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February 2015 Estimating Structural Mean Models with Multiple Instrumental Variables Using the Generalised Method of Moments
Paul S. Clarke, Tom M. Palmer, Frank Windmeijer
Statist. Sci. 30(1): 96-117 (February 2015). DOI: 10.1214/14-STS503

Abstract

Instrumental variables analysis using genetic markers as instruments is now a widely used technique in epidemiology and biostatistics. As single markers tend to explain only a small proportion of phenotypic variation, there is increasing interest in using multiple genetic markers to obtain more precise estimates of causal parameters. Structural mean models (SMMs) are semiparametric models that use instrumental variables to identify causal parameters. Recently, interest has started to focus on using these models with multiple instruments, particularly for multiplicative and logistic SMMs. In this paper we show how additive, multiplicative and logistic SMMs with multiple orthogonal binary instrumental variables can be estimated efficiently in models with no further (continuous) covariates, using the generalised method of moments (GMM) estimator. We discuss how the Hansen J-test can be used to test for model misspecification, and how standard GMM software routines can be used to fit SMMs. We further show that multiplicative SMMs, like the additive SMM, identify a weighted average of local causal effects if selection is monotonic. We use these methods to reanalyse a study of the relationship between adiposity and hypertension using SMMs with two genetic markers as instruments for adiposity. We find strong effects of adiposity on hypertension.

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Paul S. Clarke. Tom M. Palmer. Frank Windmeijer. "Estimating Structural Mean Models with Multiple Instrumental Variables Using the Generalised Method of Moments." Statist. Sci. 30 (1) 96 - 117, February 2015. https://doi.org/10.1214/14-STS503

Information

Published: February 2015
First available in Project Euclid: 4 March 2015

zbMATH: 1332.62408
MathSciNet: MR3317756
Digital Object Identifier: 10.1214/14-STS503

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.30 • No. 1 • February 2015
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