Application of Hierarchical Bayesian Linear Model in Meta-Analysis

Meta-analysis is an evidence based tool for combining results from independent studies to obtain a concise estimate. Broadly the two parametric statistical models used in this method are the fixed effect model and the random effect model. The appropriateness of these models in incorporating variability between studies and resolving the problem of unpublished studies in meta-analysis has long been debated among statisticians. The Bayesian inference has been adopted extensively in clinical decision making. This communication provides a detailed account of the theory of Hierarchical Bayesian Linear Model (HBLM) in determining the summary estimates in meta-analysis of clinical trials. It has been shown that HBLM is a generalized model from which the results of the classical fixed effect and random effect model can be derived by treating the value of variation between studies, as either 0 or the non-iterative estimate by the methods of moments. It also provides a method for estimating the study specific estimate that helps in computing predictive probabilities. The Bayesian model has been found to be more useful in incorporating other sources of variation as it is based on Generalized Linear model.