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	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.

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 May 29, 2024, 2:08 a.m.