European Journal of Epidemiology

, Volume 27, Issue 10, pp 761–770 | Cite as

Assessing the discriminative ability of risk models for more than two outcome categories

  • Ben Van Calster
  • Yvonne Vergouwe
  • Caspar W. N. Looman
  • Vanya Van Belle
  • Dirk Timmerman
  • Ewout W. Steyerberg
METHODS

Abstract

The discriminative ability of risk models for dichotomous outcomes is often evaluated with the concordance index (c-index). However, many medical prediction problems are polytomous, meaning that more than two outcome categories need to be predicted. Unfortunately such problems are often dichotomized in prediction research. We present a perspective on the evaluation of discriminative ability of polytomous risk models, which may instigate researchers to consider polytomous prediction models more often. First, we suggest a “discrimination plot” as a tool to visualize the model’s discriminative ability. Second, we discuss the use of one overall polytomous c-index versus a set of dichotomous measures to summarize the performance of the model. Third, we address several aspects to consider when constructing a polytomous c-index. These involve the assessment of concordance in pairs versus sets of patients, weighting by outcome prevalence, the value related to models with random performance, the reduction to the dichotomous c-index for dichotomous problems, and interpretation. We illustrate these issues on case studies dealing with ovarian cancer (four outcome categories) and testicular cancer (three categories). We recommend the use of a discrimination plot together with an overall c-index such as the Polytomous Discrimination Index. If the overall c-index suggests that the model has relevant discriminative ability, pairwise c-indexes for each pair of outcome categories are informative. For pairwise c-indexes we recommend the ‘conditional-risk’ method which is consistent with the analytical approach of the multinomial logistic regression used to develop polytomous risk models.

Keywords

Polytomous risk prediction Discrimination c-index Discrimination plot 

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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Ben Van Calster
    • 1
    • 2
  • Yvonne Vergouwe
    • 2
  • Caspar W. N. Looman
    • 2
  • Vanya Van Belle
    • 3
    • 4
  • Dirk Timmerman
    • 1
  • Ewout W. Steyerberg
    • 2
  1. 1.Department of Development and RegenerationKU Leuven, University of LeuvenLeuvenBelgium
  2. 2.Department of Public HealthErasmus MCRotterdamThe Netherlands
  3. 3.Department of Electrical EngineeringKU LeuvenLeuvenBelgium
  4. 4.IBBT- Future Health DepartmentKU LeuvenLeuvenBelgium

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