Abstract

The risk difference is frequently used as a measure of the actual gain in the success rate between two treatments within a center (i.e. hospital). Interest is devoted to combining the risk difference across several centers under homogeneity but allowing for baseline-risk heterogeneity in each of the treatment arms. The purpose is to compare the efficiency of six estimators for the common risk difference. The six estimators consist of the Pooling method ignoring the stratification of centers, several popular sets of different weights, and a new estimator. A simulation study was done to compare bias, variance and mean-square error. The sample sizes in each center varied as 4, 8, 16, 32, 64 and the number of centers as 4, 8, 16, 32, 64. The major result is that the new estimate is an attractive compromise when choosing between the estimators of the set of the center-specific sample size weights and the estimators of the set of the inverse-variance weights. It is not an optimal strategy, but it widely extends to cover heterogeneity cases. For small sample size (n8), the Cochran and the Mantel–Haenszel estimators are most efficient because of their smallest mean square errors. Cochran and Mantel–Haenszel estimates are also unbiased and consistent with respect to both sample size and center size. For large sample size (n32), Lipsitz et al. and Rothman–Boice estimates whose weights are the inverses of variances are the most appropriate. Lipsitz et al. and Rothman–Boice estimates are considerably biased (even if asymptotically unbiased with respect to the sample size). The Pooling estimate is very close and similar to Cochran's estimate under homogeneity of equal risk difference across centers. We recommend to use Cochran, Mantel–Haenszel, or the Pooling estimators when n8, to use Lipsitz et al. and Rothman–Boice estimators when n32, and to use the new estimator when strong baseline heterogeneity occurs.

Author Keywords: DerSimonian–Laird; Homogeneity; Heterogeneity adjusted estimator; Meta-analysis; Pooling of sparse clinical trials; Random effect model; Risk difference

Article Outline

1. Introduction

2. Common weighting strategies

2.1. Cochran's weights

2.2. Böhning–Sarol estimator as a Mantel–Haenszel type

2.3. Weighted least-square estimators

2.4. The Rothman and Boice estimator

2.5. The pooling estimator under homogeneity

3. A new estimator under baseline-risk heterogeneity

4. A simulation study

5. Results

5.1. Bias, variance, and consistency

5.2. Mean-square errors

6. Conclusions and discussions

Acknowledgements

References