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Background: Mendelian randomization (MR) is a useful approach to causalinference from observational studies when randomised controlled trials are notfeasible. However, study heterogeneity of two association studies required inMR is often overlooked. When dealing with large studies, recently developedBayesian MR is limited by its computational expensiveness. Methods: Weaddressed study heterogeneity by proposing a random effect Bayesian MR modelwith multiple exposures and outcomes. For large studies, we adopted a subsetposterior aggregation method to tackle the problem of computation. Inparticular, we divided data into subsets and combine estimated subset causaleffects obtained from the subsets". The performance of our method was evaluatedby a number of simulations, in which part of exposure data was missing.Results: Random effect Bayesian MR outperformed conventional inverse-varianceweighted estimation, whether the true causal effects are zero or non-zero. Datapartitioning of large studies had little impact on variations of the estimatedcausal effects, whereas it notably affected unbiasedness of the estimates withweak instruments and high missing rate of data. Our simulation results indicatethat data partitioning is a good way of improving computational efficiency, forlittle cost of decrease in unbiasedness of the estimates, as long as the samplesize of subsets is reasonably large. Conclusions: We have further advancedBayesian MR by including random effects to explicitly account for studyheterogeneity. We also adopted a subset posterior aggregation method to addressthe issue of computational expensiveness of MCMC, which is important especiallywhen dealing with large studies. Our proposed work is likely to pave the wayfor more general model settings, as Bayesian approach itself renders greatflexibility in model constructions.

Bayesian Mendelian randomization with study heterogeneity and data partitioning for large studies