Multilevel modelling of HIV in Swaziland using frequentist and Bayesian approaches.

Abstract

Multilevel models account for different levels of aggregation that may be present in the data. Researchers are sometimes faced with the task of analysing data that are collected at different levels such that attributes about individual cases are provided as well as the attributes of groupings of these individual cases. Data with multilevel structure is common in the social sciences and other fields such as epidemiology. Ignoring hierarchies in data (where they exist) can have damaging consequences to subsequent statistical inference. This study applied multilevel models from frequentist and Bayesian perspectives to the Swaziland Demographic and Health Survey (SDHS) data. The first model fitted to the data was a Bayesian generalised linear mixed model (GLMM) using two estimation techniques: the Integrated Laplace Approximation (INLA) and Monte Carlo Markov Chain (MCMC) methods. The study aimed at identifying determinants of HIV in Swaziland and as well as comparing the different statistical models. The outcome variable of interest in this study is HIV status and it is binary, in all the models fitted the logit link was used. The results of the analysis showed that the INLA estimation approach is superior to the MCMC approach in Bayesian GLMMs in terms of computational speed. The INLA approach produced the results within seconds compared to the many minutes taken by the MCMC methods. There were minimal differences observed between the Bayesian multilevel model and the frequentist multilevel model. A notable difference observed between the Bayesian GLMMs and the the multilevel models is that of differing estimates for cluster effects. In the Bayesian GLMM, the estimates for the cluster effects are larger than the ones from the multilevel models. The inclusion of cluster level variables in the multilevel models reduced the unexplained group level variation. In an attempt to identify key drivers of HIV in Swaziland, this study found that age, age at first sex, marital status and the number of sexual partners one had in the last 12 months are associated with HIV serostatus. Weak between cluster variations were found in both men and women.