Collider Bias Correction for Multiple Covariates in GWAS Using Robust Multivariable Mendelian Randomization

This repository contains the data for the paper "Collider Bias Correction for Multiple Covariates in GWASUsing Robust Multivariable Mendelian Randomization". The file names indicate the corresponding simulation set up or real data example. Simulation data is in spreadsheet. Real data application results are in text files. In the spreadsheets of simulations, sheet name indicates the specific simulation set up. For example, in the file "simulation_correlated_SNPs_30%_invalid_IVs.xlsx", sheet "p_2=1, rho=0" indicates thesimulation when p_2=1 and rho=0. In each file, column names indicate the MVMR method used to obtain the result. For example: In the files of real data applcation: The abbreviation "mPC" refers to metabolomic principle components. beta_no_correction: the SNP effect estimate without bias correction. beta_cml or beta_MVMR_cml: the standard error of SNP effect estimate after the bias correction of MVMR-cML. SE_UVMR_cml: the standard error of SNP effect estimate after the bias correction of UVMR-cML. p_value_Egger or p_value_MVMR_Egger: the p-value of SNP effect estimate after the bias correction of MVMR-Egger regression. In the files of simulation, column names follow the same style. For MVMR-cML, there are two columns of mean standard errors: Mean_SE_cml1: the mean standard error obtained with Equation (14) in paper.Mean_SE_cml2: the mean standard error obtained with Delta method in supplementary.Correspondingly:Type_I_error_or_Power_cml1: the type-I error or power obtained by Mean_SE_cml1.Type_I_error_or_Power_cml2: the type-I error or power obtained by Mean_SE_cml2. The GWAS data of metabolomic PCs is also available. The column names follows the plink output file. The detailed explanations are available at https://www.cog-genomics.org/plink/2.0/formats#glm_linear