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A sensitivity analysis in an observational study determines the magnitude ofbias from nonrandom treatment assignment that would need to be present to alterthe qualitative conclusions of a na\"{\i}ve analysis that presumes all biaseswere removed by matching or by other analytic adjustments. The power of asensitivity analysis and the design sensitivity anticipate the outcome of asensitivity analysis under an assumed model for the generation of the data. Itis known that the power of a sensitivity analysis is affected by the choice oftest statistic, and, in particular, that a statistic with good Pitmanefficiency in a randomized experiment, such as Wilcoxon's signed rankstatistic, may have low power in a sensitivity analysis and low designsensitivity when compared to other statistics. For instance, for an additivetreatment effect and errors that are Normal or logistic or $t$-distributed with3 degrees of freedom, Brown's combined quantile average test has Pitmanefficiency close to that of Wilcoxon's test but has higher power in asensitivity analysis, while a version of Noether's test has poor Pitmanefficiency in a randomized experiment but much higher design sensitivity so itis vastly more powerful than Wilcoxon's statistic in a sensitivity analysis ifthe sample size is sufficiently large.

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