A comparison of risk difference estimators in multi-center studies under baseline-risk heterogeneity

The risk di$erence is frequently used as a measure of the actual gain in the success rate between two treatments within a center (i.e. hospital). Interest is devoted to combining the risk di$erence across several centers under homogeneity but allowing for baseline-risk heterogeneity in each of the treatment arms. The purpose is to compare the e5ciency of six estimators for the common risk di$erence. The six estimators consist of the Pooling method ignoring the strati8cation of centers, several popular sets of di$erent 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-speci8c 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 (n6 8), the Cochran and the Mantel–Haenszel estimators are most e5cient 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 (n¿ 32), 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 di$erence across centers. We recommend to use Cochran, Mantel–Haenszel, or the Pooling estimators when n6 8, to use ∗Corresponding author. E-mail address: [email protected] (C. Viwatwongkasem). 0167-9473/03/$ see front matter c © 2002 Elsevier Science B.V. All rights reserved. PII: S0167 -9473(02)00175 -5 632 C. Viwatwongkasem, W. Bohning / Computational Statistics & Data Analysis 41 (2003) 631–644 Lipsitz et al. and Rothman–Boice estimators when n¿ 32, and to use the new estimator when strong baseline heterogeneity occurs. c © 2002 Elsevier Science B.V. All rights reserved.