On the Relationship between Treatment Effect Heterogeneity and the Variability Ratio Effect Size Statistic

TL;DR

This paper explores the mathematical relationship between treatment effect heterogeneity and the variability ratio effect size statistic, providing bounds and simulations to clarify their connection in medical studies.

Contribution

It derives precise bounds linking treatment effect heterogeneity to the variability ratio, clarifying their relationship and implications for interpreting effect size estimates.

Findings

Derived bounds on TEH in terms of VR

Simulated scenarios showing TEH with VR equal to 1

Implications for interpreting VR in medical interventions

Abstract

Recently, the variability ratio (VR) effect size statistic has been used with increasing frequency in the study of differences in variation of a measured variable between two study populations. More specifically, the VR effect size statistic allows for the detection of treatment effect heterogeneity (TEH) of medical interventions. While a VR that is different from 1 is widely acknowledged to implicate a treatment effect heterogeneity (TEH) the exact relationship between those two quantities has not been discussed in detail thus far. In this note we derive a precise connection between TEH and VR. In particular, we derive precise upper and lower bounds on the TEH in terms of VR. Moreover, we provide an exemplary simulation for which VR is equal to 1 and there exist TEH. Our result has implications for the interpretation of VR effect size estimates regarding its connection to treatment effect heterogeneity of (medical) interventions.