Measuring the temporal prognostic utility of a baseline risk score
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Measuring the temporal prognostic utility of a baseline risk score Sean M. Devlin1
· Mithat Gönen1 · Glenn Heller1
Received: 24 June 2019 / Accepted: 30 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract 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. Keywords Proportional hazards · Prognostic modeling · Concordance probability
1 Introduction Biomarker discovery has become an integral part of clinical research and the number of potential biomarkers has grown exponentially with the advent of molecular tech-
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10985020-09503-3) contains supplementary material, which is available to authorized users.
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Sean M. Devlin [email protected] Department of Epidemiology and Biostatistics, Memorial Sloan Kettering Cancer Center, New York, NY, USA
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nologies. These developments have led to the need for specialized statistical methods focusing on the evaluation of novel markers and their utility within statistical models for the prediction of clinical outcomes. One common tool to assess the performance of a statistical model is the concordance probability. For survival models, the concordance probability assesses the relative level of agreement between the model-based risk scores and the survival times of patients. An estimate of the concordance probability, however, does not provide information on the durability of a baseline risk score over time. This is a critical component when integrating new biomarkers into clinical care and patient surveillance. If a model is able to segregat
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