1. The document discusses approaches for estimating national indicators related to key populations, such as the size of female sex workers, when existing data are incomplete. 2. It describes using an augmented inverse probability weighted estimator to combine data from surveys of a subset of areas with covariate data available nationwide in order to estimate proportions for the entire country. 3. Sensitivity analyses and discussion with stakeholders are recommended to understand uncertainties and ensure the method's assumptions adequately reflect the population.

1. Extrapolation of data from key
population surveys and
programs
Jessie K. Edwards
University of North Carolina at Chapel Hill
jessedwards@unc.edu
2016 International AIDS Conference
Durban, South Africa
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2. Perspective
To improve public health, we must
make a series of urgent decisions.
• Resource allocation
• Intervention strategies
• Prioritization
Sometimes, we must act without perfect
data.
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3. Perspective
• But, we rarely act from a position of complete
ignorance.
• To make decisions, we (often implicitly) summarize
any existing information and our remaining
uncertainty.
• This talk walks through some approaches to
formalize this process in a specific setting.
3

4. Our Setting
Decision makers often need national estimates of
indicators related to key populations
- For advocacy purposes
- To set national targets
- To inform funding allocation by international bodies
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5. What do we want to know?
- Size estimates of key populations
- Female sex workers
- Men who have sex with men
- Transgender people
- Prevalence of HIV and other diseases
- Distribution of risk factors for disease transmission
- Program coverage
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6. Challenges
Usually, information to describe a national HIV
epidemic has gaps.
Subgroups of the population may be
underrepresented
Geographic areas of the country may be
excluded
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7. We need a principled approach to
come up with national estimates
when existing data are incomplete.
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8. Ongoing efforts
WHO / UNAIDS meeting in March on strategic
indicators for key pops
MeSH co-convened, UNC, LSHTM, JHSPH
participants
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9. Illustrative example
What is the size of the population of
female sex workers in the Dominican
Republic?
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10. Overview
1. Need for a national estimate: Specifically sizes of
key populations, including female sex workers
• Funders request this information
• National estimates guide MOH priorities
2. Inventory of existing data: Size estimates from 37 of
154 municipalities collected in priority provinces
using a venue-based sampling approach
3. Statistical approaches to compute national
estimate: The focus of this talk.
4. Consensus building + decision making: Project is
ongoing – due to data security concerns, this
example is illustrative only (data are hypothetical)
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11. Parameter of interest
𝜓 = 𝐸 𝑌 = proportion of women who exchange sex for cash
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In simulations, I set 𝜓 = 2.0%

12. Missing data problem
But we only have measurements in a subset of the
geographic areas from programmatic data collection in 2014
(let’s denote these regions by 𝑆𝑗 = 1)
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13. Missing data problem
Our challenge is to use data from the sampled
areas to make inference to the entire country
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14. Approach
Original data:
Because data were collected for programmatic
purposes, 𝐸 𝑌 𝑆𝑗 = 1 > 𝐸(𝑌)
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In simulated example, 𝐸 𝑌 𝑆𝑗 = 1 = 4.1%

15. Approach
Original data:
Expect that 𝐸 𝑌 𝑊 = 𝑤, 𝑆𝑗 = 1 = 𝐸(𝑌|𝑊 = 𝑤), but
did not collect data in all strata of 𝑊.
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In simulated example, 𝑤 𝐸 𝑌 𝑊 = 𝑤, 𝑆𝑗 = 1 𝑃(𝑊 = 𝑤|𝑆𝑗 = 1) =
3.5%

16. Approach
Original data + targeted additional data collection
Expect that 𝐸 𝑌 𝑊 = 𝑤, 𝑆𝑗 = 1 = 𝐸(𝑌|𝑊 = 𝑤), and
𝑃 𝑆𝑗 = 1|𝑊 = 𝑤 > 0 for all 𝑊
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17. Obtaining information on 𝑾
The programmatic data collection activities only
collected data on 𝑌.
But contextual data (𝑊) can be found other places
• Census information
• Geographic databases
• Other population health surveys
• DHS
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18. Covariates in 𝑾 for DR example
From national data (publically available online):
• Age distribution
• Male/female ratio
• Employment data
• Population density
• Poverty
• Country of origin
From DHS
• Average number of years of education among women
• HIV prevalence
• Adolescent pregnancy indicators
From other sources (directly from stakeholders)
• Indicator of tourist area
• Indicator that the municipality was on a major transit corridor
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19. Challenges using population-based surveys
Challenges with DHS data
• Indicators are generalizable to regional level, but we
needed municipal estimates
• Random displacement of GPS coordinates for
clusters
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20. Summarizing DHS data
1. Create 𝑊 “surface” by interpolating values of 𝑊
between DHS clusters using a fine grid
2. Summarize values of 𝑊 by municipality
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21. Summarizing DHS data
1. Create 𝑊 “surface” by interpolating values of 𝑊
between DHS clusters using a fine grid
2. Summarize values of 𝑊 by municipality
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22. Now a standard missing data problem
We have data on 𝑌 for 50 municipalities
We have data on 𝑊 for all 154 municipalities
Could use any computation approach for estimating a
mean in the presence of missing data.
• Up-weight existing data to represent distribution of 𝑊 in
entire country
• Predict estimates in municipalities without data from a
regression model containing 𝑊
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Here, we use the augmented inverse probability
weighted (AIPW) estimator for 𝝍.

23. The AIPW estimator
The AIPW is a
consistent,
semiparametric efficient,
and doubly robust,
estimator of 𝜓.
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24. AIPW estimator is consistent, semiparametric efficient,
and doubly robust
What does that mean and why should we care?
• Takes covariates 𝑊 into account
• Smaller variance than traditional weighting approaches
• Two chances to correctly specify parametric models
• Model for inclusion in data collection (like weighting
approaches) AND model for the outcome of interest (like
regression-prediction approaches)
• In weighting only or regression model only approaches, if the
parametric model is misspecified, results are biased.
• Here, if either of these models is correct, estimate of 𝜓 will be
correct
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25. Data use/consensus building
In this example, stakeholders convened a workshop
after the activity to understand the results and
1. Suggest sensitivity analyses
• What if a different set of variables were included in 𝑊?
• What if variables in 𝑊 were measured differently?
• What if variables in 𝑊 were modeled differently?
2. Discuss areas of uncertainty
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26. Loose ends
Quantifying uncertainty
• How sure are we that assumptions hold?
• How much faith do we have in existing estimates of 𝑌?
• How well is 𝑊 captured?
• Are we sure that we have measured all predictors of 𝑌
that differ between municipalities with and without data?
• Crucial for making decisions (i.e., maximizing
expected utility)
• Best incorporated in a Bayesian framework
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27. Loose ends
What if we had not been able to collect additional
data?
That is, what if we had had NO DATA within key
of 𝑊?
e.g., What if all data had been collected in urban areas?
We could augment our existing
knowledge/information using
• Parametric extrapolation
• Bayesian methods
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28. Discussion
Decisions can’t always wait for perfect and complete
data.
We can use modern statistical tools to produce useful
results from incomplete data.
Inference may be updated as more information arises.
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29. This presentation was produced with partial support from the
United States Agency for International Development (USAID)
under the terms of MEASURE Evaluation cooperative
agreement AID-OAA-L-14-00004. MEASURE Evaluation is
implemented by the Carolina Population Center, University of
North Carolina at Chapel Hill in partnership with ICF
International; John Snow, Inc.; Management Sciences for
Health; Palladium; and Tulane University. Views expressed are
not necessarily those of USAID or the United States
government .
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