sg.mart: Stabilized One-Step Estimating Impact of Treating Optimal...

In alexluedtke12/sg: Targeted Learning for Subgroup Analyses

Stabilized One-Step Estimating Impact of Treating Optimal Subgroup

Description

This function estimates the impact of treating the optimal subgroup using a stabilized one-step estimator.

Usage

sg.mart(W, A, Y, SL.library, g0 = NULL, family = binomial(),
  sig.truncs = 0.1, alpha = 0.05, elln = ceiling(nrow(W)/10),
  num.chunks = 10, num.SL.rep = 5)

Arguments

W	data frame with observations in the rows and baseline covariates used to form the subgroup in columns.
A	binary treatment vector, where 1 indicates that an individual was treated.
Y	real-valued outcome.
SL.library	SuperLearner library (see documentation for SuperLearner in the corresponding package) used to estimate outcome regression, treatment mechanism (if unknown), and conditional average treatment effect function.
g0	if known (as in a randomized controlled trial), a vector of probabilities of treatment A=1 given covariates. If NULL, SuperLearner will be used to estimate these probabilities.
family	binomial() if outcome bounded in [0,1], or gaussian() otherwise.
sig.truncs	vector of values at which the standard deviation estimate is truncated. See Details.
alpha	confidence level for returned confidence interval set to (1-alpha)*100%.
elln	number of observations to set aside for the first evaluation of the nuisance functions. Recommend around nrow(W)/10, unless willing to significantly slow down run time by setting num.chunks to (n-elln)/k for a small constant k (e.g. 1 or 2) – in that case can set elln=20 or so.
num.chunks	number of chunks to use when computing the nuisance functions – using more chunks should slightly improve statistical properties but slow down the runtime. Allowed values between 1 and nrow(W)-elln. Recommend at least 10.

Details

Stabilized one-step estimator for the impact of treating the optimal subgroup. Users will generally find this estimator more conservative (biased down) than the CV-TMLE. While asymptotic results and prior simulations show that this estimator performs as well as the CV-TMLE in large samples, the CV-TMLE outperforms this estimator provided the necessary regularity conditions hold for the CV-TMLE. Unlike for the CV-TMLE confidence interval, we have theoretical justication for the stabilized one-step confidence interval when the treatment effect is null with positive probability.

sig.truncs is useful if the treatment effect is negative (or small) in all strata of covariates, since in these cases we expect that the variance estimate will converge to zero and coverage of the non-truncated confidence interval may suffer. The truncation ensures that the standard deviation estimate is never too small so that coverage of the lower bound is at worst conservative. Coverage of the upper bound also relies on being able to estimate the optimal subgroup well in terms of mean outcome (see the cited papers).

Note: Have not implemented resource-constrained stabilized one-step estimator.

Value

a list containing

est	Vector containing estimates of the impact of treating the optimal subgroup. Items in the vector correspond to different choices of sig.truncs (order maintained).
ci	Matrix containing confidence intervals for the impact of treating the optimal subgroup. Left column contains lower bounds, right column contains upper bounds. Rows correspond to different choices of sig.truncs (order maintained).

References

“Evaluating the Impact of Treating the Optimal Subgroup,” technical report to be released soon.

A. R. Luedtke and M. J. van der Laan, “Statistical inference for the mean outcome under a possibly non-unique optimal treatment strategy,” Annals of Statistics, vol. 44, no. 2, pp. 713-742, 2016.

Examples

SL.library = c('SL.mean','SL.glm')
Qbar = function(a,w){plogis(0.2*a*(w$W1>0))}
n = 1000
W = data.frame(W1=rnorm(n),W2=rnorm(n),W3=rnorm(n),W4=rnorm(n))
A = rbinom(n,1,1/2)
Y = rnorm(n,Qbar(A,W),sd=0.025)

sg.mart(W,A,Y,SL.library=SL.library,family=binomial(),sig.truncs=c(0.001,0.1))

alexluedtke12/sg documentation built on May 24, 2023, 6:36 a.m.