c-Statistic Versus Logistic Regression for Assessing the Performance of Qualitative Diagnostic Accuracy

Abstract

Clinical trials require adequate tests for making a diagnosis, and patient follow up. Whatever test, investigators need to know how good the test is. The performance of quantitative diagnostic tests, can be estimated from linear regression with the diagnostic result as predictor (independent) variable and the severities of disease as outcome (dependent) variable: the closer the outcome is to the best fit regression line the better the test is with a perfect test if R-square (the squared regression coefficient) equals 1. However, unfortunately, in clinical research many diagnostic tests have qualitative rather than quantitative outcome variables, e.g., a clinical event/disease or not, and linear regression is not applicable for judging the goodness of such tests. Instead, sensitivity (chance of a true positive test) and specificity (chance of a true negative test) are usually calculated, but the problem is that these two estimators are inversely correlated, and that multiple thresholds for the definition of a positive test can be given. Figure 49.1 shows the frequency distributions of patients without (left half) and with the disease (right half) with on the x-axis the individual patient results and on the y-axis “how often observed”.