Reflection on modern methods: causal inference considerations for heterogeneous disease etiology

Molecular pathological epidemiology research provides information about pathogenic mechanisms. A common study goal is to evaluate whether the effects of risk factors on disease incidence vary between different disease subtypes. A popular approach to carrying out this type of research is to implement a multinomial regression in which each of the non-zero values corresponds to a bona fide disease subtype. Then, heterogeneity in the exposure effects across subtypes is examined by comparing the coefficients of the exposure between the different subtypes. In this paper, we explain why this common method potentially cannot recover causal effects, even when all confounders are measured, due to a particular type of selection bias. This bias can be explained by recognizing that the multinomial regression is equivalent to a series of logistic regressions; each compares cases of a certain subtype to the controls. We further explain how this bias arises using directed acyclic graphs and we demonstrate the potential magnitude of the bias by analysis of a hypothetical data set and by a simulation study.