# Presentation: 947367

## Survey Weighted BRFSS Small Area   Estimates for North Carolina Counties	

- Centers for Disease Control and Prevention (CDC) Assessment Initiative and
- National Association for Public Health Statistics and Information Systems (NAPHSIS) Leadership Institute, Atlanta, GA
-  February 19-21, 2003
- Presented by Glen Laird
- Co-authored by: Ralph Folsom, Akhil Vaish, Neeraja Sathe and Jie Liu
- RTI International
- _Acknowledgement_: Supported in part by a CDC(NCHS) grant to the UNC Center for Health
- 			Statistics Research, Chapel Hill, NC

## 1. Overview

- This research was motivated by the earlier (1999) small area estimation (SAE) work of Folsom, Shah, and Vaish (FSV) for the National Survey on Drug Use and Health (NSDUH).
- FSV developed a survey weighted hierarchical Bayes (HB) procedure (PROC GIBBS) for fitting the logistic mixed model.
- The PROC GIBBS solution has several appealing properties that guard against SAE bias due to non-ignorable sample designs.

## 2. Appealing Properties of PROC GIBBS

- _Self Benchmarking_: Population weighted averages of the PROC GIBBS SAEs across all counties will closely match associated state level direct survey estimates.
- _Design Consistency_: For states with sufficiently large samples the PROC GIBBS SAEs will closely match the corresponding direct county estimates.
- _Unit Level Modeling_: PROC GIBBS fits logistic mixed models to person level binary indicators of disease status. Person level fixed predictors are accommodated.

## 3. North Carolina BRFSS County Level SAEs

- This illustration of SAE methodology focuses on North Carolina county level prevalence estimates by age group for _lifetime diabetes_ and _past month cigarette use_.
- We model pooled 1996-2000 BRFSS survey data from North Carolina.
- Survey weighted county SAEs are contrasted with unweighted SAEs and direct survey estimates.

## 4. HB Logistic Mixed Model

- Fit a HB logistic mixed model to diabetes and cigarette use indicators yaijk for age group-a survey respondent-k residing in county-j of Health Service Area (HSA)-i.
- Assume yaijk ~ Ber(μaijk) with logit(μaijk) = xaijkβa+ηia+υij
- 	*i* = 1, ..., 6 (HSA),         *j*=1, ..., *R*i,
- 	*η**i **= *(*η**i*1 ·· *η**i*4 )T ~ *N*4 ( 0, *D**η** *)
- 	*υ**ij *~ *N *( 0, *σ**υ*2 ).

## 5. HB Model Priors

## 6. Parameters of Interest

- County prevalence estimates by age group-a
- Health Service Area prevalence estimates by age group

## 7. Final Comments

- We are currently working on an SAE model for county level smoking change estimates with 1996-1998 data compared to 1999-2001.
- A beta test version of PROC GIBBS will be available this summer.
- We (Singh, Folsom and Vaish) are working on an improved version that takes full account of all survey design effects by using an estimating function based Gaussian likelihood.
- Future plans include allowance for spatial correlation between the small area random effects.

## 8. References

- Folsom , R. E., Shah, B., and Vaish, A. K. (1999). Substance abuse in states: A methodological report on model based estimates from the 1994-1996 National Household Surveys on Drug Abuse. *Proceedings of the Section on Survey Research Methods of the American Statistical Association* (pp. 371-375).
- Singh, A., Folsom , R. E., and Vaish, A. K. (2002). A Hierarchical Bayes Generalization of the Fay-Herriot Method to Unit Level Nonlinear Mixed Models for Small Area Estimation. *Proceedings of the Section on Survey Research Methods of the American Statistical Association.* (to appear)

## Comparison of Weighted SAEs, Un-weighted SAEs, and Design Based Estimates for Diabetes for Top and Bottom Five Counties in NC for Persons Ages 18 or Older

## Comparison of Weighted SAEs, Un-weighted SAEs, and Design Based Estimates for Current Smoking for Top and Bottom Five Counties in NC for Persons Ages 18 or Older