Detecting outlying studies in meta-regression models using a forward search algorithm

When considering data from many trials, it is likely that some of them present a markedly different intervention effect or exert an undue influence on the summary results. We develop a forward search algorithm for identifying outlying and influential studies in meta-analysis models. The forward search algorithm starts by fitting the hypothesized model to a small subset of likely outlier-free studies and proceeds by adding studies into the set one-by-one that are determined to be closest to the fitted model of the existing set. As each study is added to the set, plots of estimated parameters and measures of fit are monitored to identify outliers by sharp changes in the forward plots. We apply the proposed outlier detection method to two real data sets; a metaanalysis of 26 studies that examines the effect of writing-to-learn interventions on academic achievement adjusting for three possible effect modifiers, and a meta-analysis of 70 studies that compares a fluoride toothpaste treatment to placebo for preventing dental caries in children. A simple simulated example is used to illustrate the steps of the proposed methodology and a small scale simulation study is conducted to evaluate the performance of the proposed method.