Introduction

• The MR-Egger model can consistently estimate the causal effect in the presence of pleiotropy given the InSIDE assumption holds (Bowden, Davey Smith, and Burgess (2015)).
• Schmidt and Dudbridge (2017) used weakly informative priors for the MR-Egger model. Other authors have investigated alternative prior distributions in MR analyses (Berzuini et al. (2018)).

The objectives of this research work are to:

• implement Bayesian estimation of IVW and MR-Egger models for a range of prior distributions in an R package.
• investigate model performance for a range of simulated pleiotropic scenarios and a range of priors.

Methods

• We implemented Bayesian estimation of the IVW and MR-Egger models in an R package mrbayes which automates fitting these models in the JAGS software.

• We provide the user with a choice of priors or let them specify their own.

• The MR-Egger model is written as; \[\frac{\Gamma_j}{\sigma_{y_j}^2} = \frac{\alpha}{{\sigma_{y_j}^2}} + \frac{\beta\gamma_j}{{\sigma_{y_j}^2}} + \varepsilon_j,\quad \varepsilon_j \sim N(0,\sigma^2)\]

• Uninformative Prior \[p(\alpha) \sim N(0,1000),\ p(\beta) \sim N(0,1000),\ p(\sigma) \sim U(10,10)\]

• Weakly Informative Prior \[p(\alpha) \sim N(0,1),\ p(\beta) \sim N(0,1),\ p(\sigma) \sim U(10,10)\]

• Pseudo-Horseshoe Prior\[p(\alpha) \sim N(0,1),\ p(\beta) \sim C(0,1),\ p(\sigma) \sim IG(0.5,0.5)\]

• Figure 1 shows the densities of the priors.

Results

Conclusion

• We present Bayesian estimation of the IVW and MR-Egger models in our mrbayes package.
• In future work we could implement Bayesian estimation of MVMR models and perform estimation using other programs such as Stan.

References

Figures and Tables

Figure 1: Density of alternative prior distributions implemented in our package.

Figure 2: Distribution of causal effect estimates under directional pleiotropy.

Figure 3: Scatter plot of genotype-disease versus genotype-phenotype estimates for the effect of BMI on insulin resistance.