Statistical Methods for Biomarker Research: Risk Prediction, Cancer Screening, and Sequential Decision

Abstract

Advances in science and technology have enabled the measurement of novel biomarkers, promising significant improvements in public health and medicine. This dissertation develops statistical tools to support biomarker research in three distinct settings. The first project focuses on evaluating risk prediction models derived from biomarker data. We propose a family of weighted Brier scores emphasizing the clinical utility of risk prediction models in their intended applications. In the second project, we tackle the problem of designing cancer screening trials. We develop a probabilistic model to project the time-varying screening effect from early-detection biomarker performance. In the third project, we consider a setting in which expensive biomarkers are measured for a subset of patients. We propose and study a two-step sequential classifier to aid decision-making while controlling errors at prespecified levels.