Approaches to estimate bidirectional causal effects using Mendelian randomization with application to body mass index and fasting glucose

Mendelian randomization (MR) is an epidemiological framework using genetic variants as instrumental variables (IVs) to examine the causal effect of exposures on outcomes. Statistical methods based on unidirectional MR (UMR) are widely used to estimate the causal effects of exposures on outcomes in observational studies. To estimate the bidirectional causal effects between two phenotypes, investigators have naively applied UMR methods separately in each direction. However, bidirectional causal effects between two phenotypes create a feedback loop that biases the estimation when UMR methods are naively applied. To overcome this limitation, we proposed two novel approaches to estimate bidirectional causal effects using MR: BiRatio and BiLIML, which are extensions of the standard ratio, and limited information maximum likelihood (LIML) methods, respectively. We compared the performance of the two proposed methods with the naive application of UMR methods through extensive simulations of several scenarios involving varying numbers of strong and weak IVs. Our simulation results showed that when multiple strong IVs are used, the proposed methods provided accurate bidirectional causal effect estimation in terms of median absolute bias and relative median absolute bias. Furthermore, compared to the BiRatio method, the BiLIML method provided a more accurate estimation of causal effects when weak IVs were used. Therefore, based on our simulations, we concluded that the BiLIML should be used for bidirectional causal effect estimation. We applied the proposed methods to investigate the potential bidirectional relationship between obesity and diabetes using the data from the Multi-Ethnic Study of Atherosclerosis cohort. We used body mass index (BMI) and fasting glucose (FG) as measures of obesity and type 2 diabetes, respectively. Our results from the BiLIML method revealed the bidirectional causal relationship between BMI and FG in across all racial populations. Specifically, in the White/Caucasian population, a 1 kg/m2 increase in BMI increased FG by 0.70 mg/dL (95% confidence interval [CI]: 0.3517- 1.0489; p = 8.43×10-5), and 1 mg/dL increase in FG increased BMI by 0.10 kg/m2 (95% CI: 0.0441-0.1640; p = 6.79×10-4). Our study provides novel findings and quantifies the effect sizes of the bidirectional causal relationship between BMI and FG. However, further studies are needed to understand the biological and functional mechanisms underlying the bidirectional pathway.