Journal
STATISTICS IN MEDICINE
Volume 32, Issue 4, Pages 661-672Publisher
WILEY
DOI: 10.1002/sim.5598
Keywords
logistic regression; predictive model; predictive accuracy; Brier score; discrimination; c-statistic; ROC curve
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Funding
- Ontario Ministry of Health and Long-Term Care
- Canadian Institutes of Health Research (CIHR) [MOP 86508]
- Heart and Stroke Foundation of Ontario
- Netherlands Organization for Scientific Research [9120.8004]
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The change in c-statistic is frequently used to summarize the change in predictive accuracy when a novel risk factor is added to an existing logistic regression model. We explored the relationship between the absolute change in the c-statistic, Brier score, generalized R2, and the discrimination slope when a risk factor was added to an existing model in an extensive set of Monte Carlo simulations. The increase in model accuracy due to the inclusion of a novel marker was proportional to both the prevalence of the marker and to the odds ratio relating the marker to the outcome but inversely proportional to the accuracy of the logistic regression model with the marker omitted. We observed greater improvements in model accuracy when the novel risk factor or marker was uncorrelated with the existing predictor variable compared with when the risk factor has a positive correlation with the existing predictor variable. We illustrated these findings by using a study on mortality prediction in patients hospitalized with heart failure. In conclusion, the increase in predictive accuracy by adding a marker should be considered in the context of the accuracy of the initial model. Copyright (C) 2012 John Wiley & Sons, Ltd.
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