Power of the Rank Test for Multi-Strata Case-Control Studies with Ordinal Exposure Variables

In epidemiological studies of rare diseases (i.e., rare types of cancer) researchers often face major difficulty in obtaining enough cases of the disease to make valid comparisons using odds-ratio estimators. Moreover, they may wish to adjust for the influence of certain extraneous factors so that the effect of the variables of interest can be more clearly visible. This is especially so in case-control studies when it is known that the effects of the risk factor are confounded with such variables as age, sex, and individual physical characteristics of the subjects. These confounding variables often make it difficult (or even impossible) to directly compare the exposed and unexposed groups. Typically, to evaluate the effect of the risk factor in these situations within the odds-ratio framework, methods based on data stratification and within-stratum dichotomization are used. The latter is usually accomplished by classifying cases and controls within each stratum as either exposed or unexposed to the risk factor under investigation. Whereas the stratification is often unavoidable, it may not be practical to dichotomize exposure. Instead, one might wish to consider multiple levels of the exposure variable, based on some appropriate ordinal or even continuous scale (cf., e.g., Greenberg and Tamburro [1 ]).