Explaining heterogeneity in meta-analysis: a comparison of methods.

Exploring the possible reasons for heterogeneity between studies is an important aspect of conducting a meta-analysis. This paper compares a number of methods which can be used to investigate whether a particular covariate, with a value defined for each study in the meta-analysis, explains any heterogeneity. The main example is from a meta-analysis of randomized trials of serum cholesterol reduction, in which the log-odds ratio for coronary events is related to the average extent of cholesterol reduction achieved in each trial. Different forms of weighted normal errors regression and random effects logistic regression are compared. These analyses quantify the extent to which heterogeneity is explained, as well as the effect of cholesterol reduction on the risk of coronary events. In a second example, the relationship between treatment effect estimates and their precision is examined, in order to assess the evidence for publication bias. We conclude that methods which allow for an additive component of residual heterogeneity should be used. In weighted regression, a restricted maximum likelihood estimator is appropriate, although a number of other estimators are also available. Methods which use the original form of the data explicitly, for example the binomial model for observed proportions rather than assuming normality of the log-odds ratios, are now computationally feasible. Although such methods are preferable in principle, they often give similar results in practice.