Generalization error bounds of dynamic treatment regimes in penalized regression-based learning
针对多阶段干预中如何从大量预后变量中找出最优动态治疗方案的问题，提出了带L1惩罚的回归学习方法，并给出了估计方案的泛化误差上界，通过模拟和抑郁症临床试验数据验证了方法优势。
A dynamic treatment regime (DTR) is a sequence of decision rules, one per stage of intervention, that maps up-to-date patient information to a recommended treatment. Discovering an appropriate DTR for a given disease is a challenging issue especially when a large set of prognostic variables are observed. To address this problem, we propose penalized regression-based learning methods with l1 penalty to estimate the optimal DTR that would maximize the expected outcome if implemented. We also provide generalization error bounds of the estimated DTR in the setting of finite number of stages with multiple treatment options. We first examine the relationship between value and Q-functions and derive a finite sample upper bound on the difference in values between the optimal and the estimated DTRs. For practical implementation, we develop an algorithm with partial regularization via orthogonality to construct the optimal DTR. The advantages of the proposed methods are demonstrated with extensive simulation studies and data analysis of depression clinical trials.