Choosing between modified Poisson and log-binomial regression: evidence for the superiority of modified Poisson regression under heterogeneous risk ratios

Although logistic regression is commonly used to obtain a summary measure of the exposure-outcome association, log-binomial regression and modified (robust) Poisson regression are two increasingly popular methods for estimating the risk ratio with adjustment for multiple confounders. Most previous simulation studies using these two methods assumed a homogeneous exposure-outcome association across covariates. However, in real-world epidemiological applications, heterogeneity across covariates is often present. Furthermore, it remains unclear how differences in the estimation procedures between these two methods affect their performance in the presence of such heterogeneity. The theoretical examination and simulation results indicated that modified Poisson regression yielded practically valid estimates of the standardized risk ratio for the total population, except when both risk ratio heterogeneity and covariate-exposure associations were strong. In contrast, log-binomial regression yielded estimates interpretable as standardized risk ratios only when the risk ratios were either homogeneous or only mildly heterogeneous. These conclusions were supported by a breast cancer epidemiological study, in which heterogeneity in the exposure-outcome association was suspected. These findings suggest that modified Poisson regression would be preferable to log-binomial regression under heterogeneous risk ratios because it provides a practically valid estimator of the standardized risk ratio in broader scenarios.