Concordance measure and discriminatory accuracy in transformation cure models

Abstract

Many populations of early-stage cancer patients have non-negligible latent cure fractions that can be modeled using transformation cure models. However, there is a lack of statistical metrics to evaluate prognostic utility of biomarkers in this context due to the challenges associated with unknown cure status and heavy censorship. In this article, we develop general concordance measures as evaluation metrics for the discriminatory accuracy of transformation cure models including the so-called promotion time cure models and mixture cure models. We introduce explicit formulas for the consistent estimates of the concordance measures, and show that their asymptotically normal distributions do not depend on the unknown censoring distribution. The estimates work for both parametric and semiparametric transformation models as well as transformation cure models. Numerical feasibility of the estimates and their robustness to the censoring distributions are illustrated via simulation studies and demonstrated using a melanoma data set.

Keywords: Concordance probability; Cure fraction; Mixture cure model; Predictive accuracy; Prognostics for censored survival; c-index.