Quasi-Empirical Bayes Methodology for Improving Meta-Analysis

ABSTRACT

This article addresses the problem of heterogeneity among various studies to be combined in a meta-analysis. We adopt quasi-empirical Bayes methodology to predict the odds ratios for each study. As a result, the predicted odds ratios are pulled toward the estimated common odds ratio of the various studies under consideration. With strong heterogeneity among the studies, we jointly consider the display of the 95% CIs of the ORs and a Dixon's test (1950) for “outliers” to exclude the “extreme” estimated ORs. We demonstrate the effectiveness of our methodology based on the data analyzed by Thompson and Pocock (1987) demonstrating the power of the new approach to meta-analysis to find statistical agreement in what looks like great disagreement via a chi-squared test. We believe our technique (i.e., minimum mean-square sense) will go a long way toward increasing the trustworthiness of meta-analysis.

Key Words:

• Bayes
• Confidence intervals
• Empirical Bayes
• Stein-type estimators

ACKNOWLEDGMENT

The research has been supported by the NSERC Discovery Grant of the first author. The authors gratefully acknowledge the critical comments of the earlier version by the referees, which improved the clarity of the revision.