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

Abstract

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 ρw,a2 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.

Estimated Life Expectancy Without Recurrent Cardiovascular Events in Patients With Vascular Disease: The SMART‐REACH Model

“…Third, the limited discriminatory ability of the SMART‐REACH model is comparable to previous risk scores for patients with clinically manifest vascular disease 4, 5, 29, 30. Previous studies have shown that additional risk factors are unlikely to result in relevant improvement 4, 38. This discriminatory ability may be due to the fact that selecting patients on the basis of a certain disease (vascular disease) results in a relatively homogenous population, in which discrimination becomes more difficult.…”

Survival Model Construction Guided by Fit and Predictive Strength

“…A large number of competing approaches appears possible since there is a large body of literature on goodness-of-fit procedures and a large body on predictive measures. Combinations of these could provide tools analogous to those described here and this has already been considered by some authors (Emura and Chen, 2014;Austin, Pencina, and Steyerberg, 2015). However, in order to make analogous claims to ours concerning predictive performance for some particular combination, we would require equivalent theorems to those presented in Sections 2 and 3.…”

“…Harrel's c-index is one of the most popular measures and could be used, as could most of the others, in place of what we propose in this article. In a recent contribution, Austin, Pencina, and Steyerberg (2015) look closely at several of these and, in particular, one of the early suggestions of Kent and O'Quigley (1988). Although not formally proved, O'Quigley, Xu, and Stare (2004) outline reasons to suppose that the measures of Kent andO'Quigley (1988), O'Quigley andFlandre (1994), and Xu and O'Quigley (1999) would behave very similarly.…”

Evaluating disease prediction models using a cohort whose covariate distribution differs from that of the target population

“…Since estimates of predictive model performance can vary with the covariate distribution of the subjects, 1–4 these differences can cause misleading estimates of model performance in the target population.…”