TMLE for a vector-valued (multivariate) binary treatment

With a treatment vector the propensity is the sequential factorisation g(a|X) = prod_j P(A_j = a_j | X, A_{<j} = a_{<j}), fitted by one logistic per component with the preceding components as regressors. The counterfactual probability evaluates those same fitted coefficients at the counterfactual history, not a refit – refitting would condition on the observed history and target a different parameter.

Usage

Tmlmct(y, A, X)

Arguments

y

Outcome.

A

Binary treatment vector, one column per component.

X

Covariates.

Value

List with estimate, se, eps, q, n.

Details

Given g the machinery is the point-treatment one with the indicator on the whole vector: H = I(A = 1)/g(1|X) - I(A = 0)/g(0|X), eps = sum H (y - Q)/sum H^2, psi = mean[Q*(1, X) - Q*(0, X)]. With one component this is exactly the binary point-treatment TMLE.

References

Lendle, S. D. et al. (2017). Journal of Statistical Software 81(1); Robins, J. M. (1986). Mathematical Modelling 7:1393-1512.

Examples

Tmlmct(y = c(1, 2, 3, 4, 5, 6, 7, 8), A = c(1, 2, 3, 4, 5, 6, 7, 8), X = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $estimate
#> [1] -7.412053e+15
#> 
#> $se
#> [1] 1.216516
#> 
#> $eps
#> [1] -3.65625
#> 
#> $q
#> [1] 1
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "TMLE for a vector-valued binary treatment"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"