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Misuse of DeLong test to compare AUCs for nested models
Author(s) -
Demler Olga V.,
Pencina Michael J.,
D'Agostino Ralph B.
Publication year - 2012
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5328
Subject(s) - confidence interval , statistics , estimator , nested set model , receiver operating characteristic , outcome (game theory) , test (biology) , econometrics , score test , wald test , null hypothesis , argument (complex analysis) , computer science , mathematics , statistical hypothesis testing , medicine , data mining , biology , paleontology , mathematical economics , relational database
The area under the receiver operating characteristics curve (AUC of ROC) is a widely used measure of discrimination in risk prediction models. Routinely, the Mann–Whitney statistics is used as an estimator of AUC, while the change in AUC is tested by the DeLong test. However, very often, in settings where the model is developed and tested on the same dataset, the added predictor is statistically significantly associated with the outcome but fails to produce a significant improvement in the AUC. No conclusive resolution exists to explain this finding. In this paper, we will show that the reason lies in the inappropriate application of the DeLong test in the setting of nested models. Using numerical simulations and a theoretical argument based on generalized U ‐statistics, we show that if the added predictor is not statistically significantly associated with the outcome, the null distribution is non‐normal, contrary to the assumption of DeLong test. Our simulations of different scenarios show that the loss of power because of such a misuse of the DeLong test leads to a conservative test for small and moderate effect sizes. This problem does not exist in cases of predictors that are associated with the outcome and for non‐nested models. We suggest that for nested models, only the test of association be performed for the new predictors, and if the result is significant, change in AUC be estimated with an appropriate confidence interval, which can be based on the DeLong approach. Copyright © 2012 John Wiley & Sons, Ltd.