iqLearn (version 1.5)

qLearnS2: Q-learning: second-stage regression

Description

Same as learnIQ2. Estimates the optimal second-stage decision rule using a linear regression of the response on second-stage history and treatment.

Usage

qLearnS2(H2, ...)
# S3 method for formula
qLearnS2(formula, data, treatName, intNames, ...)
# S3 method for default
qLearnS2(H2, Y, A2, s2ints, ...)

Arguments

formula

stage 2 regression formula

data

data frame containing variables used in formula

treatName

character string indicating the stage 2 treatment name

intNames

vector of characters indicating the names of the variables that interact with the stage 2 treatment in the regression model

H2

matrix or data frame of second-stage covariates to include as main effects in the linear model

Y

response vector

A2

vector of second-stage randomized treatments

s2ints

indices pointing to columns of H2 that should be included as treatment interaction effects in the linear model

…

other arguments to be passed to lm()

Value

betaHat20

estimated main effect coefficients; first is the intercept

betaHat21

estimated treatment interaction coefficients; first is the main effect of the second-stage treatment

Ytilde

Q2 function maximized over treatment \(a2\); the predicted future outcome assuming optimal treatment is given at the second stage to be used in the next step of the Q-learning algorithm

optA2

vector of estimated optimal second-stage treatments for the patients in the training data

s2Fit

lm() object of the second-stage regression fit

s2ints

indicies of variables in H2 included as treatment interactions in the model; same as input s2ints

Details

Fits a model of the form $$E (Y | H_2, A_2) = H_{20}^{T}\beta_{20} + A_{2}H_{21}^{T}\beta_{21},$$ where \(H20\) and \(H21\) are summaries of \(H2\). For an object of type qLearnS2, summary(object) and plot(object) can be used for evaluating model fit.

References

Linn, K. A., Laber, E. B., Stefanski, L. A. (2015) "iqLearn: Interactive Q-Learning 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 Q-learning", Biometrika, 101(4), 831-847.

See Also

summary.qLearnS2, plot.qLearnS2

Examples

# NOT RUN {
## load in two-stage 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)
## second-stage 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"))
                                   
summary (fitQ2)
plot (fitQ2)
# }