Optimal treatment policies and adaptive screening for functional predictors

基于生物医学图像、质谱学或基因表达的高维患者档案有朝一日可能被用于指导治疗选择和改善结果。该项目的第一部分致力于开发新的统计方法，以评估基于这种高维度概况的个体化治疗政策的有效性。该方法涉及根据功能回归模型指定治疗和患者概况之间的交互作用，因此可以利用随机临床试验的数据来同时评估治疗策略的有效性，以所有患者遵循该政策时的平均结果来衡量，并确定患者概况的特征，以优化相互作用的效果，而不是竞争疗法。该项目的第二部分涉及以边际回归为基础校准筛查程序的新方法，以检测高维轮廓中是否存在显著的预测因素。众所周知，标准推理方法在这种情况下是失败的，这是因为所选预测者的估计回归系数的非规则限制行为。为了避免这种非规律性，为了更好地反映小样本行为，开发了一种新的Bootstrap校准过程。尽管在过去的10-20年里，许多用于分析高维患者档案数据的方法已经变得可用，但它们主要是为了寻找患者预后的关键预测因素。评估个体化治疗政策的价值以优化患者结局的问题相对较少受到关注。该项目的主要创新是开发了新的方法来估计这种最优决策规则在预期患者结果方面的价值。此外，还开发了一种新的自适应重采样测试程序来解决高维筛选中的一个中心问题，即通过计算p值来适应模型选择后参数估计的固有不稳定性。该项目对生物医学成像、质谱学和高通量基因表达技术的最新进展产生了更广泛的影响，所有这些都产生了关于单个患者的大量数据。这些数据的有效利用有可能为个别患者量身定做治疗方案提供可能。例如，建议的方法可以应用于脑成像数据以设计抑郁症的治疗方法、PET研究(其比较接受认知治疗的患者和接受抗抑郁药物治疗的患者以确定哪种治疗更有可能使给定患者受益)、质谱图以检测癌症病例和对照之间的差异以有助于个性化癌症护理、以及用于设计癌症或心血管疾病的个性化治疗的基因表达谱。另一个更广泛的影响是对由PI和Co-PI指导的博士生的培训，以及为新的研究生课程开发模块，旨在向博士生介绍函数数据分析和推理，以获得最佳治疗政策。

High-dimensional patient profiles based on biomedical images, mass spectrometry, or gene expression, might one day be used to guide treatment selection and improve outcomes. The first part of the project is devoted to the development of new statistical methodology for assessing the effectiveness of individualized treatment policies based on such high-dimensional profiles. The approach involves specifying the interaction between the treatment and patient profile in terms of a functional regression model, so data from randomized clinical trials can be utilized to simultaneously evaluate the effectiveness of the treatment policies, measured in terms of mean outcome when all patients follow the policy, and to identify features of patient profiles that optimize the interaction effect over competing treatments. The second part of the project concerns a new way of calibrating screening procedures based on marginal regression for detecting the presence of significant predictors in high-dimensional profiles. Standard inferential methods are known to fail in this setting due to the non-regular limiting behavior of the estimated regression coefficient of selected predictors. To circumvent this non-regularity, a new bootstrap calibration procedure is developed in order to better reflect small-sample behavior. Although many methods for analyzing high-dimensional patient profile data have become available over the last 10-20 years, they are primarily for the purpose of finding the key predictors of patient outcomes. Relatively little attention has been paid to the problem of assessing the value of individualized treatment policies to optimize patient outcomes. The major innovation of the project is that new ways of estimating the value of such optimal decision rules in terms of expected patient outcomes are developed. In addition, a new adaptive resampling test procedure is developed to address a central problem in high-dimensional screening by computing p-values in a way that adapts to the inherent instability of post-model-selected parameter estimates. The project has broader impacts related to recent advances in biomedical imaging, mass spectrometry, and high-throughput gene expression technology, all of which produce massive amounts of data on individual patients. The effective use of such data has the potential to open up the possibility of tailoring treatments to individual patients. The proposed methods could be applied, for example, to brain imaging data to design treatments for depression, to PET studies that compare patients treated with cognitive therapy and patients treated with anti-depressants in order to determine which treatment is more likely to benefit a given patient, to mass spectrometry profiling for detecting differences between cancer cases and controls in a way that may contribute to personalized cancer care, and to gene expression profiles for designing individualized therapies for cancer or cardiovascular disease. Another broader impact is in the training of Ph.D. students mentored by the PI and Co-PI, and in the development of modules for new graduate courses designed to introduce Ph.D. students to functional data analysis and inference for optimal treatment policies.