Bayesian Mendelian Randomization identifies disease causing proteins via pedigree data, partially observed exposures and correlated instruments
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.