  Background
  In a study performed on multiplex Multiple Sclerosis (MS) Sardinian families
to identify disease causing plasma proteins, application of Mendelian
Randomization (MR) methods encounters difficulties due to relatedness of
individuals, correlation between finely mapped genotype instrumental variables
(IVs) and presence of missing exposures.
  Method
  We specialize the method of Berzuini et al (2018) to deal with these
difficulties. The proposed method allows pedigree structure to enter the
specification of the outcome distribution via kinship matrix, and treating
missing exposures as additional parameters to be estimated from the data. It
also acknowledges possible correlation between instruments by replacing the
originally proposed independence prior for IV-specific pleiotropic effect with
a g-prior. Based on correlated (r2< 0.2) IVs, we analysed the data of four
candidate MS-causing proteins by using both the independence and the g-prior.
  Results
  95% credible intervals for causal effect for proteins IL12A and STAT4 lay
within the strictly negative real semiaxis, in both analyses, suggesting
potential causality. Those instruments whose estimated pleiotropic effect
exceeded 85% of total effect on outcome were found to act in trans. Analysis
via frequentist MR gave inconsistent results. Replacing the independence with a
g-prior led to smaller credible intervals for causal effect.
  Conclusions
  Bayesian MR may be a good way to study disease causation at a protein level
based on family data and moderately correlated instruments.
