  We expand Mendelian Randomization (MR) methodology to deal with randomly
missing data on either the exposure or the outcome variable, and furthermore
with data from nonindependent individuals (eg components of a family). Our
method rests on the Bayesian MR framework proposed by Berzuini et al (2018),
which we apply in a study of multiplex Multiple Sclerosis (MS) Sardinian
families to characterise the role of certain plasma proteins in MS causation.
The method is robust to presence of pleiotropic effects in an unknown number of
instruments, and is able to incorporate inter-individual kinship information.
Introduction of missing data allows us to overcome the bias introduced by the
(reverse) effect of treatment (in MS cases) on level of protein. From a
substantive point of view, our study results confirm recent suspicion that an
increase in circulating IL12A and STAT4 protein levels does not cause an
increase in MS risk, as originally believed, suggesting that these two proteins
may not be suitable drug targets for MS.
