z-logo
Premium
Visualizing and assessing discrimination in the logistic regression model
Author(s) -
Royston Patrick,
Altman Douglas G.
Publication year - 2010
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.3994
Subject(s) - logistic regression , statistics , receiver operating characteristic , outcome (game theory) , statistic , mathematics , event (particle physics) , plot (graphics) , contrast (vision) , econometrics , index (typography) , computer science , artificial intelligence , physics , mathematical economics , quantum mechanics , world wide web
Abstract Logistic regression models are widely used in medicine for predicting patient outcome (prognosis) and constructing diagnostic tests (diagnosis). Multivariable logistic models yield an (approximately) continuous risk score, a transformation of which gives the estimated event probability for an individual. A key aspect of model performance is discrimination, that is, the model's ability to distinguish between patients who have (or will have) an event of interest and those who do not (or will not). Graphical aids are important in understanding a logistic model. The receiver‐operating characteristic (ROC) curve is familiar, but not necessarily easy to interpret. We advocate a simple graphic that provides further insight into discrimination, namely a histogram or dot plot of the risk score in the outcome groups. The most popular performance measure for the logistic model is the c ‐index, numerically equivalent to the area under the ROC curve. We discuss the comparative merits of the c ‐index and the (standardized) mean difference in risk score between the outcome groups. The latter statistic, sometimes known generically as the effect size, has been computed in slightly different ways by several different authors, including Glass, Cohen and Hedges. An alternative measure is the overlap between the distributions in the outcome groups, defined as the area under the minimum of the two density functions. The larger the overlap, the weaker the discrimination. Under certain assumptions about the distribution of the risk score, the c ‐index, effect size and overlap are functionally related. We illustrate the ideas with simulated and real data sets. Copyright © 2010 John Wiley & Sons, Ltd.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here