Robust rank‐based meta‐analyses for two‐sample designs with application to platelet counts of malaria infection data

Abstract

AbstractIn this paper, we propose robust meta‐analysis procedures for individual studies that report a broad range of robust summary statistics for a two‐sample problem. Summary statistics of individual studies could be presented in different forms including full data, medians of the two samples, the Hodges‐Lehman and Wilcoxon estimates of the location shift parameters. Data synthesis is made under both fixed‐effect and random‐effect meta‐analysis models. We systematically compare these robust meta‐analysis procedures via simulation studies to meta‐analysis procedure based on sample means and variances from individual studies under a wide range of error distributions. We show that the coverage probabilities of the robust meta‐analysis confidence intervals are quite close to the nominal confidence level. We also show that mean square error (MSE) of the robust meta‐analysis estimator is considerably smaller than that of the non‐robust meta‐analysis estimator under the contaminated normal, heavy tailed and skewed error distributions. The robust meta‐analysis procedures are then applied to platelet count reduction for malaria infected patients in Ghana.