RATE.surv: Responder Average Treatment Effect

In targeted: Targeted Inference

Responder Average Treatment Effect

Description

Estimation of the Average Treatment Effect among Responders for Survival Outcomes

Usage

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,
  ...
)

Arguments

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	Arguments to SuperLearner for the post treatment indicator
call.censoring	Similar to call.response.
args.censoring	Similar to args.response.
preprocess	(optional) Data preprocessing function
...	Additional arguments to lower level functions

Details

Estimation of

\frac{P(T \leq \tau|A=1) - P(T \leq \tau|A=1)}{E[D|A=1]}

under right censoring based on plug-in estimates of P(T \leq \tau|A=a) and E[D|A=1].

An efficient one-step estimator of P(T \leq \tau|A=a) is constructed using the efficient influence function

\frac{I\{A=a\}}{P(A = a)} \Big(\frac{\Delta}{S^c_{0}(\tilde T|X)} I\{\tilde T \leq \tau\} + \int_0^\tau \frac{S_0(u|X)-S_0(\tau|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(\tau|A=a, W) - P(T \leq \tau|A=a).

An efficient one-step estimator of E[D|A=1] is constructed using the efficient influence function

\frac{A}{P(A = 1)}\left(D-E[D|A=1, W]\right) + E[D|A=1, W] -E[D|A=1].

Value

estimate object

Author(s)

Andreas Nordland, Klaus K. Holst

targeted documentation built on Jan. 12, 2026, 9:08 a.m.