The targeted estimate solves the efficient score equation, so its
influence curve gives an honest standard error where the plug-in mean
of a machine-learning fit does not. psi_init shows the size of
the correction.
Usage
Tmlerd(Y, A, QAW, Q1W, Q0W, g1W, gbound = 0.025, level = 0.95)
Arguments
- Y
Outcome in [0, 1].
- A
Binary treatment.
- QAW, Q1W, Q0W
Initial outcome predictions.
- g1W
Initial propensity.
- gbound
Propensity truncation level.
- level
Confidence level.
Value
List with estimate, se, ci_lower,
ci_upper, p_value, mu1, mu0,
psi_init, epsilon, ic_mean, n.
Details
Formula: fluctuate on H1 = A/g1(W), H0 = (1-A)/g0(W);
psi = mean(Q*(1,W)) - mean(Q*(0,W));
se = sqrt(var(IC)/n)
References
Verified against the reference implementation in the CRAN
package tmle 2.1.1 (Gruber & van der Laan), its fluctuation glm and
calcParameters influence curves. That package is van der Laan's
group's own software for van der Laan & Rose (2011), Targeted
Learning.
Examples
set.seed(17)
n <- 400
A <- rbinom(n, 1, 0.5)
Y <- rbinom(n, 1, 0.3 + 0.2 * A)
Tmlerd(Y, A, QAW = ifelse(A == 1, 0.5, 0.3), Q1W = rep(0.5, n), Q0W = rep(0.3, n), g1W = rep(0.5, n))[c("estimate", "se")]
#> $estimate
#> [1] 0.2681676
#>
#> $se
#> [1] 0.0478545
#>
