TMLE for the marginal hazard ratio when proportional hazards fails

Under non-proportional hazards there is no single Cox coefficient to report, so the target is built from the two marginal survival curves: the counterfactual survivals at the last observed event time are targeted separately and the contrast is the ratio of the marginal cumulative hazards, Lambda_a(t0) = -log S_a(t0).

Usage

Tmlhrz(time, event, D, X)

Arguments

time

Observed follow-up time.

event

1 if the event was observed, 0 if right censored.

D

Binary treatment.

X

Baseline covariates.

Value

List with estimate, se, s1, s0, eps, t0, n.

Details

The nuisance step is a pooled logistic hazard on the person-period expansion (one row per subject per at-risk grid point, design [1, t, A, W]). The targeting step fluctuates the hazard on the logit scale along H_a(t) = -I(A = a)/g_a(W) * S_a(t0|W)/S_a(t-|W), solving the pooled score for a single eps by fixed-iteration Newton, and psi_a = mean_i S*_a(t0|W_i).

References

Moore, K. L. & van der Laan, M. J. (2009). Statistics in Medicine 28(1):39-64; van der Laan, M. J. & Rubin, D. (2006). IJB 2(1):11.

Examples

Tmlhrz(time = c(1, 2, 3, 4, 5, 6, 7, 8), event = c(0, 1, 0, 1, 1, 0, 1, 0),
  D = c(1, 2, 3, 4, 5, 6, 7, 8), X = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $estimate
#> [1] 0.7175405
#> 
#> $se
#> [1] 0.02154213
#> 
#> $s1
#> [1] 6.843088e-14
#> 
#> $s0
#> [1] 4.49733e-19
#> 
#> $eps
#> [1] 0
#> 
#> $t0
#> [1] 7
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "TMLE for the marginal hazard ratio under non-proportional hazards"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"