Pitfalls of the concordance index for survival outcomes

Prognostic models are useful tools for assessing a patient's risk of experiencing adverse health events. In practice, these models must be validated before implementation to ensure that they are clinically useful. The concordance index (C-Index) is a popular statistic that is used for model validation, and it is often applied to models with binary or survival outcome variables. In this paper, we summarize existing criticism of the C-Index and show that many limitations are accentuated when applied to survival outcomes, and to continuous outcomes more generally. We present several examples that show the challenges in achieving high concordance with survival outcomes, and we argue that the C-Index is often not clinically meaningful in this setting. We derive a relationship between the concordance probability and the coefficient of determination under an ordinary least squares model with normally distributed predictors, which highlights the limitations of the C-Index for continuous outcomes. Finally, we recommend existing alternatives that more closely align with common uses of survival models.