Observational-study sensitivity: amplification, U-statistic bounds, crosscut test and design sensitivity
Source:R/ObsSensitivity.R
GammaFromLambdaDelta.RdGammaFromLambdaDelta: Gamma = (Lambda Delta + 1) / (Lambda + Delta)
and the Wolfe-family bounds 1 / (1 + Delta) and Delta / (1 + Delta)
on Pr(W > 0 | C, |W| = w) (Design of Observational Studies, eqs.
3.28-3.29). AmplifyGamma: Delta = (Gamma Lambda - 1) / (Lambda - Gamma)
for each Lambda > Gamma. UStatisticSensitivity: normal upper
bound on the P-value of Rosenbaum's U-statistic (m, m1, m2) with scores
sum_l C(q - 1, l - 1) C(I - q, m - l) / C(I, m) (exact for
I <= 50) or their limit, as DOS2::senU. CrosscutTest: corner
table beyond the ct quantiles and the Fisher noncentral
hypergeometric upper tail with odds Gamma (as DOS2::crosscut).
CrosscutDesignSensitivity: (p_LL p_HH) / (p_LH p_HL) for
bivariate Normal dose and response, Sheppard's integral by tanh-sinh.
Usage
GammaFromLambdaDelta(lam, delta)
AmplifyGamma(gamma, lam)
UStatisticSensitivity(
d,
gamma = 1,
m = 2,
m1 = 2,
m2 = 2,
exact = NULL,
alternative = "greater"
)
CrosscutTest(x, y, ct = 0.25, gamma = 1)
CrosscutDesignSensitivity(rho, eta)Arguments
- lam
Lambda value(s).
- delta
Delta value(s).
- gamma
Sensitivity parameter Gamma.
- d
Matched-pair differences.
- m, m1, m2
U-statistic subset size and rank window.
- exact
Exact scores (default when there are at most 50 pairs).
- alternative
"greater", "less" or "twosided".
- x, y
Doses and responses.
- ct
Corner quantile (at most 1/2).
- rho
Correlation(s).
- eta
Corner quantile(s).