Using the ROC Curve to Measure Association and Evaluate

Logistic regression and its corresponding odds ratio(s) (OR) are the most popular measure of association between a continuous or categorical variable with a binary outcome in epidemiology. For example, in epidemeology, we would be interested in the association between health status and life style measures. For a significantly associated predictor of a binary outcome, we can estimate the probability of a random observation being in one category and classify the observation into two groups based on the value of the predictor. For example, it is believed that arsenic exposure is associated with blackfoot disease. Such exposure can be continuous, i.e., the level of chronic arsenic exposure through drinking water, or binary, i.e., exposed versus non-exposed. However, using logistic regression and the odds ratio sometimes produces results that are puzzling and misleading: Kraemer and Pepe et al. [1,2] provided very good discussions about the paradoxical situations about the odds ratio, especially in the presence of strongly associated predictors.