Random Effects Models for Combining Results from Controlled and Uncontrolled Studies in a Meta-Analysis

A random effects model is used to analyze meta-analyses containing both controlled and uncontrolled studies. A noniterative estimator of the treatment effect is derived using least squares, with the between-study variance substituted by an empirical Bayes estimator. The estimator is shown to be strongly consistent when the between-study variance is known, and the variance estimator is also shown to be strongly consistent. The estimator is shown to have desirable heuristic properties.