Rosenbaum sensitivity bounds for matched pairs

How strong would hidden bias have to be to explain away a matched-pairs result? gam is Gamma, the most the odds of treatment can differ within a pair because of an unobserved covariate (1: no hidden bias). rswp() gives the bounds on the one-sided p-value of Wilcoxon's signed-rank test at each Gamma (Rosenbaum 1987), from the normal approximation, and the Gamma at which the upper bound reaches alpha. rshl() gives the bounds on the Hodges-Lehmann estimate of the effect (Rosenbaum 1993), computed exactly from the Walsh averages, with no grid.

Usage

rswp(d, gam = 1, alpha = 0.05)

rshl(d, gam = 1)

Arguments

d

The treated-minus-control differences: finite numbers, one per pair.

gam

Values of Gamma: numbers from 1.

alpha

The level for the critical Gamma, strictly between 0 and 0.5.

Value

rswp(): a list of p (a data frame of gam, plo, pup), gcrit (the critical Gamma, below 1 when the test is not significant without bias) and t (the signed-rank statistic). rshl(): a data frame of gam, lo, hi. NaN when every difference is 0.

References

Rosenbaum, P. R. (1987). Sensitivity analysis for certain permutation inferences in matched observational studies. Biometrika, 74(1), 13-26. doi:10.1093/biomet/74.1.13

Rosenbaum, P. R. (1993). Hodges-Lehmann point estimates of treatment effect in observational studies. Journal of the American Statistical Association, 88(424), 1250-1253. doi:10.1080/01621459.1993.10476405

Examples

set.seed(1)
d <- rnorm(50, 0.5)
rswp(d, gam = c(1, 1.5, 2))
#> $p
#>   gam          plo          pup
#> 1 1.0 7.807040e-06 7.807040e-06
#> 2 1.5 7.347225e-09 8.087079e-04
#> 3 2.0 7.012883e-12 8.061278e-03
#> 
#> $gcrit
#> [1] 2.741017
#> 
#> $t
#> [1] 1085
#> 
rshl(d, gam = c(1, 1.5, 2))
#>   gam        lo        hi
#> 1 1.0 0.6526343 0.6526343
#> 2 1.5 0.4985346 0.7876529
#> 3 2.0 0.3952356 0.8803900