Meta-Analysis: A Comparison of Fixed Effects and Random Effects Models with Illustrative Examples

Abstract

Meta-analysis has been widely used in clinical research because it provides a useful tool for combining results from a series of trials addressing the same question. Two major approaches for study-to-study variation can be used in a meta-analysis: the fixed effects model which assumes that each study has the same true effect size, and the random effects model which assumes that the true effect size is a random variable that varies between studies. When there are covariates arising from the study, regression models can be used to explain the effects of these covariates on the between study variation in effect size. The purpose of this project is to draw some general conclusions about the statistical methods used in meta-analyses by re-examining several clinical examples which presented some problems. Four illustrative examples of recent meta-analyses were selected and re-examined. Both fixed effects and random effects models were used. In addition, regression models were used in two examples. Some general conclusions were made about the statistical aspects of meta-analysis from this project. The overall estimate of the fixed effects model tends to be overly influenced by large trials and may results in contradictory conclusions when extreme trials (small vs. large samples) are combined. Therefore, it is advocated that the weights allocated to each trial in any meta-analysis should be explicitly calculated and displayed. The random effects model takes a more balanced account of all studies and considers other unknown factors which may affect the effect size. Therefore, the random effects model and random effects regression model are more appropriate for these clinical data meta-analyses.