TMLE for the marginal probabilistic index

The probabilistic index is a functional of the two counterfactual marginal distributions, not of a regression coefficient, so it is built from a bank of threshold TMLEs: for every distinct observed outcome value F_a(t) = P(Y(a) <= t) is targeted, and the index is the Riemann-Stieltjes integral psi = sum_j [(F_0(t_{j-1}) + F_0(t_j))/2] dF_1(t_j), whose mid-point weight is the half-credit-for-ties convention. Because Y(1) and Y(0) enter only through their marginals this is the MARGINAL probabilistic index, not the within-pair one.

Usage

Tmlmpi(y, D, X)

Arguments

y

Outcome.

D

Binary treatment.

X

Covariates.

Value

List with estimate, se, n_grid, n.

References

Thas, O., De Neve, J., Clement, L. & Ottoy, J. P. (2012). JRSS B 74(4):623-671; van der Laan, M. J. & Rubin, D. (2006). IJB 2(1):11.

Examples

Tmlmpi(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] 0.5
#> 
#> $se
#> [1] 6.938894e-18
#> 
#> $n_grid
#> [1] 8
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "TMLE for the marginal probabilistic index"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"