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.
In the context of time‐to‐event analysis, a primary objective is to model the risk of experiencing a particular event in relation to a set of observed predictors. The Concordance Index (C‐Index) is a statistic frequently used in practice to assess how well such models discriminate between various risk levels in a population. However, the properties of conventional C‐Index estimators when applied to left‐truncated time‐to‐event data have not been well studied, despite the fact that left‐truncation is commonly encountered in observational studies. We show that the limiting values of the conventional C‐Index estimators depend on the underlying distribution of truncation times, which is similar to the situation with right‐censoring as discussed in Uno et al. (2011) [On the C‐statistics for evaluating overall adequacy of risk prediction procedures with censored survival data. Statistics in Medicine 30(10), 1105–1117]. We develop a new C‐Index estimator based on inverse probability weighting (IPW) that corrects for this limitation, and we generalize this estimator to settings with left‐truncated and right‐censored data. The proposed IPW estimators are highly robust to the underlying truncation distribution and often outperform the conventional methods in terms of bias, mean squared error, and coverage probability. We apply these estimators to evaluate a predictive survival model for mortality among patients with end‐stage renal disease.
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