TMLE whose initial outcome model uses baseline covariates only

Restricting the initial fit to pre-treatment information keeps post-randomisation quantities out of Q, so the targeting step removes residual imbalance on its own rather than sharing the job with an adjustment that would open a collider path.

Usage

Tmlbas(y, D, X, baseline)

Arguments

y: Outcome.
D: Binary treatment.
X: Pre-treatment covariates.
baseline: Baseline level of the outcome.

Value

List with estimate, se, eps, n.

Details

Formula: H = D/g - (1 - D)/(1 - g), eps = sum H (y - Q) / sum H^2, Q* = Q + eps H, psi = mean[Q*(1, W) - Q*(0, W)].

References

Tsiatis, A. A. et al. (2008). Statistics in Medicine 27:4658-4677; van der Laan, M. J. & Rubin, D. (2006). IJB 2(1):11.

Examples

Tmlbas(y = c(1, 2, 3, 4, 5, 6, 7, 8), D = 5L, X = c(1, 2, 3, 4, 5, 6, 7, 8),
  baseline = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $estimate
#> [1] 0.8695652
#> 
#> $se
#> [1] 143.0052
#> 
#> $eps
#> [1] 0.02119565
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "TMLE with a pre-treatment-only initial outcome model"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"