Constrained Instruments and their Application to Mendelian Randomization with Pleiotropy

In Mendelian randomization (MR), genetic variants are used to construct instrumental variables, which enable inference about the causal relationship between a phenotype of interest and a response or disease outcome. However, standard MR inference requires several assumptions, including the assumption that the genetic variants only influence the response through the phenotype of interest. Pleiotropy occurs when a genetic variant has an effect on more than one phenotype; therefore, a pleiotropic genetic variant may be an invalid instrumental variable. Hence, a naive method for constructing instrumental variables may lead to biased estimation of the causality between the phenotype and the response. Here, we present a set of intuitive methods (Constrained Instrumental Variable methods [ CIV ]) to construct valid instrumental variables and perform adjusted causal effect estimation when pleiotropy exists, focusing particularly on the situation where pleiotropic phenotypes have been measured. Our approach includes an automatic and valid selection of genetic variants when building the instrumental variables. We also provide details of the features of many existing methods, together with a comparison of their performance in a large series of simulations. CIV methods performed consistently better than many comparators across four different pleiotropic violations of the MR assumptions. We analyzed data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) Mueller et al. (2005) to disentangle causal relationships of several biomarkers with AD progression. The results showed that CIV methods can provide causal effect estimates, as well as selection of valid instruments while accounting for pleiotropy.