Exercises using packages bigsnpr and bigstatsr
Florian Privé
April 18, 2019
Source:vignettes/exo.Rmd
exo.RmdIn this document, I show how to use some of the features of packages {bigsnpr} and {bigstatsr}. Note that many functions used here come from package {bigstatsr} and could therefore be used on other data encoded as matrix-like (outside of the field of genotype data).
Get data
Download data
and unzip files. I store those files in a directory called
"tmp-data" here.
You can see there how I generated these data from the 1000 Genomes project.
Read from the PLINK files
## Loading required package: bigstatsr
# Read from bed/bim/fam, it will create new files.
snp_readBed("tmp-data/public-data.bed")## [1] "C:\\Users\\au639593\\OneDrive - Aarhus universitet\\Desktop\\bigsnpr\\tmp-data\\public-data.rds"
# Attach the "bigSNP" object in R session
obj.bigSNP <- snp_attach("tmp-data/public-data.rds")
# See how it looks like
str(obj.bigSNP, max.level = 2, strict.width = "cut")## List of 3
## $ genotypes:Reference class 'FBM.code256' [package "bigstatsr"] with 16 ..
## ..and 26 methods, of which 12 are possibly relevant:
## .. add_columns, as.FBM, bm, bm.desc, check_dimensions,
## .. check_write_permissions, copy#envRefClass, initialize,
## .. initialize#FBM, save, show#envRefClass, show#FBM
## $ fam :'data.frame': 559 obs. of 6 variables:
## ..$ family.ID : chr [1:559] "EUR_GBR" "EUR_GBR" "EUR_GBR" "EUR_GBR" ...
## ..$ sample.ID : chr [1:559] "HG00096" "HG00097" "HG00099" "HG00100" ...
## ..$ paternal.ID: int [1:559] 0 0 0 0 0 0 0 0 0 0 ...
## ..$ maternal.ID: int [1:559] 0 0 0 0 0 0 0 0 0 0 ...
## ..$ sex : int [1:559] 1 2 2 2 1 2 1 2 2 1 ...
## ..$ affection : int [1:559] 1 2 1 1 1 1 2 1 2 1 ...
## $ map :'data.frame': 130816 obs. of 6 variables:
## ..$ chromosome : int [1:130816] 2 2 2 2 2 2 2 2 2 2 ...
## ..$ marker.ID : chr [1:130816] "rs13400442" "rs7594567" "rs7597758" "..
## ..$ genetic.dist: int [1:130816] 0 0 0 0 0 0 0 0 0 0 ...
## ..$ physical.pos: int [1:130816] 18506 21833 22398 28228 32003 32005 36..
## ..$ allele1 : chr [1:130816] "C" "G" "T" "A" ...
## ..$ allele2 : chr [1:130816] "T" "C" "C" "G" ...
## - attr(*, "class")= chr "bigSNP"
# Get aliases for useful slots
G <- obj.bigSNP$genotypes
CHR <- obj.bigSNP$map$chromosome
POS <- obj.bigSNP$map$physical.pos
y <- obj.bigSNP$fam$affection - 1
sex <- obj.bigSNP$fam$sex
pop <- obj.bigSNP$fam$family.ID
NCORES <- nb_cores()
# Check some counts for the 10 first SNPs
big_counts(G, ind.col = 1:10)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## 0 504 468 421 483 476 420 380 383 478 389
## 1 48 69 107 66 73 124 136 135 70 133
## 2 7 22 31 10 10 15 43 41 11 37
## <NA> 0 0 0 0 0 0 0 0 0 0What you must do
You need to
Explore the data
Assess population structure of the data
Find the variables associated with the disease status (
y)-
Predict the disease status using the following indices as training/test sets:
# Divide the indices in training/test sets set.seed(1) ind.train <- sample(nrow(G), 400) ind.test <- setdiff(rows_along(G), ind.train)
For this, you can use whatever tools you want because the data is quite small. In the following section, I give some (scalable) solutions using using packages {bigstatsr} and {bigsnpr}.
Solution using {bigstatsr} and {bigsnpr}
Population structure: Principal Component Analysis
Let us compute first principal components of the scaled genotype matrix:
# Compute partial SVD (10 PCs by default) using random projections
# big_scale() computes means and standard deviations for scaling
svd <- big_randomSVD(G, big_scale(), ncores = NCORES)
# Scree plot
plot(svd)
## Warning: package 'ggplot2' was built under R version 4.2.3
# Loadings (effects of each variable for each PC)
plot(svd, type = "loadings", loadings = 1:10, coeff = 0.4)
Looking at the loadings, we can see that the PCA captures some variation due to large correlation between variables. To learn more about this possible pitfall, please look at this vignette.
Association: Genome-Wide Association Study (GWAS)
# Association of each variable of `G` with `y` (adjusting for 10 PCs)
gwas <- big_univLogReg(G, y, covar.train = svd$u, ncores = NCORES)
# Histogram of p-values
plot(gwas)
## Warning: Removed 117734 rows containing missing values or values outside the scale
## range (`geom_point()`).
# Manhattan plot
snp_manhattan(gwas, CHR, POS, npoints = 20e3) +
geom_hline(yintercept = -log10(5e-8), color = "red")
Polygenic Risk Score (PRS)
with Clumping and Thresholding (C+T)
\[\rm{PRS}_i = \sum_{\substack{j \in S_\text{clumping} \\ p_j~<~p_T}} \hat\beta_j \cdot G_{i,j}~,\]
where \(\hat\beta_j\) (\(p_j\)) are the effect sizes (p-values) estimated from the GWAS and \(G_{i,j}\) is the allele count (genotype) for individual \(i\) and SNP \(j\).
sumstats <- bigreadr::fread2("tmp-data/public-data-sumstats.txt")
lpval <- -log10(sumstats$p)
ind.keep <- snp_clumping(G, CHR, ind.row = ind.train, S = lpval, infos.pos = POS, ncores = 3)
THR <- seq_log(1, 8, length.out = 20)
prs <- snp_PRS(G, sumstats$beta[ind.keep], ind.keep = ind.keep,
lpS.keep = lpval[ind.keep], thr.list = THR)
# Learn the optimal threshold on the training set
aucs <- apply(prs[ind.train, ], 2, AUC, target = y[ind.train])
plot(THR, aucs, xlab = "-log10(p-value)", ylab = "AUC", pch = 20)
## [1] 0.6689111(TODO: ADD SCT)
with Penalized Logistic Regression (PLR)
\[\arg\!\min_{\beta_0,~\beta}(\lambda, \alpha)\left\{ \underbrace{ -\sum_{i=1}^n \left( y_i \log\left(p_i\right) + (1 - y_i) \log\left(1 - p_i\right) \right) }_\text{Loss function} + \underbrace{ \lambda \left((1-\alpha)\frac{1}{2}\|\beta\|_2^2 + \alpha \|\beta\|_1\right) }_\text{Penalization} \right\}\]
where
\(p_i=1/\left(1+\exp\left(-(\beta_0 + x_i^T\beta)\right)\right)\)
\(x\) is denoting the genotypes and covariables (e.g. principal components),
\(y\) is the disease status we want to predict,
\(\lambda\) is a regularization parameter that needs to be determined and
\(\alpha\) determines relative parts of the regularization \(0 \le \alpha \le 1\).
If you want to learn more about our implementation of PLR, please look at this paper.
# Penalized logistic regression for many alphas and lambdas
mod <- big_spLogReg(G, y[ind.train], ind.train, covar.train = svd$u[ind.train, ],
K = 5, alphas = 10^(-(0:4)), ncores = NCORES)
# Plot regularization paths (from high lambda to low lambda)
# for each validation set (color) and each alpha (facet)
plot(mod)## Warning: The `guide` argument in `scale_*()` cannot be `FALSE`. This was deprecated
## in ggplot2 3.3.4.
## ℹ Please use "none" instead.
## ℹ The deprecated feature was likely used in the bigstatsr package.
## Please report the issue at
## <https://github.com/privefl/bigstatsr/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
# Get summaries of models
summary(mod)## # A tibble: 5 × 9
## alpha power_adaptive power_scale validation_loss intercept beta nb_var
## <dbl> <dbl> <dbl> <dbl> <dbl> <list> <int>
## 1 0.0001 0 1 0.557 -1.41 <dbl> 67876
## 2 0.001 0 1 0.550 -1.94 <dbl> 16008
## 3 0.01 0 1 0.547 -2.16 <dbl> 2928
## 4 0.1 0 1 0.545 -2.30 <dbl> 722
## 5 1 0 1 0.543 -2.40 <dbl> 398
## # ℹ 2 more variables: message <list>, all_conv <lgl>
# Get the predictions for the test set
pred <- predict(mod, G, ind.test, covar.row = svd$u[ind.test, ])
# Assess the Area Under the ROC Curve
AUC(pred, y[ind.test])## [1] 0.7148903