Optimal treatment policies and adaptive screening for functional predictors

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.