TMLE for the marginal recurrent-event rate ratio

With recurrent events the natural marginal summary is the RATE, not a hazard ratio: the mean function of the counting process is identified without any assumption on the dependence between a subject's successive events, which is what makes the Lin-Wei-Yang-Ying rate model usable when that dependence is unknown. Each subject contributes N_i/T_i; the outcome regression is on that rate, the clever covariate is H = D/g - (1 - D)/(1 - g), and mu_a = mean_i Q*(a, X_i), estimate = mu_1/mu_0. The SE is the delta-method combination of the two arms' influence curves, so it is a ratio SE, not a difference SE.

Usage

Tmlrec(time, event, D, X)

Arguments

time

Follow-up duration of each subject; must be positive.

event

Number of events observed for each subject.

D

Binary treatment.

X

Baseline covariates.

Value

List with estimate, se, mu1, mu0, eps, n.

References

Lin, D. Y., Wei, L. J., Yang, I. & Ying, Z. (2000). JRSS B 62(4):711-730; van der Laan, M. J. & Rubin, D. (2006). IJB 2(1):11.

Examples

Tmlrec(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] 0.63529
#> 
#> $se
#> [1] 0.04434003
#> 
#> $mu1
#> [1] 4.950943e+14
#> 
#> $mu0
#> [1] 7.793201e+14
#> 
#> $eps
#> [1] -3.455345e+12
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "TMLE for the marginal recurrent-event rate ratio"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"