# senWilcoxExact: Exact Sensitivity Analysis for Wilcoxon's Signed-rank... In DOS2: Design of Observational Studies, Companion to the Second Edition

## Description

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.

## Usage

 `1` ```senWilcoxExact(d, gamma = 1) ```

## Arguments

 `d` 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` gamma >= 1 is the value of the sensitivity parameter.

## Details

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.

## Value

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.

## Note

The 'senWilcox' function uses a large-sample approximation, adding confidence intervals and point estimates.

## Author(s)

Paul R. Rosenbaum

## References

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.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```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) ```

DOS2 documentation built on Sept. 16, 2019, 5:03 p.m.