Effect modification in matched observational studies

TruncatedProductPvalue: Zaykin's truncated product of independent P-values and its P-value as a binomial mixture of gamma laws. WilcoxonSensitivityMoments: upper-bound null mean and variance of Wilcoxon's signed-rank statistic at bias Gamma. SubmaxComparisons: comparison matrix for p binary covariates. SubmaxTest: maximum of K correlated standardized deviates against the Monte Carlo quantile of the maximum of N(0, rho). Identical to the Python arm morie.fn.effectmod.

Usage

TruncatedProductPvalue(p, alpha_tilde = 0.05)

WilcoxonSensitivityMoments(n_pairs, Gamma = 1)

SubmaxComparisons(p)

SubmaxTest(T, mu, V, C, alpha = 0.05, nsim = 100000L, seed = 1)

Arguments

p

P-values, or number of binary covariates for SubmaxComparisons.

alpha_tilde

Truncation point.

n_pairs

Number of matched pairs.

Gamma

Sensitivity parameter (at least 1).

T

Group statistics.

mu, V

Null upper-bound means and variances of the group statistics.

C

Comparison matrix (K rows, one column per group).

alpha

Level.

nsim

Monte Carlo draws for the critical constant.

seed

Philox seed.

Value

List (matrix for SubmaxComparisons).

References

Zaykin, D. V., Zhivotovsky, L. A., Westfall, P. H. and Weir, B. S. (2002). Truncated product method for combining P-values. Genetic Epidemiology 22, 170-185.

Lee, K., Small, D. S. and Rosenbaum, P. R. (2018). A powerful approach to the study of moderate effect modification in observational studies. Biometrics 74, 1161-1170.

Examples

TruncatedProductPvalue(c(0.025, 0.4))$pvalue
#> [1] 0.05
m <- WilcoxonSensitivityMoments(10)
SubmaxTest(c(40, 30), rep(m$mu, 2), rep(m$nu, 2), SubmaxComparisons(1), nsim = 2000)$D
#> [1] 1.0811250 1.2741180 0.2548236