Instrumental Variables And The Trouble With Analyses Of Mixtures

Abstract

Introduction: The analysis of health effects of exposure mixtures is a critically important issue in human epidemiology, and increasing effort is being devoted to establishing methods to analyze exposure mixtures in epidemiological studies. Instrumental variables are a statistical tool that can be extremely useful in causal inference. Instrumental variables are variables (Z) that are associated with exposure (A) but not associated with outcome (Y) except through exposure (A). If the assumptions hold, an instrumental variable (Z) can be used to estimate causal effects of A on Y by eliminating confounding bias of A→Y even from unmeasured confounders (U). Recently, however, it has been shown that in a simple model of the association between A and Y, conditioning on Z amplifies bias from unmeasured confounders U. We argue that in datasets of exposure mixtures, some components can act as instrumental variables, and therefore, in some analyses, amplify bias from confounders. Methods: Through the use of Directed Acyclic Graphs (DAGs) we describe instrumental variables, imperfect instrumental variables (Z that are related to Y other than through A), and illustrate how in some cases components of mixtures can act as instrumental variables. Results: Approaches to the analysis of mixtures that involve regressing the outcome on several components of the mixture simultaneously, can amplify bias in the effect estimates of other components of the mixture. This problem can persist even if some components of the mixture are imperfect instrumental variables. The bias amplification gets worse with stronger correlation between mixture components, and with more mixture components in the model that act as (even imperfect) instrumental variables. Conclusions: In designing approaches to the analysis of exposure mixtures in epidemiological studies, consideration of possible bias amplification from conditioning on (even imperfect) instrumental variables needs to be carefully considered.