RATE.surv | R Documentation |
Estimation of the Average Treatment Effect among Responders for Survival Outcomes
RATE.surv( response, post.treatment, treatment, censoring, tau, data, M = 5, pr.treatment, call.response, args.response = list(), SL.args.post.treatment = list(family = binomial(), SL.library = c("SL.mean", "SL.glm")), call.censoring, args.censoring = list(), preprocess = NULL, ... )
response |
Response formula (e.g., Surv(time, event) ~ D + W). |
post.treatment |
Post treatment marker formula (e.g., D ~ W). |
treatment |
Treatment formula (e.g., A ~ 1). |
censoring |
Censoring formula (e.g., Surv(time, event == 0) ~ D + A + W)). |
tau |
Time-point of interest, see Details. |
data |
data.frame. |
M |
Number of folds in cross-fitting (M=1 is no cross-fitting). |
pr.treatment |
(optional) Randomization probability of treatment. |
call.response |
Model call for the response model (e.g. "mets::phreg"). |
args.response |
Additional arguments to the response model. |
SL.args.post.treatment |
Additional arguments to SuperLearner for the post treatment indicator model. |
call.censoring |
Similar to call.response. |
args.censoring |
Similar to args.response. |
preprocess |
(optional) Data pre-processing function. |
... |
Additional arguments to lower level data pre-processing functions. |
Estimation of
\frac{P(T ≤q τ|A=1) - P(T ≤q τ|A=1)}{E[D|A=1]}
under right censoring based on plug-in estimates of P(T ≤q τ|A=a) and E[D|A=1].
An efficient one-step estimator of P(T ≤q τ|A=a) is constructed using the efficient influence function
\frac{I\{A=a\}}{P(A = a)} \Big(\frac{Δ}{S^c_{0}(\tilde T|X)} I\{\tilde T ≤q τ\} + \int_0^τ \frac{S_0(u|X)-S_0(τ|X)}{S_0(u|X)S^c_0(u|X)} d M^c_0(u|X))\Big)\\ + \Big(1 - \frac{I\{A=a\}}{P(A = a)}\Big)F_0(τ|A=a, W) - P(T ≤q τ|A=a).
An efficient one-step estimator of E[D|A=1] is constructed using the efficient influence function
\frac{A}{P(A = 1)}≤ft(D-E[D|A=1, W]\right) + E[D|A=1, W] -E[D|A=1].
estimate object
Andreas Nordland, Klaus K. Holst
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