This github contains simulation codes of GRM, encGRM and encG-reg.

• Fig 1 Resolution for varying relatedness using GRM, encGRM and encG-reg.

• Fig 3 Sampling variance of GRM, encGRM and encG-reg in simulations.

• Fig S1 Heatmap presenting the role random matrix played in matrix multiplication.

• Fig S2 Validation for the sampling variance for GRM (assumption: binomial distribution).

We offered a user-friendly protocol for encG-reg.

This protocol can be automated, such as by a web server that coordinates the study.

There are four steps in total, where steps 1 and 3 are performed by each collaborator and steps 2 and 4 are performed by a central analyst.

We provide suggested commands for your possible reference, and your environment should have plink1.9, plink2.0 and R installed.

Set environmental variables (!!!!NEED TO BE MODIFIED!!!!)

Please replace YOUR_COHORT_ID with the Cohort ID.

Please replace YOUR_PREFIX with your plink bfile prefix.

user=*YOUR_COHORT_ID*
bfile=*YOUR_PREFIX*

Inclusion criteria:

(1) Autosome SNPs only;

(2) SNPs with minor allele frequency (MAF) > 0.05 only;

(3) SNPs with missing rate < 0.2 only.

Suggested plink command:

plink --bfile ${bfile} --autosome --snps-only --maf 0.05 --geno 0.2 --no-pheno --make-bed --out ${user}
plink --bfile ${user} --freq --out ${user}

We adopt one of the plink1.9 formats ".frq" plink1.9 formats:frq as a standard format for sharing summary data. ".frq" files include the following contents.

An example of 1KG-CHN.frq is:

Return *.frq to central site. To be a good citizen in this collaboration, the suggested name of *.frq file will be "YOUR_COHORT_ID.frq".

Upon the *.frq files received, central site identifies the shared SNPs across cohorts and choose the optimal SNP set, which will be used for randomization algorithm. As the genotypes are generated in their respective platforms, to make life easier central site excludes: palindromic bi-allelic loci, say A-T, G-C; strand-flipped loci, say A-G in one cohort but T-C in another.

To examine across-cohort quality control, we used CONVERGE data set as the reference control to reveal any possible mistake made in Step 1. This examination includes MAF density plot between CONVERGE and every data set from the collaborators, and plot special shift between major and minor alleles when MAF approaches 0.5.

We took the intersection of all SNP lists among all cohorts based on their SNP ID in *.frq files. In total, 1462 SNPs were in common among 12 cohorts of 1KG-CHN, UKB-CHN, CONVERGE, MESA, SBWCH, CAS1, CAS2, Fudan, Yikon1, Yikon2 and WBBC.

We conduct principal component analysis based on reported allele frequencies (fPCA) and use the population genetics Fst statistic to verify the genetic origin of each cohort (fStructure).

Central site determines m and k upon the survived SNPs. The number of shared SNPs are enough for identifying 1st-degree relatedness, we would offer a list of shared SNPs.

Central site sends GenerateRandMat.R, random seed, k, an SNP list, and 1KG-CHN binary plink format files to each collaborator.

This step is similar to generate risk profile score in genetic prediction. Although a routine profile scoring step is very unlikely misconducted alone, unfortunate systematic mistakes may creep in because of some discordant reference alleles across the cohorts. As foolproof verification, every collaborator will receive 1KG-CHN and merge into their own data Step 3.2.

Set environmental variables (!!!!NEED TO BE MODIFIED!!!!)

Again, please replace YOUR_COHORT_ID with the Cohort ID.

user=*YOUR_COHORT_ID*

Users are asked to generate an m-by-k matrix whose elements are sample from N(0,1/m)

Obtain the number of markers (m)

awk 'END{print NR}' Golden.snpA1 > Golden.m

This Rscript automatically reads parameters stored in Golden.m and Golden.k and generate Golden.key, an m-by-k matrix.

Rscript GenerateRandMat.R Golden

You are supposed to see a matrix like this

Combine key with SNPID and A1 alleles by columns.

paste -d "\t" Golden.snpA1 Golden.key > Golden.snpA1key

You are supposed to see a data table like this

First extract SNPs in your bfiles by plink.

awk '{print $1}' Golden.snpA1 > Golden.snp
plink --bfile ${user} --extract Golden.snp --make-bed --out ${user}.extract

Then merge 1KG-CHN with your bfiles into new plink files named Golden.merged

These files will be used in Step 3.3 plink2 "--score".

plink --bfile 1KG-CHN.extract --bmerge ${user}.extract --make-bed --out Golden.merged

Users are asked to encrypt their genotype matrix with the random matrix by plink2.0 and return the encrypted genotype matrix to central site.

Use plink2 "--score" to generate encrypted genotype matrix. (variance-standardize: genotypes are scaled by SNP)

k=`cat Golden.k`
plink2 --bfile Golden.merged --score Golden.snpA1key 1 2 variance-standardize --score-col-nums 3-$(($k+2)) --out Golden.${user}

Return Golden.${user}.sscore to central site.

We adopt one of the plink2.0 formats ".sscore" plink2.0 formats:sscore as a standard sharing format for sharing encrypted genotype data. ".sscore" files include the following contents.

First extract SNPs in your bfiles by plink.

awk '{print $1}' Golden.snpA1 > Golden.snp
plink --bfile ${user} --extract Golden.snp --make-bed --out ${user}.extract

Then merge 1KG-CHN with your bfiles into new plink files named Golden.merged.

These files will be used in Step 3.3 plink2 "--score".

plink --bfile 1KG-CHN.extract --bmerge ${user}.extract --make-bed --out Golden.merged

Users are asked to encrypt their genotype matrix with the same random matrix by plink2.0 and return the encrypted genotype matrix to central site.

Use plink2 "--score" to generate encrypted genotype matrix.

k=`cat Golden.k`
plink2 --bfile Golden.merged --score Golden.snpA1key 1 2 variance-standardize --score-col-nums 3-$(($k+2)) --out Golden.${user}

(variance-standardize: genotypes are scaled by SNP)

Return Golden.${user}.sscore to central site.

Cohort-wise comparison for overlapping relatives will be conducted by central site. A foolproof implementation in Step 3.2 leads to at least 1KG-CHN samples consistently identified as "overlap" between every pair of cohorts in Step 4. Looking forward other possible overlapping that may pop out as expected as unexpected.

Bingo!

Zhang Q-X, Liu T, Guo X, Zhen J, Yang M-y, Khederzadeh S, et al. (2024) Searching across-cohort relatives in 54,092 GWAS samples via encrypted genotype regression. PLoS Genet 20(1):e1011037. https://doi.org/10.1371/journal.pgen.1011037