Optimal Dose-Response Learning

类风湿性关节炎、丙型肝炎和癌症等疾病的医学治疗通常需要在多个疗程中给药。高剂量能更好地控制疾病，但也有更高的副作用风险。较低剂量的副作用较小，但可能导致疾病控制不足。由于每个病人对治疗的反应都是不确定的，因此有效平衡这种权衡的需求遍及所有医学领域。因此，在个性化医疗领域，最近对反应导向给药的想法产生了浓厚的兴趣。目标是根据观察到的每个病人病情的演变，在正确的时间给正确的病人施用正确的剂量。为了达到这一目标，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，专家小组和政府管理机构呼吁提供分析工具，以促进这种边做边学。该奖项的研究目标是开发一个数学严谨、理论和计算框架，用于在临床试验中治疗一组患者以进行反应导向给药时进行最佳剂量-反应学习。在美国，数以百万计的病人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有可能产生相当大的社会影响。更具体地说，该项目计划使用贝叶斯随机动态规划公式和基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于队列的疾病状况，决策等于给予的剂量。负效用函数模拟了队列对剂量和试验结束时达到的疾病状况的厌恶。假设决策者的先验信念与剂量-响应参数的分布是共轭的。因此，信息状态等于先验的超参数，并通过一个简单的公式进行更新。决策的目标是尽量减少所给剂量和所达到疾病状况的总预期负效用。这个公式的精确解在计算上是棘手的。因此，设计了两种近似控制方案，即半随机确定性等效控制和确定性等效控制。结构性质，如单调性，平稳性和分离的结果给药策略将分析和利用有效的解决方案。变化，如最优停止问题，模型选择问题，问题与不完善的测量将被研究。类风湿关节炎的临床数据将用于校准模型，并验证和比较通过计算机模拟得出的给药策略。

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.