Exact sensitivity analysis for Wilcoxon's signed rank statistic in observational studies. Performs a sensitivity analysis for the one-sided P-value. The method can be used in small samples without ties; however, it is primarily of theoretical interest, as the large sample approximation in 'senWilcox' is fine for most samples of practical size.
A vector of treated-minus-control matched pair differences in outcomes. There must be no ties in |d| when computing the exact distribution. If ties are present, use 'senWilcox' instead.
gamma >= 1 is the value of the sensitivity parameter.
The exact method is discussed in Section 3.12 of "Design of Observational Studies", second edition. Tables 3.2 and 3.3 of Section 3.5 use these exact calculations.
The upper bound on the one-sided, upper-tailed P-value testing no treatment effect in the presence of a bias in treatment assignment of at most gamma.
The 'senWilcox' function uses a large-sample approximation, adding confidence intervals and point estimates.
Paul R. Rosenbaum
Pagano, M. and Tritchler, D. (1983) <doi:10.1080/01621459.1983.10477990> "On obtaining permutation distributions in polynomial time". Journal of the American Statistical Association, 78, 435-440.
Rosenbaum, P. R. (1987) <doi:10.1093/biomet/74.1.13> "Sensitivity analysis for certain permutation inferences in matched observational studies". Biometrika, 74(1), 13-26.
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data(werfel) d<-werfel$serpc_p-werfel$cerpc_p # Reproduces the exact one-sided P-value computed in Section 3.9 of # "Design of Observational Studies". senWilcoxExact(d,gamma=2) # Agrees with the usual Wilcoxon procedures when gamma=1. senWilcoxExact(d,gamma=1) stats::wilcox.test(d,alternative="greater") # Reproduces the one-sided confidence interval for gamma=3 in Table 3.3 # of "Design of Observational Studies". senWilcoxExact(d-0.0935,gamma=3) senWilcoxExact(d-0.0936,gamma=3)
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