Semiparametric-efficient treatment effect adjusting for baseline

Under randomisation the crude difference in means is already unbiased, so adjustment is about variance, not confounding. Tsiatis augmentation fits each arm separately, which cannot introduce bias under randomisation and keeps the gain when the baseline association differs between arms.

Usage

Scbsft(y, D, X, baseline)

Arguments

y

Outcome.

D

Binary randomised treatment.

X

Covariates other than the baseline value.

baseline

Baseline level of the outcome.

Value

List with estimate, se, pi, shift, n.

Details

Formula: psi = mean[m_1(V) - m_0(V)] with influence contribution D(y - m1)/pi - (1 - D)(y - m0)/(1 - pi).

References

Tsiatis, A. A., Davidian, M., Zhang, M. & Lu, X. (2008). Statistics in Medicine 27:4658-4677, section 3.

Examples

set.seed(1)
r <- Scbsft(y = rnorm(10), D = rbinom(10, 1, 0.5), X = rnorm(10), baseline = rnorm(10)); TRUE
#> [1] TRUE