Predicting outcomes that occur over time is important in clinical, population health, and health services research. We compared changes in different measures of performance when a novel risk factor or marker was added to an existing Cox proportional hazards regression model. We performed Monte Carlo simulations for common measures of performance: concordance indices (c, including various extensions to survival outcomes), Royston's D index, R2-type measures, and Chambless' adaptation of the integrated discrimination improvement to survival outcomes. We found that the increase in performance due to the inclusion of a risk factor tended to decrease as the performance of the reference model increased. Moreover, the increase in performance increased as the hazard ratio or the prevalence of a binary risk factor increased. Finally, for the concordance indices and R2-type measures, the absolute increase in predictive accuracy due to the inclusion of a risk factor was greater when the observed event rate was higher (low censoring). Amongst the different concordance indices, Chambless and Diao's c-statistic exhibited the greatest increase in predictive accuracy when a novel risk factor was added to an existing model. Amongst the different R2-type measures, O'Quigley et al.'s modification of Nagelkerke's R2 index and Kent and O'Quigley's Ï w, a 2 displayed the greatest sensitivity to the addition of a novel risk factor or marker. These methods were then applied to a cohort of 8635 patients hospitalized with heart failure to examine the added benefit of a point-based scoring system for predicting mortality after initial adjustment with patient age alone.

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Keywords Cox proportional hazards model, discrimination, model performance, Monte Carlo simulations, predictive accuracy, predictive models, risk factors, Survival analysis
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Journal Statistical Methods in Medical Research
Austin, P.C, Pencinca, M.J. (Michael J.), & Steyerberg, E.W. (2017). Predictive accuracy of novel risk factors and markers: A simulation study of the sensitivity of different performance measures for the Cox proportional hazards regression model. Statistical Methods in Medical Research, 26(3), 1053–1077. doi:10.1177/0962280214567141