Simple Sum 2

Simple Sum 2 is a summary statistics-based colocalization tool that extends the frequently implemented Simple Sum method (Gong et al, 2019) to a flexible procedure (SS2) that integrates GWAS summary statistics with eQTL summary statistics across any number of gene-by-tissue pairs, is applicable when there are overlapping participants in the two studies and can be applied to GWAS summary statistics computed through meta-analysis, even with related individuals.

• The sampledata folder provides all the sample datasets for conducting the Simple Sum 2 colocalization analysis, including the GWAS and eQTL files for two genes: MUC20 and MUC4 in tissue human nasal epithelial.

• SS2_functions.R contains all the R functions for conducting the SS2 test which has been implemented in a web-based tool: LocusFocus, with an additional R option for using the chi-square statsitics as eQTL evidence measure.

• Commands to run Simple Sum 2 for one GWAS/eQTL combination:

  1. Obtain the GWAS p-values from the GWAS summary statistics file: gwas_file=read.table(file='sampledata/GWAS_file_gene_MUC4_tissue_Human_nasal_epithelial.txt )',header=T) gwas_pvalue=gwas_file$ALL.FIXED.PVAL

  2. Obtain the eQTL p-values from the eQTL summary statistics file: eQTL_file=read.table(file='sampledata/eqtl_file_gene_MUC4_tissue_Human_nasal_epithelial.txt',header=T) eqtl_pvalue=eqtl_file$pval

  3. Obtain the covariance matrix for the GWAS and eQTL summary statistics, respectively: cov_GWAS=as.matrix(read.table(file='sampledata/ldGWAS_file_gene_MUC4_tissue_Human_nasal_epithelial.txt',header=F)) cov_eQTL=as.matrix(read.table(file='sampledata/ldeqtl_file_gene_MUC4_tissue_Human_nasal_epithelial.txt',header=F))

  4. Run SS2 colocalization analysis: stage1(eqtl_pvalue,cov_eQTL) produces the p-value for the stage 1 test. stage2(eqtl_pvalue,gwas_pvalue,cov_GWAS,use_evidence='log10p') produces the p-value for the stage 2 test by using -log10(eQTL p) as eQTL evidence measure. The p-value calculated by using the chi-square statistics as eQTL evidence measure can be done by specifying use_evidence='Tsquare'.

• SS2_sampledataset_code.R implements the above commands by calling functions in SS2_functions.R.

• ld_function.R provides the R functions for calculating the covariance matrix of Z-scores obtained from meta-analysis with either independent or related samples.

  • R function getcov_Zmeta produces the covariance of Z-scores from a meta-analysis according to the equation:

    

    : the Z-score for SNP obtained from a meta-analysis with sub-studies. : the Z-score for SNP from study . : the weight for SNP from study . : the total number of SNPs at the locus.

  • Input variables for getcov_Zmeta:

    1. weightmatrix: a matrix, where the th element is the weight . An example is provided in the file weightmatrix.txt
    2. var_subgroup: a list with elements, where each element is the covariance matrix of Z-scores for a particular study. An example is provided in the file 13subgroup_ld.Rdata.

  • R function get_subgroup_var calculates the covariance of Z-scores for studies that contain related individuals, according to equation:

    

  • Input variables for get_subgroup_var:

    1. G: a genotype matrix
    2. X: a matrix of covariates (i.e. sex and age), including the intercept.
    3. Sigma( ): a matrix contains information for sample relatedness. When the Sigma is unknown, the user could obtain the estimated Sigma by using R package nlme or GMMAT.

  • Examples for using R function get_subgroup_var and get_subgroup_var are provided in the Rscript ld_function.R.