Bayesian Mendelian randomization with an interval causal null hypothesis: ternary decision rules and loss function...

Area of Science:

• Statistical Genetics
• Causal Inference
• Biostatistics

Background:

• Traditional Mendelian Randomization (MR) often relies on point null hypotheses.
• Testing for practical equivalence to no effect is crucial in many causal inference scenarios.
• Existing Bayesian MR frameworks may not adequately handle interval null hypotheses.

Purpose of the Study:

• To enhance the Bayesian Mendelian Randomization (MR) framework by incorporating interval null causal hypotheses.
• To define
• no effect" based on a user-specified region of practical equivalence (ROPE).
• To develop a robust statistical approach for hypothesis testing in MR with interval nulls.

Main Methods:

• Extension of the Berzuini et al. Bayesian MR framework.
• Utilizing Bayesian posterior odds for hypothesis testing within the ROPE.
• Employing mixture priors for the causal effect parameter.
• Leveraging Markov chain Monte Carlo (MCMC) with weighted importance resampling for efficient inference.
• Implementing a ternary decision logic for uncertain outcomes.
• Calibration via loss function.

Main Results:

• A novel method for Bayesian MR with interval null hypotheses is presented.
• The approach provides simulation-consistent estimates of posterior odds and Bayes factors.
• Efficient computational strategies using MCMC and resampling are demonstrated.
• The method allows for uncertain test decisions when evidence is inconclusive.
• Illustrative analysis of obesity's causal effect on juvenile myocardial infarction.

Conclusions:

• The enhanced Bayesian MR framework offers a more nuanced approach to causal inference by considering practical equivalence.
• The proposed methodology improves the decision-making process in MR studies, especially when dealing with interval null hypotheses.
• This work provides a valuable tool for researchers investigating causal relationships in complex biological systems.