JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1049 10.6339/22-JDS1049 Statistical Data Science Modeling County-Level Rare Disease Prevalence Using Bayesian Hierarchical Sampling Weighted Zero-Inflated Regression✩ https://orcid.org/0000-0001-8160-9683 XieHuihxie@cdc.gov1∗ RolkaDeborah B.1 BarkerLawrence E.2 Centers for Disease Control and Prevention, National Center for Chronic Disease Prevention and Health Promotion, Division of Diabetes Translation, Atlanta, Georgia, USA Centers for Disease Control and Prevention, National Center for Chronic Disease Prevention and Health Promotion, Office of the Director, Atlanta, Georgia, USA (retired)

The findings and conclusions in this report are those of the authors and do not necessarily represent the official position of the Centers for Disease Control and Prevention.

Corresponding author. Email: hxie@cdc.gov. 20232262022211145157 Supplementary Material

Figure 4: Agreement between BRFSS model-based estimates and ACS 1-year reports of county-level DDRS based on 225 selected counties in 2015. The reference line denotes if model-based estimates and standard references (e.g., ACS 1-year report) were identical. Among the four models (BHBI, BZBI, BPLW and BBZ), estimates of BHBI and BZBI present both large variances and bias; Most counties have a positive estimated bias. Estimates of BBZ tend to stay closer to the reference line with least bias and variance. These results are matched with those in 2019.

Figure 5: Agreement between BRFSS model-based estimates and ACS 1-year reports of county-level DDRS based on 225 selected counties in 2016. The reference line denotes if model-based estimates and standard references (e.g., ACS 1-year report) were identical. Among the four models (BHBI, BZBI, BPLW and BBZ), estimates of BHBI and BZBI present both large variances and bias; Most counties have a positive estimated bias. Estimates of BBZ tend to stay closer to the reference line with least bias and variance. These results are matched with those in 2019.

141220212642022 2023 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2023 Open access article under the CC BY license.

Estimates of county-level disease prevalence have a variety of applications. Such estimation is often done via model-based small-area estimation using survey data. However, for conditions with low prevalence (i.e., rare diseases or newly diagnosed diseases), counties with a high fraction of zero counts in surveys are common. They are often more common than the model used would lead one to expect; such zeros are called ‘excess zeros’. The excess zeros can be structural (there are no cases to find) or sampling (there are cases, but none were selected for sampling). These issues are often addressed by combining multiple years of data. However, this approach can obscure trends in annual estimates and prevent estimates from being timely. Using single-year survey data, we proposed a Bayesian weighted Binomial Zero-inflated (BBZ) model to estimate county-level rare diseases prevalence. The BBZ model accounts for excess zero counts, the sampling weights and uses a power prior. We evaluated BBZ with American Community Survey results and simulated data. We showed that BBZ yielded less bias and smaller variance than estimates based on the binomial distribution, a common approach to this problem. Since BBZ uses only a single year of survey data, BBZ produces more timely county-level incidence estimates. These timely estimates help pinpoint the special areas of county-level needs and help medical researchers and public health practitioners promptly evaluate rare diseases trends and associations with other health conditions.

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