Problems in the Average-Risk Interpretation of Categorical Dose-Response Analyses

In a recent article,1 I commented that categorical risk models depended on the assumption of homogeneous within-category risks, a step-function assumption that I labeled absurd. I also dismissed the average-risk inter? pretation of such regressions as questionable. In an accompanying editorial, Weinberg2 agreed that the stepfunction assumption was absurd but argued that the average-risk interpretation rendered the homogeneity assumption unnecessary. I here clarify the basis of my comment by illustrating how the apparent dose-response relation conveyed by a categorical analysis may be biased if there is substantial within-category heterogeneity of risk. The fact that the categorical relative risks are interpretable as ratios of average risks does not address this problem. I also comment on other justifications for categorical analysis of continuous variables.