qLearn: Based on the input contrast vectors, compute point estimates...

In qLearn: Estimation and inference for Q-learning

Description

Suppose the goal is to find the point estimates and CIs for stage 1 and stage 2 contrasts C1^T θ1 and C2^T θ2. 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

A list containing:

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

Author(s)

Jingyi Xin [e-mail], Bibhas Chakraborty [e-mail], and Eric B.Laber [e-mail]

References

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

See Also

getModel chooseMDoubleBootstrap

Examples

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)

qLearn documentation built on May 2, 2019, 9:18 a.m.