Clinical decision-making often involves selecting tests that are costly, invasive, or time-consuming, motivating individualized, sequential strategies for what to measure and when to stop ascertaining. We study the problem of learning cost-optimal sequential decision policies from retrospective data, where test availability depends on prior results, inducing informative missingness. Under a sequential missing-at-random mechanism, we develop a doubly robust Q-learning framework for estimating optimal policies. The method introduces path-specific inverse probability weights that account for heterogeneous test trajectories and satisfy a normalization property conditional on the observed history. By combining these weights with auxiliary contrast models, we construct orthogonal pseudo-outcomes that enable unbiased policy learning when either the acquisition model or the contrast model is correctly specified. We establish oracle inequalities for the stage-wise contrast estimators, along with convergence rates, regret bounds, and misclassification rates for the learned policy. Simulations demonstrate improved cost-adjusted performance over weighted and complete-case baselines, and an application to a prostate cancer cohort study illustrates how the method reduces testing cost without compromising predictive accuracy.

翻译：临床决策通常涉及选择成本高昂、侵入性强或耗时长的测试，这促使我们需要制定个体化的序贯策略以决定测量内容及停止确认时机。我们研究从回顾性数据中学习成本最优序贯决策策略的问题，其中测试可用性取决于先前结果，从而产生信息性缺失。在序贯随机缺失机制下，我们开发了一个双重稳健Q学习框架来估计最优策略。该方法引入路径特异性逆概率权重，该权重可解释异质性测试轨迹，并在给定历史观测条件下满足归一化性质。通过将这些权重与辅助对比模型相结合，我们构建了正交伪结果，使得当获取模型或对比模型任一被正确设定时，可实现无偏策略学习。我们建立了阶段对比估计量的神谕不等式，同时给出了学习策略的收敛速率、遗憾界和误分类率。仿真实验表明，与加权基准和完全案例基线相比，该方法实现了更优的成本调整性能。针对前列腺癌队列研究的应用案例阐明了该方法如何在不牺牲预测准确性的前提下降低测试成本。