Time-dependent predictive accuracy: Extending binary classification accuracy methods for censored survival data

In this dissertation, we characterize the prognostic value of a scalar score or a marker for censored survival data by extending standard binary classification accuracy summaries like sensitivity or True Positive (TP) fraction, specificity or 1 - False Positive (FP) fraction, Receiver Operating Characteristic (ROC) curve and Area Under the ROC Curve (AUC). The first step to evaluate predictive accuracy of a marker often involves a typical case-control study. In such studies, the case and control status of the subjects remain fixed and the potential for the marker as a diagnostic tool is evaluated. However, in other studies, it may be desirable to use the markers for prediction of time to an event. For example, markers may be used to identify subjects who would acquire the disease or experience the event of interest by a pre-determined time, say within 2 years of evaluation, or to ascertain subjects who are most likely for an imminent failure. Thus, extending the binary predictive accuracy ideas for prospective study with a time-to-event outcome is important. Extending the diagnostic methodology to a time-to-event setting frequently involves unique challenges. Here, we introduce novel statistical methodology to solve some of these problems.;First, we propose time-dependent accuracy measures for a marker when we have censored survival times and competing risks. We extend time-dependent definitions of TP and FP to incorporate cause of failure for competing risks outcomes. Next, we propose a direct, non-parametric estimator of the time-dependent AUC curve, and show that the proposed estimator performs comparably or better than the existing semi-parametric AUC curve estimator. The proposed method extends non-parametric AUC estimates for binary data, and we establish asymptotic properties. An overall measure of concordance between the marker and failure time is also proposed. Time-dependent markers can also be accommodated in the estimation to capture the evolving nature of the marker. Finally, we introduce a time-averaged ROC curve to summarize the predictive accuracy of a marker accrued over time. We also introduce methods for comparison of markers via this summary ROC curve and demonstrate that this approach may be used to optimize screening schedules for diseases such as breast cancer.