Using James–Stein Estimators in Homogeneity Tests of the Risk Difference

ABSTRACT

In multi-center clinical trials in which the success/failure of two treatments are measured, 2 × 2 × K contingency data are obtained, where K is the number of centers in the study. In this context, the risk difference may be preferred (over the odds ratio or relative risk) as a measure of the efficacy of the new treatment. To summarize the risk difference across centers, the estimated risk difference for each center must be comparable. Although several weighted least squares (WLS) tests of homogeneity of the risk difference have been proposed for the sparse data situation (1,2), none of these tests perform satisfactorily when each center has small samples. In the sparse data situation, the weights given to each center's risk difference estimate are imprecise and may be undefined. James–Stein estimates have been shown to be more precise (in terms of mean squared error) than their maximum likelihood counterparts. In this article, we investigate the use of James–Stein estimates for these weights. These estimates shrink the individual risk estimates towards the overall center mean and thus avoid problems encountered when risk estimates are zero or one. We use Monte Carlo simulations to show that using these estimates in the WLS test of homogeneity of risk differences improves their performance in terms of Type I error.

Keywords:

• Meta-analysis
• Multi-center data
• Shrinkage estimators
• Treatment difference

Notes

^aData from Cooper et al. (1993).