Abstract
We consider the estimation of an optimal dynamic two time-point treatment rule defined as the rule that maximizes the mean outcome under the dynamic treatment, where the candidate rules are restricted to depend only on a user-supplied subset of the baseline and intermediate covariates. This estimation problem is addressed in a statistical model for the data distribution that is nonparametric, beyond possible knowledge about the treatment and censoring mechanisms. We propose data adaptive estimators of this optimal dynamic regime which are defined by sequential loss-based learning under both the blip function and weighted classification frameworks. Rather than \textit{a priori} selecting an estimation framework and algorithm, we propose combining estimators from both frameworks using a super-learning based cross-validation selector that seeks to minimize an appropriate cross-validated risk. One of the proposed risks directly measures the performance of the mean outcome under the optimal rule. The resulting selector is guaranteed to asymptotically perform as well as the best convex combination of candidate algorithms in terms of loss-based dissimilarity under conditions. We offer simulation results to support our theoretical findings. This work expands upon that of an earlier technical report (van der Laan, 2013) with new results and simulations, and is accompanied by a work which develops inference for the mean outcome under the optimal rule (van der Laan and Luedtke, 2014).
Disciplines
Biostatistics
Suggested Citation
Luedtke, Alexander R. and van der Laan, Mark J., "Super-Learning of an Optimal Dynamic Treatment Rule" (July 2014). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 326.
https://biostats.bepress.com/ucbbiostat/paper326