Statistical Inference Methods for Predictive Classification based on Baseline Clinical Variables or Biomarkers

Abstract

One of significant challenges in precision medicine is, based on baseline clinical variables or biomarkers, identifying a subgroup of patients who may benefit more from a treatment in terms of a specific clinical outcome. The treatment effect heterogeneity is often evaluated through testing the interaction between treatment and subgroup. In practice, a cutpoint estimate is usually required to define the subgroup, especially when only a single continuous biomarker is available. However, in much of the clinical literature this cutpoint is treated as fixed and known, which can inflate type I error rates. Several corrections have been proposed, but most rely on regression models and may be sensitive to misspecification. Moreover, theoretical justifications are incomplete for some of corrections. This thesis consists of three parts. In the first part, when there is a single continuous baseline biomarker and the outcome is continuous, we propose a profile procedure to estimate the cutpoint based on a nonparametric measure of treatment-subgroup interaction, called as the probability index, and develop bootstrap procedures to test the interaction with the estimated cutpoint. It is shown that the estimate of the cutpoint achieves cubic-rate convergence and asymptotically follows a scaled Chernoff distribution. The second and third parts consider the case where the clinical outcome is the time-to-event or survival time with potential censoring. Because previous procedures proposed under the Cox model lack theoretical justification, in the second part, when there is only one baseline biomarker, we propose a bootstrap-based adjustment to the interaction test between the treatment and subgroup defined by an estimate of cutpoint derived from a profile method under a change-point Cox model. The asymptotic consistency of our proposed procedure is established under some regularity conditions. In the third part, nonparametric procedures are developed to identify the subgroup based on multiple baseline biomarkers when the outcome is right-censored time-to-event data. We extend the probability index framework by incorporating a single-index threshold and an inverse probability of censoring weighted approach for estimation. For all procedures, simulation studies are conducted to assess their finite-sample performance, and applications to clinical datasets are carried out to demonstrate their practical relevance.