Sensitivity of Two-Sample Permutation Inferences in Observational Studies
Abstract In observational studies, subjects are not randomly assigned to treatment or control, so they may differ in their chances of receiving the treatment. A simple method is developed and demonstrated for displaying the sensitivity of conventional two-group permutation inferences to departures from random assignment of treatments. The unmatched case, discussed here, differs in certain technical and computational details from the matched case, discussed previously; however, the underlying model and the method for quantifying departures from randomization are the same. The method may be applied to Wilcoxon's rank sum test, the Gehan and log-rank tests for censored outcomes, Mantel's test for scored categories, and Fisher's exact test for binary responses. The method embeds the usual randomization reference distribution in a one-parameter family of departures involving an unobserved covariate that would have been controlled by adjustments had it been observed. As this parameter is varied, the sensitivity...