Constructing Statistical Intervals for Small Area Estimates Based on Generalized Linear Mixed Model in Health Surveys.

Yan Wang,Janet B Croft,Kurt J Greenlund,Xingyou Zhang,Hua Lu

doi:10.4236/ojs.2022.121005

Yan Wang, Janet B Croft + Show 3 more

Open Access

https://doi.org/10.4236/ojs.2022.121005

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Abstract

Generalized Linear Mixed Model (GLMM) has been widely used in small area estimation for health indicators. Bayesian estimation is usually used to construct statistical intervals, however, its computational intensity is a big challenge for large complex surveys. Frequentist approaches, such as bootstrapping, and Monte Carlo (MC) simulation, are also applied but not evaluated in terms of the interval magnitude, width, and the computational time consumed. The 2013 Florida Behavioral Risk Factor Surveillance System data was used as a case study. County-level estimated prevalence of three health-related outcomes was obtained through a GLMM; and their 95% confidence intervals (CIs) were generated from bootstrapping and MC simulation. The intervals were compared to 95% credential intervals through a hierarchial Bayesian model. The results showed that 95% CIs for county-level estimates of each outcome by using MC simulation were similar to the 95% credible intervals generated by Bayesian estimation and were the most computationally efficient. It could be a viable option for constructing statistical intervals for small area estimation in public health practice.

Highlights

County-level estimated prevalence of three health-related outcomes was obtained through a Generalized Linear Mixed Model (GLMM); and their 95% confidence intervals (CIs) were generated from bootstrapping and Monte Carlo (MC) simulation
The results showed that 95% CIs for county-level estimates of each outcome by using MC simulation were similar to the 95% credible intervals generated by Bayesian estimation and were the most computationally efficient
The posterior distribution of the parameter could be simulated through Markov Chain Monte Carlo (MCMC) samples and a posterior distribution of small area estimate is produced

Summary

Introduction

The posterior distribution of the parameter could be simulated through Markov Chain Monte Carlo (MCMC) samples and a posterior distribution of small area estimate is produced This approach is computationally intensive for large datasets with complex data structures, such as the nationwide Behavioral Risk Factor Surveillance System (BRFSS). Monte Carlo simulation is another useful tool to generate sample statistics by using point estimates of model parameters and their asymptotic covariance matrix of these estimates [12]. These two approaches’ performance has not been evaluated in the context of statistical interval construction of prediction through real complex health surveys

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