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

Area of Science:

• Statistics
• Public Health
• Biostatistics

Background:

• Generalized Linear Mixed Models (GLMM) are common for small area estimation of health indicators.
• Bayesian estimation is typically used for statistical intervals but is computationally intensive for large surveys.
• Frequentist methods like bootstrapping and Monte Carlo (MC) simulation are alternatives but lack comprehensive evaluation.

Purpose of the Study:

• To evaluate frequentist approaches, specifically bootstrapping and MC simulation, for constructing statistical intervals in small area estimation.
• To compare the magnitude, width, and computational time of intervals generated by bootstrapping and MC simulation against Bayesian credible intervals.
• To assess the viability of MC simulation as an efficient alternative for public health applications.

Main Methods:

• Utilized the 2013 Florida Behavioral Risk Factor Surveillance System data.
• Applied a Generalized Linear Mixed Model (GLMM) to estimate county-level prevalence of three health outcomes.
• Generated 95% confidence intervals (CIs) using bootstrapping and MC simulation, comparing them to Bayesian credible intervals from a hierarchical Bayesian model.

Main Results:

• 95% CIs from MC simulation closely matched 95% credible intervals from Bayesian estimation for county-level health outcome prevalence.
• MC simulation demonstrated superior computational efficiency compared to other methods.
• Bootstrapping and MC simulation intervals were evaluated for magnitude and width, with MC simulation showing promise.

Conclusions:

• Monte Carlo simulation is a computationally efficient and viable option for constructing statistical intervals in small area estimation for public health.
• The study provides evidence supporting MC simulation as a practical alternative to computationally intensive Bayesian methods.
• Findings suggest MC simulation can reliably generate statistical intervals for health indicators in large, complex survey data.