Post-Selection Inference for Survival Outcomes in Precision Medicine

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.