Use of instrumental variables in the analysis of generalized linear models in the presence of unmeasured confounding with applications to epidemiological research

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A major, often unstated, concern of researchers carrying out epidemiological studies of medical therapy is the potential impact on validity if estimates of treatment are biased due to unmeasured confounders. One technique for obtaining consistent estimates of treatment effects in the presence of unmeasured confounders is instrumental variables analysis (IVA). This technique has been well developed in the econometrics literature and is being increasingly used in epidemiological studies. However, the approach to IVA that is most commonly used in such studies is based on linear models, while many epidemiological applications make use of non-linear models, specifically generalized linear models (GLMs) such as logistic or Poisson regression. Here we present a simple method for applying IVA within the class of GLMs using the generalized method of moments approach. We explore some of the theoretical properties of the method and illustrate its use within both a simulation example and an epidemiological study where unmeasured confounding is suspected to be present. We estimate the effects of beta-blocker therapy on one-year all-cause mortality after an incident hospitalization for heart failure, in the absence of data describing disease severity, which is believed to be a confounder.