iqLearn (version 1.5)

value: Estimate plug-in value

Description

Estimate the plug-in value of the any fixed treatment regime.

Usage

value(d1, d2, Y, A1, A2)

Arguments

d1

vector of first-stage treatments corresponding to the first-stage decision rule of the proposed regime

d2

vector of second-stage treatments corresponding to the second-stage decision rule of the proposed regime

Y

vector of responses

A1

vector of first-stage randomized treatments

A2

vector of second-stage randomized treatments

Value

value

estimated plug-in value of the regime

valPosPos

estimated plug-in value of the regime that treats all patients with \(A1\)=1 and \(A2=1\)

valPosNeg

estimated plug-in value of the regime that treats all patients with \(A1\)=1 and \(A2=-1\)

valNegPos

estimated plug-in value of the regime that treats all patients with \(A1\)=-1 and \(A2\)=1

valNegNeg

estimated plug-in value of the regime that treats all patients with \(A1\)=-1 and \(A2\)=-1

Details

The formula for the plug-in value estimate is

$$\frac{\sum_i Y_i*ind1_i*ind1_i}{\sum_i ind1_i*ind2_i }$$

where \(ind1\) and \(ind2\) are indicators that the first- and second-stage randomized treatments were consistent with the regime of interest.

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.value

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]
## second-stage regression
fitIQ2 = learnIQ2 (y ~ gender + parent_BMI + month4_BMI +
  A2*(parent_BMI + month4_BMI), data=bmiData, "A2", c("parent_BMI",
                                  "month4_BMI")) 
## model conditional expected value of main effect term
fitIQ1main = learnIQ1main (~ gender + race + parent_BMI + baseline_BMI
  + A1*(gender + parent_BMI), data=bmiData, "A1", c ("gender",
                                "parent_BMI"), fitIQ2)
## model conditional mean of contrast function
fitIQ1cm = learnIQ1cm (~ gender + race + parent_BMI + baseline_BMI +
  A1*(gender + parent_BMI + baseline_BMI), data=bmiData, "A1", c
  ("gender", "parent_BMI", "baseline_BMI"), fitIQ2)
## variance modeling
fitIQ1var = learnIQ1var (~ gender + race + parent_BMI + baseline_BMI +
  A1*(parent_BMI), data=bmiData, "A1", c ("parent_BMI"), "hetero",
  fitIQ1cm)
## get optimal first-stage txts
fitIQLearn = learnIQ1 (fitIQ1main, fitIQ1cm, fitIQ1var, "nonpar")
estVal = value (fitIQLearn$optA1, fitIQ2$optA2, y, a1, a2)
estVal
# }