senWilcoxExact {DOS}

Exact Sensitivity Analysis for Wilcoxon's Signed-rank Statistic

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

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 3.9 of Design of Observational Studies (2010) and is illustrated in Section 3.5. 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). On obtaining permutation distributions in polynomial time. Journal of the American Statistical Association, 78, 435-440.

Rosenbaum, P. R. (1987). Sensitivity analysis for certain permutation inferences in matched observational studies. Biometrika, 74(1), 13-26.

Rosenbaum, P. R. (2010). Design of Observational Studies. New York: Springer. The method and example are discussed in Sections 3.5 and 3.9.

Examples

data(werfel)
d<-werfel$serpc_p-werfel$cerpc_p

# Reproduces the exact one-sided P-value computed in Section 3.9 of Rosenbaum (2010).
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 Rosenbaum (2010)
senWilcoxExact(d-0.0935,gamma=3)
senWilcoxExact(d-0.0936,gamma=3)