iqLearn (version 1.5)

learnIQ2: IQ-learning: second-stage regression

Description

Fits a linear regression of the response on second-stage history and treatment to estimate the optimal second-stage decision rule.

Usage

learnIQ2(H2, ...)
# S3 method for formula
learnIQ2(formula, data, treatName, intNames, ...)
# S3 method for default
learnIQ2(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

s2Fit

lm() object of the second-stage regression fit

optA2

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

main

estimated main effect vector, $H{20}^T$$\widehat{\beta 20}$

contrast

estimated contrast function vector, $H{21}^T$$\widehat{\beta 21}$

s2ints

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

A2

vector of second-stage randomized treatments; same as input A2

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 learnIQ2, 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.learnIQ2, plot.learnIQ2

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
fitIQ2 = learnIQ2 (s2vars, y, a2, s2ints)
fitIQ2 = learnIQ2 (y ~ gender + parent_BMI + month4_BMI +
  A2*(parent_BMI + month4_BMI), data=bmiData, "A2", c("parent_BMI",
                                  "month4_BMI"))
                                   
summary (fitIQ2)
plot (fitIQ2)
# }