Estimating the quality of optimal treatment regimes

When multiple treatment alternatives are available for a disease, an obvious question is which alternative is most effective for which patient. One may address this question by searching for optimal treatment regimes that specify for each individual the preferable treatment alternative based on that individual's baseline characteristics. When such a regime has been estimated, its quality (in terms of the expected outcome if it was used for treatment assignment of all patients in the population under study) is of obvious interest. Obtaining a good and reliable estimate of this quantity is a key challenge for which so far no satisfactory solution is available. In this paper, we consider for this purpose several estimators of the expected outcome in conjunction with several resampling methods. The latter have been evaluated before within the context of statistical learning to estimate the prediction error of estimated prediction rules. Yet, the results of these evaluations were equivocal, with different best performing methods in different studies, and with near-zero and even negative correlations between true and estimated prediction errors. Moreover, for different reasons, it is not straightforward to extrapolate the findings of these studies to the context of optimal treatment regimes. To address these issues, we set up a new and comprehensive simulation study. In this study, combinations of different estimators with .632⁺ and out-of-bag bootstrap resampling methods performed best. In addition, the study shed a surprising new light on the previously reported problematic correlations between true and estimated prediction errors in the area of statistical learning.