TMLE for a multi-state cause-specific cumulative hazard contrast

In a multi-state model each transition has its own hazard and the competing transitions remove people from the risk set, so a marginal contrast must be built transition by transition. The target is the counterfactual cumulative hazard of the FIRST transition label, Lambda_k^a(t0) = E_W[sum_{j <= t0} h_k(j | a, W)], and the estimate is Lambda_k^1(t0) - Lambda_k^0(t0).

Usage

Tmlmpc(time, state, D, X)

Arguments

time

Time of the observed transition or of censoring.

state

Label of the state entered at time; 0 = censored.

D

Binary treatment.

X

Baseline covariates.

Value

List with estimate, se, lam1, lam0, eps1, eps0, t0, n.

Details

Writing the parameter as a mean over W of a sum of conditional hazards gives its influence function directly: the score for h_k(j) is R(j)(N_k(j) - h_k(j)), so the clever covariate is H_k(j) = I(A = a)/g_a(W)/P(R(j) = 1 | a, W) with the at-risk probability the product of surviving every transition and not being censored, both from pooled logistic hazards.

References

Rytgaard, H. C., Gerds, T. A. & van der Laan, M. J. (2022). Annals of Statistics 50(5).

Examples

Tmlmpc(time = c(1, 2, 3, 4, 5, 6, 7, 8), state = 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] -0.9999998
#> 
#> $se
#> [1] 0.7887907
#> 
#> $lam1
#> [1] 1.791113
#> 
#> $lam0
#> [1] 2.791112
#> 
#> $eps1
#> [1] 29.25
#> 
#> $eps0
#> [1] 0
#> 
#> $t0
#> [1] 8
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "TMLE for a cause-specific cumulative hazard contrast"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"