Large health care data repositories such as electronic health records (EHR) open new opportunities to derive individualized treatment strategies for complicated diseases such as sepsis. In this paper, we consider the problem of estimating sequential treatment rules tailored to a patient's individual characteristics, often referred to as dynamic treatment regimes (DTRs). Our main objective is to find the optimal DTR that maximizes a discontinuous value function through direct maximization of Fisher consistent surrogate loss functions. In this regard, we demonstrate that a large class of concave surrogates fails to be Fisher consistent -- a behavior that differs from the classical binary classification problems. We further characterize a non-concave family of Fisher consistent smooth surrogate functions, which is amenable to gradient-descent type optimization algorithms. Compared to the existing direct search approach under the support vector machine framework (Zhao et al., 2015), our proposed DTR estimation via surrogate loss optimization (DTRESLO) method is more computationally scalable to large sample sizes and allows for broader functional classes for treatment policies. We establish theoretical properties for our proposed DTR estimator and obtain a sharp upper bound on the regret corresponding to our DTRESLO method. The finite sample performance of our proposed estimator is evaluated through extensive simulations. Finally, we illustrate the working principles and benefits of our method for estimating an optimal DTR for treating sepsis using EHR data from sepsis patients admitted to intensive care units.

翻译：大型医疗数据存储库（如电子健康记录）为复杂疾病（如败血症）的个性化治疗策略制定提供了新机遇。本文研究如何根据患者个体特征估计序贯治疗规则（即动态治疗方案，DTRs）。我们的主要目标是通过直接最大化Fisher一致替代损失函数，寻找能最大化非连续价值函数的最优DTR。研究表明，与经典二分类问题不同，一大类凹替代函数无法实现Fisher一致性。我们进一步刻画了一类非凹的Fisher一致平滑替代函数族，该类函数适用于梯度下降类优化算法。相较于现有支持向量机框架下的直接搜索方法（Zhao等，2015），本文提出的基于替代损失优化的DTR估计方法（DTRESLO）在大样本场景下具有更强的计算可扩展性，并允许采用更广泛的治疗策略函数类。我们建立了所提DTR估计量的理论性质，并得到了对应DTRESLO方法遗憾值的严格上界。通过大量模拟实验评估了所提估计量的有限样本性能。最后，利用重症监护病房败血症患者的电子健康记录数据，展示了该方法在估计败血症最优动态治疗方案中的工作原理与优势。