A method for analysing case-control studies with ordinal exposure variables

A method is proposed for analysing case-control studies with ordinal or continuous, but unruly, exposure levels. A test is proposed which is an appropriate linear combination of stratum-specific Wilcoxon tests. An estimator for the mean percentile shift between the case and control exposure levels is given. Methods for assessing heterogeneity of the mean percentile shift across strata are also discussed. The performance of the test as a function of the number of controls per case is studied for both local and distant alternatives. The asymptotic relative efficiency compared to the best parametric test with the same number of controls is evaluated and its performance is compared to tests based on a dichotomized exposure variable. Finally, the method is illustrated by two numerical examples.