Modeling Outcome Reporting Bias and Parameter Estimation Using Markov Chain Monte Carlo Method for Meta-analysis on 3 × 2 Tables

Abstract

A Meta-analysis, also known as systematic overview, is a statistical procedure in which the results of several independent studies are integrated, with the aim of being able to resolve issues that cannot be concluded from a single study alone. If a comparative binary outcome is being considered, generally it will be possible to construct, a 2 × 2 table, for each study. Methods for analyzing these types of data are well developed. Our interest is to investigate the study results involving two treatments, which can be summarized into 3×2 table. If all outcomes for all 3×2 tables are available, then already available methods of meta-analysis for 2×2 tables can be used to obtain results. However there are some statistical problems in reporting outcomes of 3×2 tables. It has long been accepted that research with statistically significant results is more likely to be published or submitted than non-significant results. This process of publication of outcomes based on their results is called as Outcome Reporting Bias (ORB). This can impact the results of a meta-analysis due to the biasing of the pooled treatment effect estimate. A parametric selection model is proposed to correct the reporting bias in the reporting of outcomes within a study. A Markov Chain Monte Carlo (MCMC) method is proposed to calculate maximum likelihood estimates. Proposed model is applied to an illustrative data set assuming missing data follows missing at random (MAR)1 mechanism. The computation is done by using WinBUGS, Bayesian software based on Gibbs sampling.