Targeted maximum likelihood for a rare binary outcome

A sample drawn on a rare outcome carries no information about how rare it is, so the estimator has to be told. Known-prevalence case-control weights enter both the initial fit and the targeting step. IRLS runs a fixed number of iterations and the fluctuation is the closed-form linear one, so nothing here depends on a tolerance.

Usage

Tmlric(y, D, X, prevalence)

Arguments

y

Binary outcome.

D

Binary treatment.

X

Baseline covariates; an intercept is added.

prevalence

Known population prevalence of y = 1.

Value

List with estimate, se, eps, n.

Details

Formula: H(D, X) = D / g(X) - (1 - D) / (1 - g(X)); Q* = Q + eps H with eps = sum w H (y - Q) / sum w H^2; psi is the weighted mean of Q*(1, X) - Q*(0, X).

References

Tran, L., Petersen, M., Schwab, J. & van der Laan, M. J. (2018). Robust variance estimation and inference for causal effect estimation. arXiv:1810.03030. Case-control weights follow van der Laan (2008), IJB 4(1):17.

Examples

Tmlric(y = c(1, 2, 3, 4, 5, 6, 7, 8), D = 5L, X = c(1, 2, 3, 4, 5, 6, 7, 8),
  prevalence = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $estimate
#> [1] 1.163758
#> 
#> $se
#> [1] 303.0229
#> 
#> $eps
#> [1] 0.0115212
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Case-control-weighted TMLE, rare outcome"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"