Journal
INTERNATIONAL JOURNAL OF BIOSTATISTICS
Volume 12, Issue 1, Pages 305-332Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/ijb-2015-0052
Keywords
causal inference; cross-validation; dynamic treatment; loss function; oracle inequality
Funding
- NIH [R01 AI074345-06]
- Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program
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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 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. 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.
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