Meta-analysis with application to estimating combined estimators of effect sizes in biomedical research.

Abstract

Meta-analysis is a statistical analysis that combines results from different independent studies. In meta-analysis a number of statistical methods are currently used for combining effect sizes of different studies. The simplest of these methods is based on a fixed-effects model, which assumes that all studies in the meta-analysis share a common true effect size and that the effect sizes in our meta-analysis differ only because of sampling error. Another statistical method that is used in meta-analysis, is the random-effects model, which assumes sampling variation due to fixed-effects model assumptions and random variation because the effect sizes themselves are sampled from a population of effect sizes. These models are compared to determine which model is appropriate and under what circumstances is the model appropriate. We illustrate these models by applying each model to a collection of 3 studies examining the effectiveness of new drug versus placebo to treat patients with duodenal ulcers and meta-analysis of 9 studies of the use of diuretics during pregnancy to prevent the development of pre-eclampsia. Results indicated that the choice between the two model depends on the question of which model fits the distribution of effect sizes better and takes account of the relevant source(s) of error. We further study the meta-analysis of longitudinal studies where effect sizes are reported at multiple time points. Univariate meta-analysis is a statistical approach which may be used to study effect sizes reported at multiple time point. The problem with this approach is that it ignores correlation between the effect sizes, which might increase the standard error of the point estimates. We used the linear mixed-effects model, which borrows ideas from multivariate meta-analysis. One of the advantages of the linear mixed-effects model is that it accounts for correlation between effect sizes both within and between studies. The independence model where separate univariate meta-analysis is done at each of the time points was compared against models where correlation was accounted for different alternatives; including random study effects, correlated random time effects and/or correlated within-study errors, or unstructured covariance structures. We implemented these methods through an example of meta-analysis of 16 randomized clinical trials of radiotherapy and chemotherapy versus radiotherapy alone for the post-operative treatment of patients with malignant gliomas, where in each trial, survival is evaluated at 6, 12, 18 and 24 months post randomization. The results revealed that models that accounted for correlations had better fit. Keywords: meta-analysis, fixed-effects model, random-effects model, heterogeneity, publication bias, linear mixed-effects model.