Targeted Learning Ensembles for Optimal Individualized Treatment Rules with Time-to-Event Outcomes

Abstract: We consider estimation of an optimal individualized treatment rule from observational and randomized studies when a high-dimensional vector of baseline variables is available. Our optimality criterion is with respect to delaying expected time to occurrence of an event of interest (e.g., death or relapse of cancer). We leverage semiparametric efficiency theory to construct estimators with desirable properties such as double robustness. We propose two estimators of the optimal rule, which arise from considering two loss functions aimed at (i) directly estimating the conditional treatment effect (also know as the blip function), and (ii) recasting the problem as a weighted classification problem that uses the 0-1 loss function. Our estimated rules are super learning ensembles that minimize the cross-validated risk of a linear combination in a user-supplied library of candidate estimators. We prove oracle inequalities bounding the finite sample excess risk of the estimator. The bounds depend on the excess risk of the oracle selector and a doubly robust term related to estimation of the nuisance parameters. We discuss some important implications of these oracle inequalities such as the convergence rates of the value of our estimator to that of the oracle selector. We illustrate our methods in the analysis of a phase III randomized study testing the efficacy of a new therapy for the treatment of breast cancer.