Comparative exposure ratios: a non-parametric, multifactor technique for case-control studies

The odds ratio in a two-by-two table is widely used in case-control studies to measure association between disease and a binary risk factor. In this article we propose a more general measure of association, the comparative exposure ratio (CER), which is the ratio of the number of case-control pairs where the case has greater exposure divided by the number where the control has greater exposure. In simple cases, the CER is an odds ratio or a weighted combination of odds ratios. In more general cases, a CER continues to measure association even when an odds ratio computation is not feasible. Moreover, CERs improve on odds ratios in several ways: they do not require binary risk factors, or a choice of the scale of measurement of continuous risk factors; they make it possible to investigate multiple risk factors simultaneously, without multivariate parametric assumptions; they also can be used to detect patterns that might indicate possible causal pathways. We illustrate how various choices of the definition of 'greater exposure' make the CER a powerful and flexible tool. We give expressions for confidence intervals for CERs, and verify in a pilot simulation that they are valid. Finally, we illustrate with a case-control study of cervical dysplasia how exploratory inference using CERs can be carried out.