TMLE for the value of the estimated optimal individualized rule

The rule is read off the blip rather than the outcome regression, because only its sign matters: d*(V) = I(B(V) > 0) with B(V) = E[Y(1) - Y(0) | V]. With the rule fixed the target is a mean under a known deterministic regime, so the clever covariate is H = I(D = d*(V)) / g_{d*(V)}(W) and a linear fluctuation Q* = Q + eps H, eps = sum H (y - Q)/sum H^2, solves the efficient score. psi = mean_i [Q(d_i, W_i) + eps/g_{d_i}(W_i)].

Usage

Tmlitr(y, D, W, X)

Arguments

y

Outcome.

D

Binary treatment.

W

Covariates entering the nuisance models.

X

Covariates the rule may depend on.

Value

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

Details

The reported SE is the non-uniform influence-curve SE; it is honest away from the non-uniqueness boundary B(V) = 0.

References

Luedtke, A. R. & van der Laan, M. J. (2016). Annals of Statistics 44(2):713-742.

Examples

Tmlitr(y = c(1, 2, 3, 4, 5, 6, 7, 8), D = c(1, 2, 3, 4, 5, 6, 7, 8),
  W = c(1, 2, 3, 4, 5, 6, 7, 8), X = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $estimate
#> [1] 3.371675e+16
#> 
#> $se
#> [1] 6.488792e+15
#> 
#> $eps
#> [1] 0
#> 
#> $n_treated
#> [1] 0
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "TMLE for the value of the estimated optimal individualized rule"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"