C-statistics versus logistic regression for assessing the performance of qualitative diagnostic tests

Qualitative diagnostic tests commonly produce false positive and false negative results. Smooth receiver operated characteristic (ROC) curves are used for assessing the performance of a new test against a standard test. This method, called c-statistic (concordance) has limitations. The aim of this study was to assess whether logistic regression with the odds of disease as an outcome and the test scores as covariate, can be used as an alternative approach, and to compare the performance of either of the two methods.

Using as examples simulated by vascular laboratory scores we assessed the performance of logistic regression as compared to c-statistics.

The c-statistics produced areas under the curve (AUCs) of respectively 0.954 and 0.969 (standard errors 0.007 and 0.005), means difference 0.015 with a pooled standard error of 0.0086. This meant that the new test was not significantly different from the standard test at p=0.08. Logistic regression of these data with presence of disease as a dependent and vascular laboratory scores as an independent variable produced regression coefficients of 0.45 and 0.58 with standard errors of respectively 0.04 and 0.05. This meant that the new test was a significantly better predictor of disease than the standard test at p=0.04.

Logistic regression with presence of disease as a dependent and test scores as an independent variable was better than c-statistics for assessing qualitative diagnostic tests. This may be relevant to future diagnostic research.