Background:In contemporary epidemiology,causal inference is the core of research.Therefore,Mendelian randomization(MR),which is based on the random allocation of alleles,has become increasingly popular among researchers.Most diseases develop and progress through a complex and systematic process that involves multiple key biological molecules and multi-dimensional biological interactions.The MR algorithm framework,which utilizes genetic variants as instrumental variables(IVs),provides important methodological directions for analyzing the association and causality between exposures and exposures,as well as between exposures and outcomes,and has been widely applied in the medical field.Traditional MR studies usually explore the causality between phenotypes and outcomes under a single exposure situation.However,existing methods more commonly extend MR to explore the causality between multiple exposures and outcomes,known as multivariable Mendelian randomization(MVMR).At the same time,for situations where there is a bidirectional relationship between exposures and outcomes,some directional and estimation methods of bidirectional Mendelian randomization(BI-MR)have been developed.However,these methods cannot be applied to multi-directional or multivariable reverse situations.Methods:In response to the bidirectional relationship between multiple variables in the real world,this study utilizes the BI-MR method and the MVMR method,combined with the basic theory of causality,to conduct the following research using a combination of theoretical derivation,statistical simulation research,and practical data analysis:(1)constructing a BI-MVMR graph model for bidirectional multivariable Mendelian randomization(BI-MVMR),proposing bidirectional multivariable instrumental variable(BI-MV-IV)three assumptions,and deriving the bias of causal effect estimation under different conditions of confounders,mediators,and colliders in three multivariable scenarios;(2)comparing the models under the three multivariable scenarios through systematic statistical simulation experiments and evaluating the feasibility and effectiveness of existing MVMR methods(MVMR-IVW,MVMR-Egger,MVMR-Robust,MVMR-PRESSO,and MVMR-Median)in estimating causal effects,using bias and standard error to evaluate the models;and(3)verifying the reliability of the conclusions through application study.This study explores the causal regulatory relationship between multiple exposures and outcomes between three glycemic factors(fasting glucose,HbA1c,and fasting insulin)and three cholesterol factors(HDL-C,LDL-C,and triglyceride).Results:(1)The theoretical demonstration results show that under the BI-MVMR framework,when all tools meet the assumptions,the causal effect of the main exposure on the outcome can be identified and obtained with an unbiased estimate.When BI-MV-IV3 is violated or BI-MV-IV2 and BI-MV-IV3 are violated simultaneously,the estimation of the causal effect between the exposure and outcome will have bias,which is caused by invalid tools.(2)The statistical simulation results show that under the BI-MVMR framework,when the assumptions are met,except for the MVMR-Egger method,all other methods can obtain unbiased estimates of the causal effect.When BI-MV-IV3 is violated,the bias of each method increases with the increase in reverse causality.In the three scenarios of confounders,mediators,and colliders,the MVMR-Median method and the MVMR-Robust method perform better.When BI-MV-IV2 and BI-MV-IV3 are violated,a comprehensive evaluation of all models indicates that the causal effect estimates obtained by the MVMR-Median method are better than those of other methods.(3)The application study show that there is a bidirectional relationship between triglyceride and HDL-C,and between triglyceride and LDL-C.In addition.HDL-C and HbA1c affect LDL-C,triglyceride and fasting glucose affect HbAlc.and HDL-C and fasting insulin affect fasting glucose.Conclusions:This study constructed a BI-MVMR model based on the basic theory of causal inference,combined with UVMR,MVMR,and BI-MR,and proposed three assumptions of BI-MV-IV to explore the impact and correction methods of bidirectional relationships on multi-variable models.The study applied the BI-MVMR model to investigate the bidirectional relationship between glucose and cholesterol.The main findings were as follows:(1)when there is a bidirectional relationship in the multi-variable model,if the BI-MV-IV three assumptions are satisfied,the causal effect of exposure on outcome can be identified and obtained without bias;if BI-MV-IV2 or BI-MV-IV3 assumption is not satisfied,invalid Ⅳ will cause bias in the estimation of causal effect,and the bias formula is derived.(2)In the three cases of satisfying or violating assumptions,considering confounders as collision,mediator,and confounders,comprehensive comparison of the existing five MVMR methods showed that the MVMR-Median method performed better.(3)The complex relationship between cholesterol and glucose was explained,and it was confirmed that effective management of triglyceride and glycated hemoglobin can help reduce insulin resistance.The importance of timely control of triglyceride and glycated hemoglobin to prevent diabetes,lipid metabolism abnormalities,and cardiovascular complications was emphasized. |