Statistical methods for evaluating diagnostic accuracy of biomarkers

In modern biomedical research, biomarkers play key roles in early diagnosis of chronic disease. The Receiver Operating Characteristic (ROC) curve is a common tool for evaluating diagnostic accuracy of a continuous biomarker. In the first part of the work, we consider estimation of time-dependent ROC curves when survival data are collected under outcome-dependent sampling. We derive a bias correction function for the distribution function of the baseline biomarkers and propose semiparametric bias-corrected estimators for ROC curves. The proposed estimators are shown to be consistent and asymptotically normal, while substantial biases may arise if standard estimators are used. In the second part of the work, we extend tools of ROC analysis from univariate marker to multivariate marker setting using a tree-based classification rule. Using an and-or classifier, an ROC function together with a weighted ROC function (WROC) and their conjugate counterparts are proposed. The proposed functions evaluate the performance of and-or classifiers among all possible combinations of marker values, and are ideal measures for understanding the prediction accuracy of biomarkers in the target population. In the third part of the work, we propose an analysis stream for functional magnetic resonance imaging (fMRI) data, where the high-dimensional imaging data is decomposed into population-level brain networks and subject-specific loadings. The subject-specific loadings can be used as summary measures of brain imaging for disease prediction.