Econometric approaches to epidemiologic data: relating endogeneity and unobserved heterogeneity to confounding

The concepts of endogeneity and unobserved heterogeneity are well-known among econometricians. However, these issues are rarely addressed in epidemiologic studies. This paper explores these two concepts, their relationship to each other, and the implications for analysis in epidemiologic studies. An endogenous variable is defined as a predictor variable which is partly determined by factors within the model itself, while unobserved heterogeneity is conceptualized as a vector of missing variables acting through the error term. Under certain assumptions, the simultaneous existence of an endogenous variable and unobserved heterogeneity is shown to act in a manner analogous to confounding. Specifically, this occurs due to an association between the error term in the equation and the endogenous predictor variable. The accepted econometric solution to this problem is to replace the endogenous variable with an 'instrumental variable' which is not correlated with the error term and thus not susceptible to confounding. The validity of these concepts and of the proposed solution are discussed.