  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.
