An exact adaptive test with superior design sensitivity in an observational study of treatments for ovarian cancer

A sensitivity analysis in an observational study determines the magnitude of bias from nonrandom treatment assignment that would need to be present to alter the qualitative conclusions of a na\"ıve analysis that presumes all biases were removed by matching or by other analytic adjustments. The power of a sensitivity analysis and the design sensitivity anticipate the outcome of a sensitivity analysis under an assumed model for the generation of the data. It is known that the power of a sensitivity analysis is affected by the choice of test statistic, and, in particular, that a statistic with good Pitman efficiency in a randomized experiment, such as Wilcoxon's signed rank statistic, may have low power in a sensitivity analysis and low design sensitivity when compared to other statistics. For instance, for an additive treatment effect and errors that are Normal or logistic or $t$-distributed with 3 degrees of freedom, Brown's combined quantile average test has Pitman efficiency close to that of Wilcoxon's test but has higher power in a sensitivity analysis, while a version of Noether's test has poor Pitman efficiency in a randomized experiment but much higher design sensitivity so it is vastly more powerful than Wilcoxon's statistic in a sensitivity analysis if the sample size is sufficiently large.

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