Qlearning: firststage regression
Description
Regresses the predicted future outcome maximized over a2 on firststage history and treatment to estimate the optimal firststage decision rule using Qlearning.
Usage
1 2 3 4 5 6 7 
Arguments
formula 
righthand sided stage 1 regression formula 
data 
data frame containing variables used in 
treatName 
character string indicating the stage 1 treatment name 
intNames 
vector of characters indicating the names of the variables that interact with the stage 1 treatment in the regression model 
qS2object 
object of type 
object 
object of type 
H1q 
matrix or data frame of firststage covariates to include as main effects in the linear model 
A1 
vector of firststage randomized treatments 
s1ints 
indices pointing to columns of H1q that should be included as treatment interaction effects in the linear model 
... 
other arguments to be passed to 
Details
Fits a model of the form
E (Ytilde  H1, A1) = H10^Tβ10 + A1*H11^Tβ11,
where H10 and H11 are summaries of
H1. For an object of type qLearnS1
,
summary(object)
and plot(object)
can be used for
evaluating model fit.
Value
betaHat10 
estimated main effect coeffients, beginning with the intercept 
betaHat11 
estimated treatment interaction coefficients, beginning with the main effect of treatment 
optA1 
vector of estimated optimal firststage treatments for the patients in the training data 
s1Fit 

s1ints 
indices of variables in 
Author(s)
Kristin A. Linn <kalinn@ncsu.edu>, Eric B. Laber, Leonard A. Stefanski
References
Linn, K. A., Laber, E. B., Stefanski, L. A. (2015) "iqLearn: Interactive QLearning in R", Journal of Statistical Software, 64(1), 1–25.
Laber, E. B., Linn, K. A., and Stefanski, L. A. (2014) "Interactive model building for Qlearning", Biometrika, 101(4), 831847.
See Also
summary.qLearnS2
, plot.qLearnS2
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  ## load in twostage BMI data
data (bmiData)
bmiData$A1[which (bmiData$A1=="MR")] = 1
bmiData$A1[which (bmiData$A1=="CD")] = 1
bmiData$A2[which (bmiData$A2=="MR")] = 1
bmiData$A2[which (bmiData$A2=="CD")] = 1
bmiData$A1 = as.numeric (bmiData$A1)
bmiData$A2 = as.numeric (bmiData$A2)
s1vars = bmiData[,1:4]
s2vars = bmiData[,c (1, 3, 5)]
a1 = bmiData[,7]
a2 = bmiData[,8]
## define response y to be the negative 12 month change in BMI from
## baseline
y = (bmiData[,6]  bmiData[,4])/bmiData[,4]
s2ints = c (2, 3)
## secondstage regression
fitQ2 = qLearnS2 (s2vars, y, a2, s2ints)
fitQ2 = qLearnS2 (y ~ gender + parent_BMI + month4_BMI +
A2*(parent_BMI + month4_BMI), data=bmiData, "A2", c("parent_BMI",
"month4_BMI"))
## firststage regression
fitQ1 = qLearnS1 (fitQ2, s1vars, a1, c(3,4))
fitQ1 = qLearnS1 (~ gender + race + parent_BMI + baseline_BMI +
A1*(gender + parent_BMI), data=bmiData, "A1", c ("gender",
"parent_BMI"), fitQ2)
