Statistical Inference for the Mean Outcome Under a Possibly Non-Unique Optimal Treatment Strategy

Alex Luedtke

An individualized treatment rule (ITR) is a treatment rule which assigns treatments to individuals based on (a subset of) their measured covariates. An optimal ITR is the ITR which maximizes the population mean outcome. In any given problem, there is no guarantee that the optimal ITR will outperform standard practice. The utility of personalization can be explored using a confidence interval for the mean outcome under the optimal rule. Constructing valid confidence intervals is surprisingly difficult when the treatment under consideration has no effect on the outcome. This null treatment effect seems possible in many studies. I will provide intuition for the difficulties posed by a null effect and describe an estimator which overcomes this challenge. All of the results I will present apply in a nonparametric model.

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