Measuring the temporal prognostic utility of a baseline risk score

In the time-to-event setting, the concordance probability assesses the relative level of agreement between a model-based risk score and the survival time of a patient. While it provides a measure of discrimination over the entire follow-up period of a study, the probability does not provide information on the longitudinal durability of a baseline risk score. It is possible that a baseline risk model is able to segregate short-term from long-term survivors but unable to maintain its discriminatory strength later in the follow-up period. As a consequence, this would motivate clinicians to re-evaluate the risk score longitudinally. This longitudinal re-evaluation may not, however, be feasible in many scenarios since a single baseline evaluation may be the only data collectible due to treatment or other clinical or ethical reasons. In these scenarios, an attenuation of the discriminatory power of the patient risk score over time would indicate decreased clinical utility and call into question whether this score should remain a prognostic tool at later time points. Working within the concordance probability paradigm, we propose a method to address this clinical scenario and evaluate the discriminatory power of a baseline derived risk score over time. The methodology is illustrated with two examples: a baseline risk score in colorectal cancer defined at the time of tumor resection, and for circulating tumor cells in metastatic prostate cancer.