qLearn: Based on the input contrast vectors, compute point estimates and construct confidence intervals using bootstrap for both stages

Description

Suppose the goal is to find the point estimates and CIs for stage 1 and stage 2 contrasts $ C1^T \theta1$ and $ C2^T \theta2$. Given $ C1$, $ C2$, regular n-out-of-n bootstrap will be used in stage 2 and different bootstrap scheme can be used in stage 1 analysis by assigning different value to s1Method. "Fixed Xi" will fix the Xi value as fixedXi and calculate the corresponding m; "Double Bootstrap" will calculate m using double bootstrap method; and the default "Regular" will skip choosing m and go with a regular bootstrap. Also m can be specified in s1M if not using "Fixed Xi" or "Double Bootstrap"

Usage

qLearn(s2Formula,s1Formula,completeData,
s2Treat,interact,s2Indicator,s2Contrast,s1Contrast,
alpha=0.05,bootNum=1000,s1Method="Regular",fixedXi,
doubleBoot1Num=500,doubleBoot2Num=500,s1M,...)

Arguments

s2Formula

stage 2 regression formula

s1Formula

Stage 1 regression formula

completeData

data frame containing all the variables

s2Treat

character string: name of the stage 2 treatment variable

interact

character vector: names of variables that interact with s2Treat

s2Indicator

character string: names of the stage 2 treatment indicator variable

s2Contrast

contrast for the stage 2 coefficients

s1Contrast

contrast for the stage 1 coefficients

alpha

level of significance

bootNum

numbers of bootstrap sampling in constructing CIs

s1Method

character string: method to choose stage 1 bootstrap sample size, m; "Double Bootstrap" will calculate m using double bootstrap method; "Fixed Xi" will fix the Xi value and calculate the corresponding m; "Regular" will use a regular n-out-of-n bootstrap for stage 1.

fixedXi

fixed xi value if s1Method="Fixed Xi"

doubleBoot1Num

numbers of bootstrap sampling for first order bootstrap if s1Method="Double Bootstrap"

doubleBoot2Num

numbers of bootstrap sampling for second order bootstrap if s1Method="Double Bootstrap"

s1M

specify m if necessary

...

other arguments of the lm function

Value

s1Coefficients: stage 1 regression coefficients
s2Coefficients: stage 2 regression coefficients
s1Inference: stage 1 coefficients confidence interval based on stage1 contrast
s2Inference: stage 2 coefficients confidence interval based on stage2 contrast
s1Size: stage 1 bootstrap sample size

References

Chakraborty, B., and Laber, E.B. (2012). Inference for Optimal Dynamic Treatment Regimes using an Adaptive m-out-of-n Bootstrap Scheme. Submitted.

Examples

Run this code

set.seed(100)
# Simple Simulation on 1000 subjects
sim<-matrix(0,nrow=1000,ncol=7)
colnames(sim)<-c("H1","A1","Y1","H2","A2","Y2","IS2")
sim<-as.data.frame(sim)

# Randomly generate stage 1 covariates and stage 1 and 2 treatments
sim[,c("H1","A1","A2")]<-2*rbinom(1000*3,1,0.5)-1

# Generate stage 2 covariates based on H1 and T1
expit<-exp(0.5*sim$H1+0.5*sim$A1)/(1+exp(0.5*sim$H1+0.5*sim$A1))
sim$H2<-2*rbinom(1000,1,expit)-1

# Assume stage 1 outcome Y1 is 0
# Generate stage 2 outcome Y2 
sim$Y2<-0.5*sim$A2+0.5*sim$A2*sim$A1-0.5*sim$A1+rnorm(1000)

# Randomly assign 500 subjects to S2
sim[sample(1000,500),"IS2"]<-1 
sim[sim$IS2==0,c("A2","Y2")]<-NA

# Define models for both stages
s2Formula<-Y2~H1*A1+A1*A2+A2:H2
s1Formula<-Y1~H1*A1

## Fixed Xi as 0.05
qLearn(s2Formula,s1Formula,sim,s2Treat="A2",interact=c("A1","H2"),
s2Indicator="IS2",s1Method="Fixed Xi",fixedXi=0.05,bootNum=100)