TY - JOUR

T1 - Estimating structural mean models with multiple instrumental variables using the generalised method of moments

AU - Clarke, Paul

AU - Palmer, Thomas Michael

AU - Windmeijer, Frank

PY - 2015

Y1 - 2015

N2 - Instrumental variables analysis using genetic markers as instrumentsis now a widely used technique in epidemiology and biostatistics. Assingle markers tend to explain only a small proportion of phenotypic variation,there is increasing interest in using multiple genetic markers to obtainmore precise estimates of causal parameters. Structural mean models(SMMs) are semiparametric models that use instrumental variables to identifycausal parameters. Recently, interest has started to focus on using thesemodels with multiple instruments, particularly for multiplicative and logisticSMMs. In this paper we show how additive, multiplicative and logisticSMMs with multiple orthogonal binary instrumental variables can be estimatedefficiently in models with no further (continuous) covariates, usingthe generalised method of moments (GMM) estimator. We discuss how theHansen J-test can be used to test for model misspecification, and how standardGMM software routines can be used to fit SMMs. We further show thatmultiplicative SMMs, like the additive SMM, identify a weighted average oflocal causal effects if selection is monotonic. We use these methods to reanalysea study of the relationship between adiposity and hypertension usingSMMs with two genetic markers as instruments for adiposity. We find strongeffects of adiposity on hypertension.

AB - Instrumental variables analysis using genetic markers as instrumentsis now a widely used technique in epidemiology and biostatistics. Assingle markers tend to explain only a small proportion of phenotypic variation,there is increasing interest in using multiple genetic markers to obtainmore precise estimates of causal parameters. Structural mean models(SMMs) are semiparametric models that use instrumental variables to identifycausal parameters. Recently, interest has started to focus on using thesemodels with multiple instruments, particularly for multiplicative and logisticSMMs. In this paper we show how additive, multiplicative and logisticSMMs with multiple orthogonal binary instrumental variables can be estimatedefficiently in models with no further (continuous) covariates, usingthe generalised method of moments (GMM) estimator. We discuss how theHansen J-test can be used to test for model misspecification, and how standardGMM software routines can be used to fit SMMs. We further show thatmultiplicative SMMs, like the additive SMM, identify a weighted average oflocal causal effects if selection is monotonic. We use these methods to reanalysea study of the relationship between adiposity and hypertension usingSMMs with two genetic markers as instruments for adiposity. We find strongeffects of adiposity on hypertension.

U2 - 10.1214/14-STS503

DO - 10.1214/14-STS503

M3 - Journal article

VL - 30

SP - 96

EP - 117

JO - Statistical Science

JF - Statistical Science

SN - 0883-4237

IS - 1

ER -