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

 1 2 3 4 5 6 learnIQ2(H2, ...) ## S3 method for class 'formula' learnIQ2(formula, data, treatName, intNames, ...) ## Default S3 method: 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()

Details

Fits a model of the form

E (Y | H2, A2) = H20^Tβ20 + A2*H21^Tβ21,

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.

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, H20^T\hat{β20} contrast  estimated contrast function vector, H21^T\hat{β21} 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

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 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.

summary.learnIQ2, plot.learnIQ2

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 ## 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) 

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