Abstract
Although the Cstatistic is widely used for evaluating the performance of diagnostic tests, its limitations for evaluating the predictive performance of biomarker panels have been widely discussed. The increment in C obtained by adding a new biomarker to a predictive model has no direct interpretation, and the relevance of the Cstatistic to risk stratification is not obvious. This paper proposes that the Cstatistic should be replaced by the expected information for discriminating between cases and noncases (expected weight of evidence, denoted as Λ), and that the strength of evidence favouring one model over another should be evaluated by crossvalidation as the difference in test loglikelihoods. Contributions of independent variables to predictive performance are additive on the scale of Λ. Where the effective number of independent predictors is large, the value of Λ is sufficient to characterize fully how the predictor will stratify risk in a population with given prior probability of disease, and the Cstatistic can be interpreted as a mapping of Λ to the interval from 0.5 to 1. Even where this asymptotic relationship does not hold, there is a onetoone mapping between the distributions in cases and noncases of the weight of evidence favouring case over noncase status, and the quantiles of these distributions can be used to calculate how the predictor will stratify risk. This proposed approach to reporting predictive performance is demonstrated by analysis of a dataset on the contribution of microbiome profile to diagnosis of colorectal cancer.
Original language  English 

Journal  Statistical Methods in Medical Research 
Early online date  6 Jul 2018 
DOIs  
Publication status  Epub ahead of print  6 Jul 2018 
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Paul McKeigue
 Deanery of Molecular, Genetic and Population Health Sciences  Chair of Genetic Epidemiology and Statistical Genetics
 Usher Institute
 Centre for Population Health Sciences
Person: Academic: Research Active