Minimum MSE Weighted Estimator to Make Inferences for a Common Risk Ratio across Sparse Meta-Analysis Data

Abstract

The paper aims to discuss three interesting issues of statistical inferences for a common risk ratio ( RR ) in sparse meta-analysis data. Firstly, the conventional log-risk ratio estimator encounters a number of problems when the number of events in the experimental or control group is zero in sparse data of a 2 × 2 table. The adjusted log-risk ratio estimator with the continuity correction points based upon the minimum Bayes risk with respect to the uniform prior density over (0, 1) and the Euclidean loss function is proposed. Secondly, the interest is to find the optimal weights of the pooled estimate that minimize the mean square error ( MSE ) of subject to the constraint on where , , . Finally, the performance of this minimum MSE weighted estimator adjusted with various values of points is investigated to compare with other popular estimators, such as the Mantel-Haenszel (MH) estimator and the weighted least squares (WLS) estimator (also equivalently known as the inverse - variance weighted estimator) in senses of point estimation and hypothesis testing via simulation studies. The results of estimation illustrate that regardless of the true values of RR , the MH estimator achieves the best performance with the smallest MSE when the study size is rather large and the sample sizes within each study are small . The MSE of WLS estimator and the proposed-weight estimator adjusted by , or , or are close together and they are the best when the sample sizes are moderate to large ( and ) while the study size is rather small .