A hybrid method in combining treatment effects from matched and unmatched studies

In the biomedical studies, the general data structures have been the matched (paired) and unmatched designs. Recently, many researchers are interested in Meta-Analysis to obtain a better understanding from several clinical data of a medical treatment. The hybrid design, which is combined two data structures, may create the fundamental question for statistical methods and the challenges for statistical inferences. The applied methods are depending on the underlying distribution. If the outcomes are normally distributed, we would use the classic paired and two independent sample T-tests on the matched and unmatched cases. If not, we can apply Wilcoxon signed rank and rank sum test on each case.

To assess an overall treatment effect on a hybrid design, we can apply the inverse variance weight method used in Meta-Analysis. On the nonparametric case, we can use a test statistic which is combined on two Wilcoxon test statistics. However, these two test statistics are not in same scale. We propose the Hybrid Test Statistic based on the Hodges-Lehmann estimates of the treatment effects, which are medians in the same scale.

To compare the proposed method, we use the classic meta-analysis T-test statistic on the combined the estimates of the treatment effects from two T-test statistics. Theoretically, the efficiency of two unbiased estimators of a parameter is the ratio of their variances. With the concept of Asymptotic Relative Efficiency (ARE) developed by Pitman, we show ARE of the hybrid test statistic relative to classic meta-analysis T-test statistic using the Hodges-Lemann estimators associated with two test statistics.

From several simulation studies, we calculate the empirical type I error rate and power of the test statistics. The proposed statistic would provide effective tool to evaluate and understand the treatment effect in various public health studies as well as clinical trials.