The Use of Maximin Efficiency Robust Tests in Combining Contingency Tables and Survival Analysis

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Abstract
A test is the maximin efficiency robust test for a family of possible models underlying the data if no other test has higher minimum efficiency relative to the asymptotically optimum test for each model. Methods used to examine the efficiency robustness of rank tests for the two-sample problem are adapted to obtain maximin efficiency robust procedures for testing the equality of proportions across several 2×2 tables, for combining the results of tests for trend in several 2 x J tables in which the dose-response function is one of a set of possible monotone functions, and to analyze censored survival data when either the Wilcoxon or log-rank may be appropriate. In the survival setting the robust test has maximin efficiency 93.3% relative to the Wilcoxon or long-rank when each is optimum, in contrast to the 75% relative efficiency each statistic has when the other is optimum.

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