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Primary Submission Category: Machine Learning and Causal Inference

Finite sample and asymptotic properties of a cross-validated risk estimator of a nonparametric regimen-response curve estimate

Authors: Cuong Pham, Ashkan Ertefaie,

Presenting Author: Cuong Pham*

Dynamic treatment strategies are the decision rules that map individual characteristics to a specific type of treatment. We focus on a parametric class of rules and define a regimen-response curve function as an expected value of the counterfactual outcome under a decision rule given a set of baseline variables. The regimen-response curve is a function of the decision rule’s parameters, and it is also the optimizer of the curve corresponding to an optimal dynamic treatment strategy. Existing methods impose a parametric model on the regimen-response curve function and estimate the corresponding parameters using a marginal structural model approach. The parametric model is likely to be misspecified, particularly in time-varying settings that may lead to considerably suboptimal treatment strategies. To overcome this issue, we propose a data-adaptive approach that utilizes the highly adaptive lasso model to capture the true regimen-response curve function. We also propose a nonparametric cross-validated risk estimator of the estimated regimen-response curve.

We show that:
1. Our estimated regimen-response curve converges to the true curve in loss-based-dissimilarity faster than root-n.
2. The cross-validated risk estimator is asymptotically linear.
3. The cross-validation tuning parameter selector risk is bounded in a finite sample.

We conduct extensive simulation studies to confirm our theoretical results and examine the finite sample performance of our estimator.