There is tremendous scientific and medical interest in the use of biomarkers to better facilitate medical decision making. In this article, we present a simple framework for assessing the predictive ability of a biomarker. The methodology requires use of techniques from a subfield of survival analysis termed semicompeting risks; results are presented to make the article self-contained. As we show in the article, one natural interpretation of semicompeting risks model is in terms of modifying the classical risk set approach to survival analysis that is more germane to medical decision making. A crucial parameter for evaluating biomarkers is the predictive hazard ratio, which is different from the usual hazard ratio from Cox regression models for right-censored data. This quantity will be defined; its estimation, inference and adjustment for covariates will be discussed. Aspects of causal inference related to these procedures will also be described. The methodology is illustrated with an evaluation of serum albumin in terms of predicting death in patients with primary biliary cirrhosis.
Keywords: Association; Causal Effect; Copula; Cross-ratio; Dependence; Diagnostics.