## Chapter Objectives

Our objective in this chapter is to estimate the average causal treatment effect. In the nomenclature of potential outcomes, the treatment effect is defined as

\begin{aligned} \delta^{*} = E\left\{Y^{*}(1)\right\} - E\left\{Y^{*}(0)\right\}; \end{aligned}

that is, the treatment effect is the difference in the average potential outcomes if all patients were to receive treatment 1 and that if all patients were to receive treatment 0.

In the following pages, we provide implementations for several of the estimators of the treatment effect that were discussed in Chapter 2 of the book: the naive, the outcome regression, the stratification, the inverse probability weighted, and the doubly robust estimators. For each method, 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 for a variety of models.

The implementations discussed are not general, having been written for the example data set, and they do 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.