Sample-split TMLE on a data-adaptively selected covariate subset

Selecting the adjustment set and estimating on the same rows makes the target parameter itself a function of the data, and the usual influence-curve SE then prices the estimator but not the selection. The data-adaptive target-parameter framework fixes it by splitting: the subset is chosen on the ODD indices, the parameter is defined and estimated on the EVEN indices, and given the split the target is a fixed (if random) parameter whose influence curve needs no selection correction.

Usage

Tmlsbs(y, D, X)

Arguments

y

Outcome.

D

Binary treatment.

X

Candidate covariates.

Value

List with estimate, se, eps, selected (1-based column indices kept), n_selected, n_est, n.

Details

Selection ranks covariates by the absolute correlation with the treatment-residualised outcome on the selection half and keeps the top ceiling(p/2). The reported se is a HALF-sample standard error; it does not shrink by using the selection rows, and that is the price of an honest interval.

References

Hubbard, A. E., Kherad-Pajouh, S. & van der Laan, M. J. (2016). International Journal of Biostatistics 12(1):3-19.

Examples

Tmlsbs(y = c(1, 2, 3, 4, 5, 6, 7, 8), D = c(1, 2, 3, 4, 5, 6, 7, 8), X = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $estimate
#> [1] 6.755609e+15
#> 
#> $se
#> [1] 2.161287e+15
#> 
#> $eps
#> [1] 8.211339e+13
#> 
#> $selected
#> [1] 1
#> 
#> $n_selected
#> [1] 1
#> 
#> $n_est
#> [1] 4
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Sample-split TMLE on a data-adaptively selected covariate subset"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"