Multilevel Modeling of Binary Outcomes with Three-Level Complex Health Survey Data

Abstract

Complex survey designs often involve unequal selection probabilities of clusters or units within clusters. When estimating models for complex survey data, scaled weights are incorporated into the likelihood, producing a pseudo likelihood. In a 3-level weighted analysis for a binary outcome, we implemented two methods for scaling the sampling weights in the National Health Survey of Pakistan (NHSP). For NHSP with health care utilization as a binary outcome we found age, gender, household (HH) goods, urban/rural status, community development index, province and marital status as significant predictors of health care utilization (p-value < 0.05). The variance of the random intercepts using scaling method 1 is estimated as 0.0961 (standard error 0.0339) for PSU level, and 0.2726 (standard error 0.0995) for household level respectively. Both estimates are significantly different from zero (p-value < 0.05) and indicate considerable heterogeneity in health care utilization with respect to households and PSUs. The results of the NHSP data analysis showed that all three analyses, weighted (two scaling methods) and un-weighted, converged to almost identical results with few exceptions. This may have occurred because of the large number of 3rd and 2nd level clusters and relatively small ICC. We performed a simulation study to assess the effect of varying prevalence and intra-class correlation coefficients (ICCs) on bias of fixed effect parameters and variance components of a multilevel pseudo maximum likelihood (weighted) analysis. The simulation results showed that the performance of the scaled weighted estimators is satisfactory for both scaling methods. Incorporating simulation into the analysis of complex multilevel surveys allows the integrity of the results to be tested and is recommended as good practice.