Optimal Dose-Response Learning

类风湿性关节炎、丙型肝炎和癌症等疾病的医疗治疗通常需要分多次服用。更高的剂量可以更好地控制疾病，但产生副作用的风险也更高。较低剂量的副作用较小，但可能导致疾病控制不足。由于每个患者对治疗的反应是不确定的，有效地平衡这种权衡的需要贯穿于所有的医学领域。因此，在个性化医疗领域，最近出现了对反应引导剂量的想法的兴趣激增。目标是根据观察到的每个患者病情的演变，在正确的时间给正确的患者使用正确的剂量。为了实现这一目标，随着治疗的进展，更好地了解患者的剂量反应是至关重要的。因此，专家小组和政府监管机构呼吁使用分析工具来促进这种边做边学的做法。该奖项的研究目标是开发一个数学上严格的、理论上和计算上的框架，以便在治疗反应引导剂量临床试验中的一群患者时，进行最佳剂量-反应学习。在美国，数以百万计的患者患有需要多次治疗的疾病。因此，如果成功，这个奖项中的数学框架可能会产生相当大的社会影响。更具体地说，这个项目计划使用贝叶斯随机动态规划公式和植根于凸规划的近似解方法来促进响应学习和剂量决策。这些模型中的状态等同于队列的疾病状况，决定等同于给予的剂量。反效用函数模拟了队列人群对剂量和试验结束时达到的疾病状况的厌恶。假定决策者的先验信念与剂量-反应参数的分布是共轭的。因此，信息状态等于先前的超参数，并通过简单的公式进行更新。决策的目标是将所用剂量和所达到的疾病条件的预期总效用降至最低。这个公式的精确解在计算上是困难的。因此，设计了两种近似控制方案，即半随机确定性等价控制和确定性等价控制。将分析和利用所产生的剂量策略的结构属性，例如单调性、平稳性和可分离性，以获得有效的解决方案。将研究各种变化，如最优停止问题、模型选择问题和不完全测量问题。类风湿关节炎的临床数据将被用来校准模型，并验证和比较通过计算机模拟得出的剂量策略。

Medical treatment for diseases such as rheumatoid arthritis, hepatitis C, and cancer often requires the administration of doses in multiple sessions. Higher doses achieve better disease-control but have a higher risk of side effects. Lower doses have lesser side effects but may lead to inadequate disease-control. Since each patient's response to treatment is uncertain, the need to effectively balance this trade-off pervades all of medicine. Consequently, within the field of personalized medicine, there has been a recent surge of interest in the idea of response-guided dosing. The goal is to administer the right dose to the right patient at the right time, based on the observed evolution of each patient's disease condition. To attain this goal, it is crucial to better-learn patients' dose- response as treatment progresses. Expert panels and government regulatory bodies have therefore called for analytical tools to facilitate such learning-while-doing. The research objective of this award is to develop a mathematically rigorous, theoretical and computational framework for optimal dose-response learning while treating a cohort of patients in clinical trials for response-guided dosing. Millions of patients in the U.S. suffer from diseases that require multiple-session treatments. Thus, if successful, the mathematical framework in this award has the potential for a considerable societal impact.More specifically, this project plans to use Bayesian stochastic dynamic programming formulations and approximate solution methods rooted in convex programming to facilitate response-learning and dosing decisions. The state in these models equals the cohort's disease conditions and decisions equal the doses administered. Disutility functions model the cohort's aversion to doses and to the disease conditions reached at the end of the trial. The decision-maker's prior belief is assumed to be conjugate to the dose-response parameter's distribution. The information state thus equals the prior's hyperparameters and updates via a simple formula. The decision-make's goal is to minimize the total expected disutility of the doses administered and of the disease conditions reached. Exact solution of this formulation is computationally intractable. Two approximate control schemes called semi-stochastic certainty equivalent control and certainty equivalent control are therefore planned. Structural properties such as monotonicity, stationarity, and separability of the resulting dosing policies will be analyzed and exploited for efficient solution. Variations such as optimal stopping problems, model selection problems, and problems with imperfect measurements will be studied. Clinical data on rheumatoid arthritis will be employed to calibrate the models, and to validate and compare the dosing policies derived via computer simulations.