The calibrated model-based concordance improved assessment of discriminative ability in patient clusters of limited sample size

Abstract

BACKGROUND: Discriminative ability is an important aspect of prediction model performance, but challenging to assess in clustered (e.g., multicenter) data. Concordance (c)-indexes may be too extreme within small clusters. We aimed to define a new approach for the assessment of discriminative ability in clustered data. METHODS: We assessed discriminative ability of a prediction model for the binary outcome mortality after traumatic brain injury within centers of the CRASH trial. With multilevel logistic regression analysis, we estimated cluster-specific calibration slopes which we used to obtain the recently proposed calibrated model-based concordance (c-mbc) within each cluster. We compared the c-mbc with the naïve c-index in centers of the CRASH trial and in simulations of clusters with varying calibration slopes. RESULTS: The c-mbc was less extreme in distribution than the c-index in 19 European centers (internal validation; n = 1716) and 36 non-European centers (external validation; n = 3135) of the CRASH trial. In simulations, the c-mbc was biased but less variable than the naïve c-index, resulting in lower root mean squared errors. CONCLUSIONS: The c-mbc, based on multilevel regression analysis of the calibration slope, is an attractive alternative to the c-index as a measure of discriminative ability in multicenter studies with patient clusters of limited sample size.