Bayesian Mendelian randomization testing of interval causal null hypotheses: ternary decision rules and loss function calibration

TL;DR

This paper introduces a Bayesian Mendelian Randomization method that uses a region of practical equivalence and ternary decision rules to improve reproducibility and interpretability of causal effect testing.

Contribution

It proposes a Bayesian framework with a region null hypothesis and ternary decision rules, enhancing causal inference reliability in MR analysis.

Findings

Method effectively quantifies evidence for causal effects.

Calibration via loss function improves decision accuracy.

Application demonstrates practical utility in obesity and myocardial infarction study.

Abstract

Our approach to Mendelian Randomization (MR) analysis is designed to increase reproducibility of causal effect "discoveries" by: (i) using a Bayesian approach to inference; (ii) replacing the point null hypothesis with a region of practical equivalence consisting of values of negligible magnitude for the effect of interest, while exploiting the ability of Bayesian analysis to quantify the evidence of the effect falling inside/outside the region; (iii) rejecting the usual binary decision logic in favour of a ternary logic where the hypothesis test may result in either an acceptance or a rejection of the null, while also accommodating an "uncertain" outcome. We present an approach to calibration of the proposed method via loss function, which we use to compare our approach with a frequentist one. We illustrate the method with the aid of a study of the causal effect of obesity on risk of juvenile myocardial infarction.