also stated, that this however is only correct if the CDRs
for female and male are somewhat similar.
To investigate if this is the case in Tanzania, we will calculate the required number of clusters for the sub-
population of the sex with the lower CDR, which is the female population.
In a first step we will need to compute the estimated female population for each cluster by simply dividing the
total population by two (assuming you have 50% male and 50% female in the population). We also need to
compute the regional female CDR for 2017 using the above estimated national female CDR of 5.81 (section B.1.4).
Note: Alternatively, if the regional CDRs do not vary a lot, you could also simply divide the mean population per
cluster by two (assuming you have 50% male and 50% female in the population) and multiply this by the national
female CDR/1,000 (15’650/2*5.81/1,000 = 45.47).
In a next step we go back to our Sample Size Calculator Tool for which we used the final input parameters listed
in B.5 and which revealed that we would need to sample 100 clusters if we wanted to be able to measure a
percentage change of 42.3% or more in CSMF for the 20th cause of death. We will now replace the cluster
population size and the crude death rate in our table to the female population and its specific crude death rate.
The expected annual mean number of deaths per cluster changes from 65.0 to 29.7.
The only thing which we now change in addition is to select “No” for the question whether we want our sample
size to be calculated in a way that we can disaggregate our results by male and female. We then look at the results
and see if the required number of clusters increased or decreased form what we had before.
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
61
In our case the number of required clusters increased from 100 to 102. This means our original sample size
calculations, which simply doubled the number of required clusters, was slightly to low. However, the difference
is so small that we decide to remain with the simpler calculation.
If the number of clusters needed for “females only” would be much bigger than the number of clusters needed
based on your original sample size calculations, then simply doubling the numbers of clusters required (as done
by the Sample Size Calculator Tool) is insufficient. In this case the difference between the CDR of female and male
is so big that you would need to calculate your sample size for the sub-population of the sex with the lower CDR
only.
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
62
B.8. Calculating, the, number, of, clusters, required, separately, for, areas, with,
different,proportions,of,deaths,with,an,MCCD,
For the above example of Tanzania the percentage of total deaths with a MCCD was assumed to be 11% nationally
(see B.1.4). However, this assumption only holds true if the proportion of deaths with an MCCD is similar across
the country. In Tanzania, we suspect that this could vary depending on the urban/rural status. Thus, we will
investigate this further.
Based on DHIS2 data we know that 59% of all deaths with a MCCD come from health facilities in rural area and
41% from health facilities in urban areas (average of 2015 and 2016 data). From the calculations done in B.5 we
know we need to sample 100 wards with a total estimated number of 9,940 deaths. In B.6 we calculated that 74
of the 100 clusters should be rural and 26 urban. With an expected annual mean number of deaths per cluster of
99.4, this would mean that 7,356 deaths in the sample are expected to be in rural areas and the rest in urban
areas. This, together with the known national percentage of total deaths with a MCCD (11%) allows us to calculate
the percentage of deaths with a MCCD in rural and urban areas.
The input data is highlighted in yellow. In a first step you calculate the total number of expected deaths with a
MCCD in the sample. In a second step you compute the expected number of deaths with a MCCD in the sample
for rural and urban areas based on the percentage of MCCD deaths coming from either of these two areas. In a
third step you then use the expected number of deaths in the sample and the expected number of deaths with a
MCCD in the sample per rural/urban status to calculate the percentage of deaths with a MCCD in rural and urban
areas. In our case this reveals that 9% of deaths in rural and 17% of deaths in urban areas have a MCCD.
All other parameters being constant and the same in urban and rural areas, this will now impact how many clusters
we have to sample from each area. Thus, in the following steps we will use the urban/rural specific percentage of
deaths with a MCCD and recalculate the numbers of cluster needed per area.
The input data is highlighted in yellow, whereas the clusters needed and the total number of deaths in the sample
come from B.5 and B.6, the under-notification and non-response rate (assumed to be constant across the country)
and the national estimate of percentage of total deaths with a MCCD from B.1.4, and proportion of all deaths with
a MCCD per urban/rural area from above.
CRVS-Verbal Autopsy Sampling Strategies for Annex B. Worked example implementing
Representative VA Implementation: A Practical Guide the guidance in one country
63
1) Calculate the number of deaths in the sample for rural and urban areas based on expected annual mean
number of deaths per cluster of 99.4 (B.5) (Rural: E3/(C2+D2)*C2; Urban: E3/(C2+D2)*D2).
2) Calculate the number of death to be included in the analysis by subtracting 10% for non-response and under
notification and 11% for deaths with a MCCD (Rural: C3*(1-0.11)*(1-0.1); for Urban and Total replace C3 by
D3 and E3).
3) Calculate the number of deaths based on the rural/urban specific percentage of deaths with a MCCD by
subtracting 10% for non-response and under notification and the percentage of deaths with a MCCD (Rural:
C3*(1-C6)*(1-0.1); for Urban and Total replace C with D and E).
4) Calculate the revised number of clusters required based on the rural/urban specific percentage of deaths with
a MCCD (Rural: C2/C7*C4; for Urban and Total replace C by D and E).
After rounding, this reveals that we would need instead of 74 and 26 clusters 72 and 28 clusters in rural and urban
areas, respectively. However, in the case of Tanzania this difference is very minor and thus we decide to remain
with the simpler calculation and the assumption of a single national percentage of total deaths with a MCCD of
11% and 76 and 24 clusters in rural and urban areas.
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
64
Annex%C.%Additional%Resource%Material%
C.1. National,Crude,Death,Rate,estimates,for,Data,for,Health,Initiative ,CRVS,
VA,countries,,
CDR [/1,000]
Source
Country
World
Population
Review
(2017)
Knoema
(2017)
UN/population
division
(2015-2020)
World Bank
(2015)
Bangladesh
5.265
5.27
5.271
5.31
Brazil
6.266
6.24
6.296
6.092
Colombia
6.057
6.08
6.122
5.942
Ecuador
5.104
5.12
5.118
5.127
Ghana
8.552
7.99
7.904
8.314
Indonesia
7.198
7.16
7.184
7.096
Kenya
7.641
5.66
5.681
5.841
Malawi
6.872
7.10
7.09
7.498
Morocco
5.67
5.12
5.124
5.145
Myanmar
8.333
8.19
8.236
8.101
Philippines
6.81
6.55
6.546
6.496
Papua New
Guinea
7.6
7.09
7.089
7.133
Rwanda
6.43
5.84
5.814
6.132
Solomon Islands
5.567
4.70
4.68
4.852
Sri Lanka
7.031
6.99
7.044
6.814
Tanzania
6.351
6.49
6.351
7.015
Zambia
8.092
7.60
7.59
7.998
,
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
65
C.2. Method,for,estimating,national,level,CSMFs,
It is important to have an estimate of the CSMFs for the top 20 male and top 20 female causes at national level
that are produced by your VA system. If such estimates are not available from prior studies, these are available
on-line at https://vizhub.healthdata.org/gbd-compare/. This is the IHME GBD Compare web site.
1. Make the following settings:
• Choose: Arrow Diagram
• Set Tab to: Single
• Set Display to: Cause
• Set Rank to: Cause
• Set Category to: All causes
• Set Aggregation Level
11
to: 3
• Set Measure to: Deaths
• Set Location to: Your Country Name
• Range: any year till the year you are interested in (e.g.2010 to 2016)
• Set Age to: All
• Set Sex to your choice: Male, Female, or Both
• Set Units to: %
Note: The same could be done for rates if this is also of interest for you.
Here is a example settings for Tanzania and associated output for 2016:
2. With the above settings still active, click on the Download button at the upper right and save the data as a csv
file to open in MS Excel.
11
Aggregation level 1 (Communicable, Non-communicable and Injury) is too coarse, and Aggregation Level 4 is too disaggregated to highly
specific causes. Level 3 concords best with the VA target causes lists in general use today.
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
66
3. In Excel go to Data > Get External Data > From Text and import the csv file (delimiters is “comma”). This file
has all proportional deaths for all causes and the selected years.
4. Select the most recent year and the measure “Percent of Total Deaths”.
5. Then sort on the value to get a ranked list of the CSMFs.
6. Delete causes that are not on your VA Target Cause list (e.g., Alzheimer disease and other dementias) to
obtain the top 20 estimated CSMFs that will be seen in your VA data (best done by a clinician).
7. Afterwards, prepare a frequency distribution graphic, which will look something like this, which is an example
from Tanzania for the top 20 IHME estimated CSMFs selected related to WHO 2016 VA target cause lists for
2016.
8. Note the range of CSMFs between the 1
st
and 20
th
cause. The distribution of CSMFs for your country will likely
be such that the 1
st
rank will fall between 10 and 15%, while the 10
th
rank will be around 2%, and the 20
th
rank
will be around 1%. The top 20 causes will likely account for about 70% of all deaths.
Estimated distributions for all countries participating in the Data for Health Initiative for 2016 are provided in
Annex C.3.
The current VA target cause lists for the WHO 2016 Standard VA
12
and for the SmartVA
13
methods are provided in
C.4for comparison to your country’s distribution of leading causes. ,
12
Available at [insert URL]
13
Available at [insert URL]
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
67
C.3. Top,20,CSMF,estimates,for,Data,for,Health,Initiative,CRVS,VA,countries,,
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
68
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
69
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
70
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
71
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
72
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
73
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
74
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
75
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
76
C.4. Verbal,Autopsy,Target,Cause,Lists,
C.5. Link,to,CRVS,VA,Costing,Tool,for,downlo ad,
To download the CRVS VA Costing tool, please follow the subsequent link:
WHO 2016 VA
(64 causes & 70 codes)
ICD-
10
IHME SmartVA
(47 causes, 46 codes)
ICD-
10
1 Diarrheal diseases A09 Diarrhea/Dysentery A09
2 Pulmonary tuberculosis A16 TB A16
3 Neonatal tetanus A33 Sepsis A41
4 Tetanus A34 Hemorrhagic fever A99
5 Tetanus Obstetric A35 Measles B05
6 Pertussis A37 AIDS B24
7 Sepsis A41 Malaria B54
8 Dengue fever A90 Other Infectious Diseases B99
9 Haemorrhagic fever A99 Cancer Esophageal C15
10 Measles B05 Cancer Stomach C16
11 HIV/AIDS related death B24 Cancer colorectal C18
12 Malaria B54 Cancer Lung C34
13 Unspecified infectious disease B99 Cancer Breast C50
14 Oral neoplasm C06 Cancer Cervical C53
15 Digestive neoplasms C26 Cancer Prostrate C61
16 Respiratory neoplasms C39 Cancers Other C76
17 Breast neoplasms C50 Leukemia/Lymphomas C96
18 Female reproductive neoplasms C57 Diabetes E14
19 Male reproductive neoplasms C63 Meningitis G03
20 Other and unspecified neoplasms C80 Encephalitis G04
21 Sickle cell with crisis D57 Epilepsy G40
22 Severe anemia D64 Stroke I64
23 Diabetes mellitus E14 Other Cardiovascular Diseases I99
24 Severe malnutrition E46 Pneumonia J22
25 Meningitis and encephalitis G03 Pneumonia (newborn) P23
26 Meningitis and encephalitis G04 Cirrhosis K74
27 Epilepsy G40 Other Digestive Diseases K92
28 Acute cardiac disease (ischemic) I24 Renal Failure N19
29 Stroke I64 Maternal O95
30 Other and unspecified cardiac disease I99 Preterm Delivery P07
31 Acute respiratory infection, Pneumonia J18 Birth asphyxia P21
32 Acute respiratory infection, Pneumonia J22 Meningitis/Sepsis P36
33 Chronic obstructive pulmonary disease (COPD) J44 Stillbirth P95
34 Asthma J45 Congenital malformation Q89
35 Liver cirrhosis K74 Road Traffic V89
36 Renal failure N19 Falls W19
37 Ectopic pregnancy O00 Drowning W74
38 Other and unspecified maternal cause O05 Fires X09
39 Abortion-related death O06 Bite of Venomous Animal X27
40 Pregnancy-induced hypertension O13 Poisonings X49
41 Pregnancy-induced hypertension (eclampsia) O15 Other Injuries X58
42 Obstetric haemorrhage (ante partum) O46 Suicide X84
43 Obstetric labour O66 Violent Death / Homicide Y09
44 Ruptured uterus O71 Chronic Respiratory J44
45 Obstetric haemorrhage (post partum) O72 Ischemic Heart Disease I24
46 Pregnancy-related sepsis (ante partum) O75 Other Defined Causes of Child Deaths R99
47 Pregnancy-related sepsis (post partum) O85 Other Non-communicable Diseases R99
48 Anemia of pregnancy O99
49 Prematurity P07
50 Birth asphyxia P21
51 Neonatal pneumonia P23
52 Neonatal sepsis P63
53 Fresh stillbirth P95
54 Macerated stillbirth P95
55 Other and unspecified perinatal cause of death P96
56 Congenital malformation Q89
57 Acute abdomen R10
59 Other and unspecified non-communicable disease R99
58 Cause of death unknown R99
60 Road traffic accident V89
61 Other transport accident V99
62 Accidental fall W19
63 Accidental drowning and submersion W74
64 Accidental exposure to smoke, fire and flames X09
65 Contact with venomous animals and plants X29
66 Exposure to force of nature X39
67
Accidental poisoning and exposure to noxious substances
X49
68 Other and unspecified external cause of death X59
69 Intentional self-harm X84
70 Assault Y09
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide Annex C. Additional Materials
77
https://crvsgateway.info/learningcentre/improving-quality-and-presentation-of-crvs-data/verbal-autopsy-
costing-and-budgeting-tool
CRVS-Verbal Autopsy Sampling Strategies for
Representative VA Implementation: A Practical Guide 8. References
78
References%
Bierrenbach, A. (2008). Steps in applying Probability Proportional to Size (PPS) and calculating Basic
Probability Weights
http://www.who.int/tb/advisory_bodies/impact_measurement_taskforce/meetings/prevalence_survey
/psws_probability_prop_size_bierrenbach.pdf, World Health Organization, Geneva, Switzerland
D'Ambruoso, L., T. Boerma, P. Byass, E. Fottrell, K. Herbst, K. Kallander and Z. Mullan (2016). "The case
for verbal autopsy in health systems strengthening." Lancet Glob Health.
de Savigny, D., S. Renggli, D. Cobos Muñoz and M. Collinson (2017). Maximizing Synergies between
Health Observatories and CRVS: Guidance for INDEPTH HDSS Sites and Other CRVS Stakeholders.
INDEPTH Network and Bloomberg Philanthropies Data for Health Initiative. https://crvsgateway.info/.
de Savigny, D., I. Riley, D. Chandramohan, F. Odhiambo, E. Nichols, S. Notzon, C. AbouZahr, R. Mitra, D.
Cobos Munoz, S. Firth, N. Maire, O. Sankoh, G. Bronson, P. Setel, P. Byass, R. Jakob, T. Boerma and A. D.
Lopez (2017). "Integrating community-based verbal autopsy into civil registration and vital statistics
(CRVS): system-level considerations." Glob Health Action 10(1): 1272882.
Eldridge, S. M., D. Ashby and S. Kerry (2006). "Sample size for cluster randomized trials: effect of
coefficient of variation of cluster size and analysis method." Int J Epidemiol 35(5): 1292-1300.
Everitt, B. S. and A. Skrondal (2010). The Cambridge Dictionary of Statistics. New York, Cambridge
University Press. 4th.
Hayes, J. and L. Moulton (2009). Cluster Randomized Trails. Boca Raton, CRC Press.
Hayes, R. J., N. D. Alexander, S. Bennett and S. N. Cousens (2000). "Design and analysis issues in cluster-
randomized trials of interventions against infectious diseases." Stat Methods Med Res 9(2): 95-116.
Hayes, R. J. and S. Bennett (1999). "Simple sample size calculation for cluster-randomized trials." Int J
Epidemiol 28(2): 319-326.
International Epidemiological Association (2014). A Dictionary of Epidemiology. M. Porta, S. Greenland,
M. Hernán, I. dos Santos Silva and J. M. Last. New York, Oxford University Press. 6th.
Kerry, S. M. and J. M. Bland (1998). "The intracluster correlation coefficient in cluster randomisation."
BMJ 316(7142): 1455.
Killip, S., Z. Mahfoud and K. Pearce (2004). "What is an intracluster correlation coefficient? Crucial
concepts for primary care researchers." Ann Fam Med 2(3): 204-208.
National Bureau of Statistics and Ministry of Finance (2013). 2012 Population and housing census. Dar es
Salaam, National Bureau of Statistics and Ministry of Finance, United Republic of Tanzania.
Pagel, C., A. Prost, S. Lewycka, S. Das, T. Colbourn, R. Mahapatra, K. Azad, A. Costello and D. Osrin
(2011). "Intracluster correlation coefficients and coefficients of variation for perinatal outcomes from
five cluster-randomised controlled trials in low and middle-income countries: results and
methodological implications." Trials 12: 151.
Preisser, J. S., B. A. Reboussin, E. Y. Song and M. Wolfson (2007). "The importance and role of
intracluster correlations in planning cluster trials." Epidemiology 18(5): 552-560.
Upton, G. and I. Cook (2014). A Dictionary of Statistics. Oxford, Oxford University Press. 3rd.
