Model-based hybrid small area 

population estimates: 

Combining disparate sources of 

population data

Lance A. Waller Emily Peterson

Department of Biostatistics and Bioinformatics

Rollins School of Public Health

Emory University

lwaller@emory.edu
Outline

“Design what you can, model the rest.”

• Compromises: Differential privacy and small area estimation

• Differential Privacy and Small Area Estimates of Health Disparities

• Hybrid, model-based estimation of small area population sizes.

“Design what you can, model the rest.”
Acknowledgements

• Support: NICHHD R01: 5R01HD092580

• Emory University, Rollins School of Public Health

• Lance Waller, Emily Peterson

• Harvard T.H. Chan School of Public Health

• Brent Coull, Nancy Krieger, Jarvis Chen, Rachel Nethery, Yanran Li, Christian 

Testa, Nick Link

• Imperial College, London

• Fred Piel, Marta Blangiardo, Paul Elliott, Mahboubeh Parsaeian

• Drexel University

• Loni Tabb
Compromises: SAE and DP The picture can't be displayed.
Small Area Estimation

• Fay & Herriot (1979, JASA)

• Shrinkage estimation, James-Stein estimation

• Random intercepts borrow information

• From overall mean (SAE)

• From neighbors (Clayton and Kaldor 1987, Bcs) 

• From both (Besag, York, Mollié 1991, Ann Inst Stat Math)

• Elegant mathematics to borrow the right amount of information.
“Design what you can, model the rest.”
Differential Privacy

• Statistical summaries vs. needle-in-a-haystack 

• (Dwork IPAM-UCLA presentation on YouTube)

• Metaphor: 20 questions 

• Questions are statistical summaries

• “20” = privacy budget (debit card vs. credit card)

• Differential privacy caps probability of discovery from statistical 

summaries

• Elegant mathematics to add the right amount of noise.
“Design what you can, model the rest.”
Putting data to use

• A lot of research on differential privacy 

• US Census Bureau

• Applied to 2020 US Census data products.

• Provided in 2010 demonstration products.

• Impact on small area inference?
Differential Privacy and Small Area Estimation The picture can't be displayed.
Differential Privacy and Small Area Estimates

• 2010 (yes, 2010) US Census demonstration data product

• Both old and new (DP) disclosure avoidance.

• Releases in 2019, 2020, 2022 (spoiler alert: version is important!)

• Two recent assessments relating to small area health disparities:

• Kurz et al (2022, Health Services Research), Waller (2022 commentary)

• Li et al. (2023, Science Advances)
Kurz et al. (2022, HSR)

• Kurz et al (2022):

• County-level 2010 population counts and local Medicaid participation.

• Racialized subpopulations.

• County-level: Differential privacy introduced errors up to 10% in counts and 

proportions of local Medicaid populations.

• State-level: Negligible errors in race-specific Medicaid participation.
Waller (2022, HSR, Commentary)

• Decennial Census 

• Number of residents on particular day.

• American Community Survey

• Rotating survey estimate averaged over a period of time.

• Includes margins of error.

• Spatial correlation in estimates (high values near high values).

• Spatial correlation in margins of error (noisy values near noisy values).

• Different data products require care in combining!
Closer look at 2010 Demonstration Products

• Li et al. (2022, Sci Adv) compare:

• Original 2010 decennial census tract data (DC, data swapping)

• Oct 2019 demonstration product (DP19, differential privacy)

• May 2020 demonstration product (DP20, updated differential privacy)

• August 2022 demonstration product (DP22, most recent differential privacy)

• Notes:

• DP19, DP20: identical DP, distinct postprocessing

• DP22: revised DP parameters in response to users (increased privacy-loss 

budget, giving greater accuracy and weakening privacy guarantees).
Differential Privacy and Small Area Estimation The picture can't be displayed.

DP19, DP20

DP22
% difference in age-standardized population
Simulation assessments of bias
Next: combining disparate data products

• Small area population: How many people there? Two approaches:

• Nethery et al.: Comparing US Census data and non-Census data

• American Community Survey

• WorldPop

• Peterson et al.: Combining US Census Bureau products: 

• Decennial

• PEP

• American Community Survey
Comparing ACS and WorldPop

Nethery et al. (2021, 

SSM Population 

Health)
Accuracy vs. % poverty
Combining US Census Data Products

• Peterson et al.: Combining US Census Bureau products: 

• Decennial

• PEP

• American Community Survey

• https://arxiv.org/abs/2112.09813
Decennial

PEP

ACS

Undercount

Demographic

errors

Sampling 

errors,

Temporal 

aggregation

Sources of 

Error 
Modeling different types of error

• Hierarchical structure

True 

population

Non-sampling error

Sampling error
1000 words
https://www.newyorker.com/culture/postscript/the-beautifully-macabre-cartoons-of-gahan-wilson
A new type of map (for me)....
Predictions: Baker County
High population:

PEP catches growth,

ACS lags

Low population:

PEP catches growth,

ACS noisier
Summary

• Compromises: Differential privacy and small area estimation

• Tension in goals

• Differential Privacy and Small Area Estimates of Health Disparities

• Reducing privacy budget improved accuracy

• Hybrid, model-based estimation of small area population sizes.

• Tracking sources of uncertainty (challenging, but important)

• “Design what you can, model the rest.”
References

• Peterson EN et al. (2023) A Bayesian hierarchical small area population model accounting 

for data source specific methodologies from American Community Survey, Population 

Estimates Program, and Decennial Census Data. https://arxiv.org/abs/2112.09813

• Nethery et a. (2021) Comparing denominator sources for real-time disease incidence 

modeling: American Community Survey and WorldPop. SSM-Population Health 14, 

100786. https://doi.org/10.1016/j.ssmph.2021.100786

• Li Y et al. (2023) Impacts of census differential privacy for small-area disease mapping to 

monitor health inequities. Science Advances 9, eade888. 

• Kurz CF, König AN, Emmert-Fees KMF, Allen LD. The effect of differential privacy on Medicaid participation among racial and ethnic minority groups. Health Serv Res. 2022;57(Suppl. 2):207-213. doi:10.1111/1475-6773.14000

• Waller LA. Global and local impacts of differential privacy on estimates of health care 

inequity. Health Serv Res. 2022;57(Suppl. 2):204-206. doi:10.1111/1475-6773.14080