Fusing Individualized Treatment Rules Using Secondary Outcomes
arxiv(2024)
摘要
An individualized treatment rule (ITR) is a decision rule that recommends
treatments for patients based on their individual feature variables. In many
practices, the ideal ITR for the primary outcome is also expected to cause
minimal harm to other secondary outcomes. Therefore, our objective is to learn
an ITR that not only maximizes the value function for the primary outcome, but
also approximates the optimal rule for the secondary outcomes as closely as
possible. To achieve this goal, we introduce a fusion penalty to encourage the
ITRs based on different outcomes to yield similar recommendations. Two
algorithms are proposed to estimate the ITR using surrogate loss functions. We
prove that the agreement rate between the estimated ITR of the primary outcome
and the optimal ITRs of the secondary outcomes converges to the true agreement
rate faster than if the secondary outcomes are not taken into consideration.
Furthermore, we derive the non-asymptotic properties of the value function and
misclassification rate for the proposed method. Finally, simulation studies and
a real data example are used to demonstrate the finite-sample performance of
the proposed method.
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