Post-Selection Inference for Survival Outcomes in Precision Medicine

生物医学技术的最新突破产生了大量关于个体患者的数据。然而，通常只有相对少量的特征（如果有的话）可以预测临床结果，特别是当结果是存活时间时。在这种情况下，科学发现的一个核心方面是在大量协变量中检测出重要的预测因子。此外，在观察治疗分配的研究中，一个重要的目标是制定精准医学的策略。为了实现这一目标，重要的是要确定与治疗相互作用的协变量。由于所得到的模型拟合在告知临床决策和指导未来研究方面发挥着作用，因此为所选协变量提供推理保证至关重要。这就是后选择推理问题。该项目的总体目标是开发一个统一的假设检验程序，可用于检测在正确删失下预测生存结局的变量，以及识别可用于制定最佳治疗决策的生存结局的显著治疗-协变量相互作用。 该项目将开发新的选择后推理方法，用于筛选生存结局的高维预测因子，并使用这些方法设计新的治疗选择政策类别。这个问题是具有挑战性的，不仅是因为非正则渐近行为（检验统计量和估计量），而且因为存在删失。该计划涉及建设一个半参数化的有效估计的斜率参数（在加速故障时间模型）对应于每个预测和生存结果之间的最大边际相关性，并设计一个校准的正则化版本的这个统计提供一个正式的筛选测试，将检测显着的关联。此外，将开发基于检测到的关联来构建和评估最佳治疗政策的有效性的方法。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Recent breakthroughs in biomedical technology produce massive amounts of data on individual patients. Typically, however, only a relatively small number of features, if any, may be predictive of the clinical outcome, especially when the outcome is a survival time. A central aspect of scientific discovery in this scenario is to detect significant predictors among a large set of covariates. In addition, in studies where treatment assignments are observed, an essential goal is to develop strategies for precision medicine. To achieve this goal, it is important to identify covariates that interact with the treatment. As the resulting model fits play a role in informing clinical decisions and guiding future research, it is crucial to provide inferential guarantees for the selected covariates. This is the post-selection inference problem in a nutshell. The overarching goal of this project is to develop a unified hypothesis testing procedure that can be used to detect variables that are predictive of survival outcomes under right censoring, as well as to identify significant treatment-by-covariate interactions of survival outcomes that can be used in making optimal treatment decisions. This project will develop new methods of post-selection inference for screening high-dimensional predictors of survival outcomes and use those methods to design new classes of treatment selection policies. The problem is challenging, not only because of nonregular asymptotic behavior (of test statistics and estimators), but also because of the presence of censoring. The plan involves construction of a semi-parametrically efficient estimator of the slope parameter (in an accelerated failure time model) corresponding to the maximal marginal correlation between each predictor and the survival outcome, and devising a calibration of a regularized version of this statistic to furnish a formal screening test that will detect significant associations. Further, methods of constructing and assessing the effectiveness of optimal treatment policies based on the detected associations will be developed. The resulting procedures are expected to be more powerful and efficient than existing methods.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.