A Meta-analysis Method Integrating Multiple Mendelian Randomization Studies

Background:Meta-analysis is a research method that comprehensively collects all relevant studies,carries out rigorous evaluation and analysis one by one,and then uses quantitative or qualitative synthesis methods to process the data to reach comprehensive conclusions.In a meta-analysis.researchers always focus on the size of the aggregate effect.Meta-analysis has been widely used in Genome-Wide Association Studies(GWAS).The main purpose of meta-analysis is to aggregate GWAS data from multiple databases and improve the efficiency and accuracy of the estimation of effects between genetic variants and traits.Further,more loci related to traits were found.Different from meta-analysis.Mendelian Randomization(MR)is a method of instrumental variable analysis.The genetic variant is used as an instrumental variable to detect and quantify the causal relationship of interest.This method groups the study population according to whether the genetic variant is carried.It will not be interfered with by confounding and the interference of reverse causation,which effectively makes up for the shortcomings of traditional observational research methods.In MR Studies,two-sample MR studies are the most common.At the same time,in order to use more genetic variants and a larger sample size for analysis,the current two-sample MR studies mostly take the GWAS meta-analysis results of multiple databases as the exposure/outcome data and then use traditional MR methods to calculate the causal effect between exposure and outcome.Only a few studies have conducted a meta-analysis of MR results from different databases to obtain a final estimate of the causal effect,and there was no meta-analysis method for MR results with correlation.Methods:In our study,aiming at the problems of how to make full use of the biological information contained in each database of multiple exposure and/or multiple outcome GWAS databases and the possible correlation between multiple MR results,we proposed a method with higher accuracy than the current MR studies.Our study separately considered two meta-analysis models of fixed-effect model and random-effect model,and the basic theory of the two-sample MR structure,through theoretical derivation,statistical simulation,and application analysis to conduct the following research:(1)Our study first proposed the identification and estimation formulas of causal effect and corresponding variance estimation formulas under the two meta-analysis models respectively through theoretical derivation,and then proposed the MM(MM*)statistic to construct the MR-Meta method.(2)The statistical simulation was further designed to traverse the size of sample size,causal effect,and horizontal pleiotropy respectively while other parameters were fixed and unchanged.The MR-Meta method proposed in this study was evaluated according to the bias,accuracy,and mean square error(MSE)of causal effect estimation.At the same time,it was compared with the traditional MR methods using the GWAS meta-analysis results.(3)Finally,we illustrated these approaches with an application to the association between systolic blood pressure,diastolic blood pressure,and type 2 diabetes in European population.(4)The proposed methods were implemented in R functions.Results:(1)Theoretical derivation results:In the fixed-effect model and random-effect model,the weight matrix used by the MR-Meta method to estimate the causal effect was constructed based on the multiple correlated IVW results,and then the expression of the causal effect estimation and its variance was derived.Finally,the variance obtained by MR-Meta was compared with the variance analyzed by the IVW method using the GWAS meta-analysis result,and the MM(MM*)statistic was proposed.When the MM(MM*)statistic was greater than 1,the MR-Meta method could obtain the estimate of the causal effect with higher precision.(2)Simulation results:With other parameters fixed as initial values,the simulation results of sample size,causal effect,and horizontal pleiotropy respectively traversed showed that the MR-Meta method under the two meta-analysis models proposed in this study could obtain asymptotically unbiased estimates of the causal effect of exposure on the outcome,and the estimates were relatively stable.At the same time,with the increase of the sample size of the database,the bias,standard error,and MSE of the estimation of causal effect would decrease.When the MM(MM*)statistic was greater than 1.the standard error and MSE obtained by the MR-Meta method were smaller than those obtained by traditional MR methods.(3)Application results:Application results suggested that the risk of type 2 diabetes increases with the increase of systolic and diastolic blood pressure in the European population.Conclusions:Based on the basic theory of causal inference,this study explored how to conduct a meta-analysis of MR results from multiple exposure and outcome GWAS databases,and constructed MR-Meta methods under the fixed-effect model and the random-effect model respectively.(1)Under both models,the MR-Meta method could obtain unbiased estimates of causal effects.With the increase in the sample size of a database,the bias,standard error,and MSE of causal effect estimation would decrease.However,with the increasing causal effect or horizontal pleiotropy,bias,standard error,and MSE would all increase to a certain extent.When the MM(MM*)statistic was greater than 1,the standard error and MSE obtained by the MR-Meta method were smaller than those obtained by other MR Methods.(2)The MR-Meta method proposed in our study was used to explore the causal effect of systolic and diastolic blood pressure on type 2 diabetes in a European population,and it was found that the risk of type 2 diabetes increases with the increase of systolic and diastolic blood pressure.