Estimation of the Population Average Prescription Effect in Randomized Experiments Under Cross Validation

This function estimates the Population Average Prescription Effect with and without a budget constraint. The details of the methods for this design are given in Imai and Li (2019).

Usage

PAPEcv(T, That, Y, ind, budget = NA, centered = TRUE)

Arguments

T

A vector of the unit-level binary treatment receipt variable for each sample.

That

A matrix where the ith column is the unit-level binary treatment that would have been assigned by the individualized treatment rule generated in the ith fold. If budget is specified, please ensure that the percentage of treatment units of That is lower than the budget constraint.

Y

The outcome variable of interest.

ind

A vector of integers (between 1 and number of folds inclusive) indicating which testing set does each sample belong to.

budget

The maximum percentage of population that can be treated under the budget constraint. Should be a decimal between 0 and 1. Default is NA which assumes no budget constraint.

centered

If TRUE, the outcome variables would be centered before processing. This minimizes the variance of the estimator. Default is TRUE.

Value

A list that contains the following items:

pape

The estimated Population Average Prescription Effect.

sd

The estimated standard deviation of PAPE.

References

Imai and Li (2019). “Experimental Evaluation of Individualized Treatment Rules”,

Author

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School mili@hbs.edu, https://www.michaellz.com/;

Examples

T = c(1,0,1,0,1,0,1,0)
That = matrix(c(0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1), nrow = 8, ncol = 2)
Y = c(4,5,0,2,4,1,-4,3)
ind = c(rep(1,4),rep(2,4))
papelist <- PAPEcv(T, That, Y, ind)
papelist$pape
#> [1] -0.1666667
papelist$sd
#> [1] 1.326843