Chapter Objectives

The objective of this chapter is to estimate the value of a fixed \(\Psi\)-specific treatment regime in the setting where there are \(K \gt 1\) decision points at which treatment selection will take place. In the nomenclature of potential outcomes the value is defined as

\[ \mathcal{V}(d) = E\left\{Y^{\text{*}}(d)\right\}, \]

where \(Y^{\text{*}}(d)\) is the potential outcome that an individual would achieve if all \(K\) rules in \(d\) were followed to select treatment.

Here, we provide an implementation for the regression-based value estimator, which is based on backward induction, and the inverse probability weighted and augmented inverse probability weighted value estimators, which are based on monotone coarsening. As was done for previous methods, we

  • provide a quick review of the form of the estimator,
  • define an estimator specific form for standard error estimates,
  • present R code to illustrate how one can implement the method and standard error being discussed, and
  • show the results of those implementations.

The implementation discussed is not general, having been written for the example data set, and it does not incorporate validation steps that we believe are important in all code development. We provide more general and robust implementations through an R package DTRBook, which is available for download under the R Codes section accessed through the header above. It is hoped that these more general implementations will be useful in practice with no additional code development required by the reader.