1- Overview
This is a guide for an introductory analysis to 1) construct a polygenic risk score (PRS) using the base data (GWAS summary statistics, particularly with effect-sizes and P-values, generally publicly available) via a clumping and thresholding method (C + T); and 2) test the constructed PRS for prediction using the target data (PLINK binary data files and phenotype csv file). In general, it is the ‘user’ data).
2- Learning Objectives
- Apply quality control measures to base/target sample prior to PRS analysis;
- Perform PRS analysis (hands-on);
- Understand the graphs and outputs (hands-on)
3- Materials
Ideally for PRS analyses, you would be using the genome-wide genotype data. Here we use base data containing summary statistics and target data containing genotypes for chromosome 16 as an example to demonstrate the workflow for the prediction of simulated body mass index (BMI) data. The procedure described below will be the same for the genome-wide dataset. All the materials required for this workshop are attached here. Relevant materials for this workshop are as follows:
BMI_1kgph3_chr16_snps_summarystat.txt
3.1- Base Data
We will use as the base data part of GWAS Anthropometric 2015 BMI summary statistics ( https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4382211/), made available by the GIANT consortium and were extracted from their online portal
3.1.1- QC for Base data:
- Check SNPs Heritability: h2SNP>0.05
- LD Score Regression: https://github.com/bulik/ldsc (Bulik-Sullivan et al, Nature Genetics, 2015)
- SumHer: http://dougspeed.com/snp-heritability/ (Speed et al, Nature Genetics, 2020)
- The effect allele must be known. Both Base and Target datasets should have the same effect allele.
- Filter out SNPs with MAF < 0.01 and INFO < 0.8.
## BMI_1kgph3_chr16_snps_summarystat.txt:
# With the following columns: “SNP” = marker ID, “A1” = effect allele (could be minor allele if output from plink), “A2” = reference allele, “Freq1.Hapmap” = allele frequency according to Hapmap, “b” = effect estimate for the minor allele, “se” = standard error of the effect estimate, “p” = p-value, “N” = sample size
SNP A1 A2 Freq1.Hapmap b se p N
1 rs1000014 G A 0.8000 -0.0055 0.0049 0.2617 233462
2 rs1000047 C T 0.6917 0.0019 0.0040 0.6348 233959
3 rs1000077 C G 0.4833 0.0006 0.0038 0.8745 220681
4 rs1000078 A G 0.7000 -0.0031 0.0041 0.4496 232588
5 rs1000100 A T 0.4167 0.0006 0.0040 0.8808 233753
6 rs1000174 A G 0.3417 -0.0025 0.0052 0.6307 150418
Tip: The base data may come in different formats. For example, if marker IDs (rs IDs) are not available, we may have to derive them based on available chromosome and map positions. The effect estimate may come in the form of an odds ratio (OR), in which case we will calculate beta using the formula beta=ln(OR). It is also ideal to have the allele calls based on the positive strand. Make sure to identify the effect allele.
3.2- Target Data
Our target data for this tutorial consist of genotype data on the subset of European samples for chromosome 16 from the 1000 Genomes datasets in PLINK format. Phenotype consists of simulated BMI data. For demonstration purposes, the BMI in the target dataset was simulated randomly from a normal distribution with no reference to the genotype data.
Tip: Base and target data should share the same ancestry background.
3.2.1- QC for Target data:
- Check if your Target data is in the same genome build as Base data.
- Basic QC: e.g., geno >0.99, mind <0.02, HWE P>1x10-6, 3SD HET, MAF >0.01, INFO >0.8. Also, remove indels and multi-allelic SNPs.
- Avoid sample overlap, as well as a high degree of relatedness between individuals of Base and Target data.
- Check strand and allele calls
## 1kgph3_chr16.bed:
# binary plink pedigree genotype file; do not try to open this file
## 1kgph3_chr16.bim (as appearing in R):
# with 277,663 biallelic markers (SNPs or Ins/Del markers) – 6 columns without column names: “V1”=chromosome, “V2”=marker ID, “V3”=genetic distance, “V4”=chromosomal position in bp, “V5”=Allele1, “V6”=Allele2
V1 V2 V3 V4 V5 V6
1 16 rs185537431 0 60778 A G
2 16 rs377548396 0 62569 A G
3 16 rs368745239 0 66640 T G
4 16 rs187053456 0 70765 A C
5 16 rs193118147 0 70767 A G
6 16 rs201639477 0 75246 C CTTTTTTT
## 1kgph3_chr16.fam (as appearing in R):
# with 476 individuals – 6 columns without column names: “V1”=Family ID, “V2”=Individual ID, “V3”=Father ID, “V4”=Mother ID, “V5”=Sex (Male=1, Female=2), “V6”=Affected status (Yes=2, No=1, Unknown=-9)
V1 V2 V3 V4 V5 V6
1 HG00096 HG00096 0 0 1 -9
2 HG00097 HG00097 0 0 2 -9
3 HG00099 HG00099 0 0 2 -9
4 HG00101 HG00101 0 0 1 -9
5 HG00102 HG00102 0 0 2 -9
6 HG00103 HG00103 0 0 1 -9
## 1kgph3_dummybmi20200804.csv (as appearing in R):
# with the columns with column names: “V1”=Family ID, “V2”=Individual ID, “V3”=Father ID, “V4”=Mother ID, “V5”=Sex, “V6”=Affective status, “dummybmi”=phenotype of interest, “Sex” (male=1, female=0)
V1 V2 V3 V4 V5 V6 dummybmi sex
HG00096 HG00096 0 0 1 -9 13.42457034 1
HG00097 HG00097 0 0 2 -9 11.29648997 0
HG00099 HG00099 0 0 2 -9 10.98411446 0
HG00101 HG00101 0 0 1 -9 8.268308741 1
HG00102 HG00102 0 0 2 -9 11.1241505 0
3.3- Required Softwares
- PLINK 1.9 (http://www.cog-genomics.org/plink2/). Use the stable version (19 Oct 2020 (b6.21)).
- R (version 3.2.3+) (https://cran.r-project.org/)
4- Quality Control Checklist
The Base and Target data must be matching for the following items:
- SNP IDs (for this workshop, both base and target datasets have rsIDs)
- Chromosome and map positions (we can double-check base vs target datasets if that information is available)
- Allele 1 and Allele 2 calls
- Ambiguous SNPs to be excluded
- Allele 1 and allele 2 calls between Base and Target data – 4 scenarios:
- (i) perfect allele matches with same strand
- (ii) perfect allele matches with opposite strands
- (iii) switched allele 1 and allele 2 calls with same strand
- (iv) switched allele 1 and allele 2 calls with opposite strand
- (i) perfect allele matches with same strand
For the workshop, we are using simulated data (see above). For this dataset, we will only check strand and allele calls.
Tip: It is important to know the effect allele from the Base (GWAS summary stats) data to avoid misleading conclusions. Both Base and Target datasets must have the same effect allele.
We will remove strand-ambiguous SNPs (i.e. those with complementary alleles, either C/G or A/T SNPs) and duplicate SNPs (indicative of multiallelic markers) in both the Base and Target data. We will also resolve mismatched SNPs names between the two datasets. The unresolved, mismatching SNPs will be removed as well.
### merging base (GWAS summary stat) with target (GWAS) bim file to check strands and allele calls. The expected outputs for "nrow" are shown.
R --vanilla ## only if you are running R in your computer terminal
kg=read.table("1kgph3_chr16.bim",header=F)
bmi=read.table("BMI_1kgph3_chr16_snps_summarystat.txt",header=T)
nrow(kg) ##277,663
head(kg)
nrow(bmi) ##68,385
head(bmi)
bmikg=merge(bmi,kg,by.x="SNP",by.y="V2") # merging step
nrow(bmikg) ##68,385
head(bmikg)
Tip: If the SNPs do not have the same id between the target and base datasets, merge by chromosome, position (and alleles if the files include multi-allelic variants).
### To mark ambiguous G/C or A/T SNPs for removal
## let’s create a column (ambiguousSNPs) flagging the ambiguous SNPs as “1” in our merged file bmikg.
bmikg$ambiguousSNPs[bmikg$A1 == "A" & bmikg$A2 == "T"]<-1 bmikg$ambiguousSNPs[bmikg$A1 == "C" & bmikg$A2 == "G"]<-1 bmikg$ambiguousSNPs[bmikg$A1 == "G" & bmikg$A2 == "C"]<-1 bmikg$ambiguousSNPs[bmikg$A1 == "T" & bmikg$A2 == "A"]<-1 head(bmikg) ## ambiguousSNPs column with ambiguous markers marked as “1”, and non-ambiguous markers marked as “NA”
### To exclude ambiguous SNPs
bmikg1=bmikg[is.na(bmikg$ambiguousSNPs),] ## to keep only non-ambiguous SNPs nrow(bmikg1) ##55,752 non-unambiguous SNPs remaining
### Scenario (i): To find perfect allele matches between base GWAS summary statistics file and target GWAS genotype data (i.e., A1 (column “A1”) in GWAS summary statistics file is the same as A1 (column “V5”) in target GWAS data, and A2 (column “A2”) in base GWAS summary statistics file is the same as A2 (column “V6”) in target GWAS data) -- beta will be unchanged
bmikg1aa=bmikg1[as.character(bmikg1$A1) == bmikg1$V5 & as.character(bmikg1$A2) == bmikg1$V6,] nrow(bmikg1aa) ##28,842
### Scenario (ii): To find allele matches for flipped strand between base GWAS summary statistics file and target GWAS data -- beta will be unchanged
bmikg1ab=bmikg1[bmikg1$A1 == "A" & bmikg1$A2 == "C" & bmikg1$V5 == "T" & bmikg1$V6 == "G",] bmikg1ac=bmikg1[bmikg1$A1 == "A" & bmikg1$A2 == "G" & bmikg1$V5 == "T" & bmikg1$V6 == "C",] bmikg1ad=bmikg1[bmikg1$A1 == "C" & bmikg1$A2 == "A" & bmikg1$V5 == "G" & bmikg1$V6 == "T",] bmikg1ae=bmikg1[bmikg1$A1 == "C" & bmikg1$A2 == "T" & bmikg1$V5 == "G" & bmikg1$V6 == "A",] bmikg1af=bmikg1[bmikg1$A1 == "G" & bmikg1$A2 == "A" & bmikg1$V5 == "C" & bmikg1$V6 == "T",] bmikg1ag=bmikg1[bmikg1$A1 == "G" & bmikg1$A2 == "T" & bmikg1$V5 == "C" & bmikg1$V6 == "A",] bmikg1ah=bmikg1[bmikg1$A1 == "T" & bmikg1$A2 == "C" & bmikg1$V5 == "A" & bmikg1$V6 == "G",] bmikg1ai=bmikg1[bmikg1$A1 == "T" & bmikg1$A2 == "G" & bmikg1$V5 == "A" & bmikg1$V6 == "C",] bmikg1a=rbind(bmikg1aa,bmikg1ab,bmikg1ac,bmikg1ad,bmikg1ae,bmikg1af,bmikg1ag,bmikg1ah,bmikg1ai) # to combine all the datasets created above + bmikg1aa with non-ambiguous SNPs nrow(bmikg1a) ##28,854
### To add column “B” for the beta to be used in polygenic risk scoring (note: “b” is the original beta)
### B=b for SNPs with matching alleles above (beta will remain unchanged for Scenarios (i) and (ii))
bmikg1a$B=bmikg1a$b
### Scenario (iii): To find perfect allele switches between A1 and A2 (i.e., A1 in base GWAS summary statistics file is the same as A2 in target GWAS data, and vice versa) -- beta will have opposite sign
bmikg1ba=bmikg1[as.character(bmikg1$A1) == bmikg1$V6 & as.character(bmikg1$A2) == bmikg1$V5,] nrow(bmikg1ba) ##26,883
### Scenario (iv): To find flipped strands but perfect allele switches between A1 and A2 (i.e., A1 (column “A1”) in base GWAS summary statistics file is the same as the complementary allele for A2 (column “V6”) in target GWAS data, and vice versa) -- beta will have opposite sign
bmikg1bb=bmikg1[bmikg1$A1 == "A" & bmikg1$A2 == "C" & bmikg1$V5 == "G" & bmikg1$V6 == "T",] bmikg1bc=bmikg1[bmikg1$A1 == "A" & bmikg1$A2 == "G" & bmikg1$V5 == "C" & bmikg1$V6 == "T",] bmikg1bd=bmikg1[bmikg1$A1 == "C" & bmikg1$A2 == "A" & bmikg1$V5 == "T" & bmikg1$V6 == "G",] bmikg1be=bmikg1[bmikg1$A1 == "C" & bmikg1$A2 == "T" & bmikg1$V5 == "A" & bmikg1$V6 == "G",] bmikg1bf=bmikg1[bmikg1$A1 == "G" & bmikg1$A2 == "A" & bmikg1$V5 == "T" & bmikg1$V6 == "C",] bmikg1bg=bmikg1[bmikg1$A1 == "G" & bmikg1$A2 == "T" & bmikg1$V5 == "A" & bmikg1$V6 == "C",] bmikg1bh=bmikg1[bmikg1$A1 == "T" & bmikg1$A2 == "C" & bmikg1$V5 == "G" & bmikg1$V6 == "A",] bmikg1bi=bmikg1[bmikg1$A1 == "T" & bmikg1$A2 == "G" & bmikg1$V5 == "C" & bmikg1$V6 == "A",] bmikg1b=rbind(bmikg1ba,bmikg1bb,bmikg1bc,bmikg1bd,bmikg1be,bmikg1bf,bmikg1bg,bmikg1bh,bmikg1bi) nrow(bmikg1b) ##26,898
### NOTE: Need to check for allelic mismatches beyond those assessed in the steps above (same strands or flipped strands, same alleles or switched alleles): additional checks would include checking for INDELs (insertions/deletions) and non-matching alleles (not included in this workshop)
### HERE: our data have 0 SNPs with mismatching A1 and A2 between GWAS summary statistics and target GWAS data
### NOTE: there are 0 INDELs with mismatching A1 and A2 between Base GWAS summary stat and target GWAS data
nrow(bmikg1b)+nrow(bmikg1a) ##55,752
### B=-b for SNPs with switched alleles above (beta will have an opposite sign for Scenarios (iii) and (iv))
bmikg1b$B=0-bmikg1b$b
### ***NOTE: Use column “V5” as Allele1 & column “V6” as Allele2 & column “B” as the effect estimate***
bmikg2=rbind(bmikg1a,bmikg1b)
nrow(bmikg2) #55,752
head(bmikg2)
## Saving the base-cleaned-alleles file to be used later
write.table(bmikg2,"BMI_unambiguousSNPsposstrand-B_AllelesV5V6_20200226.txt",quote=F,sep='\t',col.names=T,row.names=F)
## Setting up and saving the file for clumping in the next step
bmikg2s=subset(bmikg2,select=c("SNP","p"))
colnames(bmikg2s)<-c("SNP","P")
write.table(bmikg2s,"BMI_SNPs_P_forclumping.txt",quote=F,sep='\t',col.names=T,row.names=F)
5- Calculation of PRS via clumping and thresholding
The following procedure is using the cleaned file generated above.
Tip: Effect sizes given as odds ratios (OR) will need to be converted to Beta (B) using the natural logarithm of the OR. In this way, the PRS can be computed using summation. (The effect estimates can be transformed from B back to OR afterward).
5.1- CLUMPING using PLINK
### The most commonly used method for computing PRS is clumping and thresholding (C+T). Before calculating PRS, the variants are first clumped, and variants that are weakly correlated (r2) with one another are retained. The clumping step prunes redundant correlated effects caused by linkage disequilibrium (LD) between variants. Thresholding will remove variants with a p-value larger than a chosen level of significance (default: 0.0001).
It requires 4 parameters: clump-p1=significance threshold of the index SNP, clump-p2=significance threshold of the tag/clumped SNP, clump-r2=LD threshold for clumping, clump-kb=threshold of physical distance for clumping in kb. Here, we are using the following parameters: clump-r2 = 0.1 and clump-kb = 250
plink --bfile 1kgph3_chr16 --clump-p1 1 --clump-p2 1 --clump-r2 0.10 --clump-kb 250 --clump BMI_SNPs_P_forclumping.txt --out 1kgph3_chr16_test_clumped_1 ## If you are using MAC, use the command below: ./plink --bfile 1kgph3_chr16 --clump-p1 1 --clump-p2 1 --clump-r2 0.10 --clump-kb 250 --clump BMI_SNPs_P_forclumping.txt --out 1kgph3_chr16_test_clumped_1
# The command above produces the output ".clumped"
In the commands below, we are combining the base-cleaned-alleles file (BMI_unambiguousSNPsposstrand-B_AllelesV5V6_20200226.txt) with SNPs retained after the clumping step.
## In R:
bmikg2=read.table("BMI_unambiguousSNPsposstrand-B_AllelesV5V6_20200226.txt",header=T)
clumped=read.table("1kgph3_chr16_test_clumped_1.clumped",header=T)
nrow(clumped)
bmikg3=merge(bmikg2,clumped,by="SNP",sort=F)
nrow(bmikg3) ##4651
5.2- THRESHOLDING using R
### As an example, we will use either (a) p-value threshold of 0.5, or (b) a range of p-value thresholds from base GWAS summary statistics to select SNPs for polygenic risk scoring in the target GWAS dataset
### Example (a) p=<0.5
bmikg3a=bmikg3[bmikg3$P<0.5,]
bmikg3a1=subset(bmikg3a,select=c("SNP","V5","B"))
nrow(bmikg3a) ##3254
# Renaming column headings from "SNP", "V5", and "B" to "SNP", "A1", and "Score"
colnames(bmikg3a1)<-c("SNP","A1","Score")
write.table(bmikg3a1,"1kgph3_chr16_test_clumped_1_threshold_5.raw",col.names=T,row.names=F,quote=F,sep='\t')
### Example (b) using a range of p-value thresholds in PLINK
#sample range list txt: The columns of this file are ‘Name of the threshold’, ‘Lower bound p-value’, and ‘Upper bound p-value’.
# In a text file, write:
0.001 0 0.001 0.05 0 0.05 0.1 0 0.1 0.2 0 0.2 0.3 0 0.3 0.4 0 0.4 0.5 0 0.5 1.0 0 1.0
#save as: range_list.txt
## writing input file for generating polygenic risk scores
bmikg3b=subset(bmikg3,select=c("SNP","V5","B"))
colnames(bmikg3b)<-c("SNP","A1","Score")
write.table(bmikg3b,"1kgph3_chr16_test_clumped_1_nothreshold.raw",col.names=T,row.names=F,quote=F,sep='\t')
## writing file for filtering based on p-values in the range_list.txt file above
bmikg3c=subset(bmikg3,select=c("SNP","P"))
write.table(bmikg3c,"1kgph3_chr16_test_clumped_1_nothreshold.snppvalues",col.names=T,row.names=F,quote=F,sep='\t')
5.3- GENERATING THE POLYGENIC RISK SCORES
### Example (a) p-value threshold of 0.5
plink --bfile 1kgph3_chr16 --score 1kgph3_chr16_test_clumped_1_threshold_5.raw --out 1kgph3_chr16_profile_5_20200226 ## If you are using MAC, use the command below: ./plink --bfile 1kgph3_chr16 --score 1kgph3_chr16_test_clumped_1_threshold_5.raw --out 1kgph3_chr16_profile_5_20200226
# The command above will generate one output file with extension "*.profile"
## 1kgph3_chr16_profile_5_20200226.profile:
## with columns: FID=Family ID, IID=Individual ID, PHENO=phenotype, CNT=number of SNPs used for scoring, CNT2=number of named (effect) alleles for each subject, SCORE=polygenic risk score for each subject
FID IID PHENO CNT CNT2 SCORE
HG00096 HG00096 -9 6508 1107 -2.34634e-05
HG00097 HG00097 -9 6508 1193 0.000309573
HG00099 HG00099 -9 6508 1156 3.56331e-05
HG00101 HG00101 -9 6508 1167 -4.76951e-05
HG00102 HG00102 -9 6508 1157 -3.64935e-05
### Example (b) using a range of p-value thresholds
plink --bfile 1kgph3_chr16 --score 1kgph3_chr16_test_clumped_1_nothreshold.raw --q-score-range range_list.txt 1kgph3_chr16_test_clumped_1_nothreshold.snppvalues --out 1kgph3_chr16_profile_20200226 ## If you are using MAC, use the command below: ./plink --bfile 1kgph3_chr16 --score 1kgph3_chr16_test_clumped_1_nothreshold.raw --q-score-range range_list.txt 1kgph3_chr16_test_clumped_1_nothreshold.snppvalues --out 1kgph3_chr16_profile_20200226
# The command above will generate eight output files with extension "*.profile"
## For example, 1kgph3_chr16_profile_20200226.0.001.profile:
## with columns: FID=Family ID, IID=Individual ID, PHENO=phenotype, CNT=number of SNPs used for scoring, CNT2=number of named (effect) alleles for each subject, SCORE=polygenic risk score for each subject
FID IID PHENO CNT CNT2 SCORE
HG00096 HG00096 -9 148 45 -0.000618919
HG00097 HG00097 -9 148 40 0.00219797
HG00099 HG00099 -9 148 44 0.00117297
HG00101 HG00101 -9 148 47 -0.00123784
HG00102 HG00102 -9 148 46 -0.00163041
6- Applications of PRS scores
6.1- REGRESSION ANALYSIS
## In R:
# Import the phenotype file
phen=read.csv("1kgph3_dummybmi20200804.csv", header=T)
head(phen)
# sex: male = 1, female =0
# import the PRS file output from plink
prs1=read.table("1kgph3_chr16_profile_5_20200226.profile",header=T) # this is output from Example (a) polygenic risk scoring with p-value threshold of 0.5
head(prs1)
nrow(prs1) ##476
# merge phenotype (dummybmi) and PRS files
prs1phen=merge(prs1,phen,by.x="FID",by.y="V1") write.csv(prs1phen,"test_clump_1_prs_5.csv",row.names=F)
# Regression analysis with quantitative outcome phenotype
prs1phen=read.csv("test_clump_1_prs_5.csv",header=T)
head(prs1phen)
lmprs<-lm(data=prs1phen, dummybmi~SCORE + sex)
summary(lmprs)
6.2- PLOTTING
## Histogram showing distribution of polygenic risk scores (shown for p-value threshold of 0.5 from Example (a))
pdf("Histogram_testscore_pT_5.pdf")
hist(prs1phen$SCORE, breaks=100, main = paste("Distribution of PRS scores (n =", length(prs1phen$SCORE), ")"))
dev.off()
## Scatterplot of BMI vs PRS (shown for p-value threshold of 0.5 from Example (a))
pdf("Scatterplot_dummybmi_vs_PRS_pT_5.pdf")
plot(prs1phen$SCORE,prs1phen$dummybmi)
abline(lm(prs1phen$dummybmi ~ prs1phen$SCORE), col = "red",
lty = 1, lwd = 1)
dev.off()
# Plots of prediction R-squared values vs p-value thresholds (for Example (b))
prs_files <- list.files(pattern = "1kgph3_chr16_profile_20200226.*.*.profile$");
prs_list <- lapply(prs_files, function(rr) read.table(rr, head=T))
r_squared<-NA
for (j in 1:length(prs_list)){
prs1phen=merge(prs_list[[j]] ,phen, by.x="FID", by.y="V1")
lmprs<-lm(data= prs1phen, dummybmi~SCORE + sex)
r_squared[j]<-summary(lmprs)$r.squared
}
p_threshold <- as.numeric(sapply(sapply(prs_files, function(rr) strsplit(rr, "_20200226*\\.")[[1]][[2]]), function(ee) strsplit(ee, ".profile")[[1]]))
## Lineplot of prediction R-squared values vs p-value thresholds
pdf("Lineplot_R-squared_vs_p-value_threshold.pdf")
plot(p_threshold, r_squared, xlab = "P-value threshold", ylab="Prediction R-squared")
lines(p_threshold, r_squared);
abline(v=p_threshold[which.max(r_squared)], col=2)
dev.off()
## Barplot of prediction R-squared values vs p-value thresholds -- colour gradient from blue for lowest R-squared value to red for highest R-squared value; legend showing R-squared values in the order of the p-value thresholds
rankfac <- rank(r_squared)
rbPal <- colorRampPalette(c('blue','red'))
Col <- rbPal(length(rankfac))[as.numeric(cut(rankfac,breaks = length(rankfac)))]
pdf("Barplot_R-squared_vs_p-value_threshold_bluetored.pdf")
barplot(r_squared, names.arg=p_threshold, xlab = "P-value threshold", ylab="Prediction R-squared",col=Col, legend=round(r_squared, digits=4), args.legend=list(title="R-squared"), xlim=c(0,12))
dev.off()
7- Additional resources for PRS analysis
Software for alternative PRS methods:
- PRSice (https://www.prsice.info/)
- LDhub (http://ldsc.broadinstitute.org/ldhub/)
- LDPred (https://github.com/bvilhjal/ldpred)
Base data:
- GWAS catalog (https://www.ebi.ac.uk/gwas/downloads/summary-statistics)
- Psychiatric Genomics Consortium (https://www.med.unc.edu/pgc/download-results/)
- GIANT Consortium online portal (http://portals.broadinstitute.org/collaboration/giant/index.php/GIANT_consortium_data_files)
- DIAGRAM (http://diagram-consortium.org/)
- Global Lipids Genetics Consortium (http://csg.sph.umich.edu/willer/public/lipids2013/)
Additional tutorial or guides:
- PRS tutorial (https://choishingwan.github.io/PRS-Tutorial/; Choi et al., 2020)
- General GWAS and PRS tutorial (https://github.com/MareesAT/GWA_tutorial/)
8- References
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