On the homogeneity of measures for binary associations

TL;DR

This paper clarifies misconceptions about the heterogeneity of effect measures like risk difference, relative risk, and odds ratio, emphasizing that their variation independence relates to interpretability rather than true homogeneity.

Contribution

It distinguishes between variation independence and homogeneity of effect measures, correcting common misconceptions in applied research.

Findings

Risk difference is often perceived as more heterogeneous, but this is due to variation independence.

Theoretical arguments for heterogeneity are based on interpretability, not actual measure homogeneity.

Clarifies the distinction between variation independence and measure homogeneity.

Abstract

Applied researchers often claim that the risk difference is more heterogeneous than the relative risk and the odds ratio. Some also argue that there are theoretical grounds for why this claim is true. In this note, we point out that these arguments reflect certain effect measures are variation independent of a nuisance parameter that is easier to interpret, rather than the homogeneity of these measures.