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

In 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.