Principal Component Analysis

Data

Let us use a subsetted version of the 1000 Genomes project data we provide. Some quality control has already been done; otherwise, you can use snp_plinkQC().

bedfile <- download_1000G("data")

Relatedness

First, let us detect all pairs of related individuals.

plink2 <- download_plink2("data")
rel <- snp_plinkKINGQC(
  plink2.path = plink2,
  bedfile.in = bedfile,
  thr.king = 2^-4.5,
  make.bed = FALSE,
  ncores = nb_cores()
)
str(rel)

## 'data.frame':    31 obs. of  8 variables:
##  $ FID1   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ ID1    : chr  "HG00120" "HG00240" "HG00542" "HG00595" ...
##  $ FID2   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ ID2    : chr  "HG00116" "HG00238" "HG00475" "HG00584" ...
##  $ NSNP   : int  1664852 1664852 1664852 1664852 1664852 1664852 1664852 1664852 1664852 1664852 ...
##  $ HETHET : num  0.111 0.1105 0.1024 0.101 0.0992 ...
##  $ IBS0   : num  0.0333 0.0367 0.0302 0.037 0.0367 ...
##  $ KINSHIP: num  0.0821 0.068 0.0854 0.0541 0.0535 ...

Principal Component Analysis (PCA)

We then compute PCA without using the related individuals. Function bed_autoSVD() should take care of Linkage Disequilibrium (LD).

(obj.bed <- bed(bedfile))

## A 'bed' object with 2490 samples and 1664852 variants.

ind.rel <- match(c(rel$IID1, rel$IID2), obj.bed$fam$sample.ID)  # /!\ use $ID1 instead with old PLINK
ind.norel <- rows_along(obj.bed)[-ind.rel]

obj.svd <- bed_autoSVD(obj.bed, ind.row = ind.norel, k = 20,
                       ncores = nb_cores())

##
## Phase of clumping (on MAC) at r^2 > 0.2.. keep 392665 variants.
## Discarding 0 variant with MAC < 10.
##
## Iteration 1:
## Computing SVD..
## 679 outlier variants detected..
## 7 long-range LD regions detected..
##
## Iteration 2:
## Computing SVD..
## 0 outlier variant detected..
##
## Converged!

Outlier sample detection

Then, we look at if there are individual outliers.

prob <- bigutilsr::prob_dist(obj.svd$u, ncores = nb_cores())
S <- prob$dist.self / sqrt(prob$dist.nn)

ggplot() +
  geom_histogram(aes(S), color = "#000000", fill = "#000000", alpha = 0.5) +
  scale_x_continuous(breaks = 0:5 / 5, limits = c(0, NA)) +
  scale_y_sqrt(breaks = c(10, 100, 500)) +
  theme_bigstatsr() +
  labs(x = "Statistic of outlierness", y = "Frequency (sqrt-scale)")

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Warning: Removed 1 rows containing missing values (geom_bar).

plot_grid(plotlist = lapply(7:10, function(k) {
  plot(obj.svd, type = "scores", scores = 2 * k - 1:0, coeff = 0.6) +
    aes(color = S) +
    scale_colour_viridis_c()
}), scale = 0.95)

plot_grid(plotlist = lapply(7:10, function(k) {
  plot(obj.svd, type = "scores", scores = 2 * k - 1:0, coeff = 0.6) +
    aes(color = S > 0.5) +  # threshold based on histogram
    scale_colour_viridis_d()
}), scale = 0.95)

PCA without outlier

We recompute PCA without outliers, starting with the previous set of variants kept (we can therefore skip the initial clumping step).

ind.row <- ind.norel[S < 0.5]
ind.col <- attr(obj.svd, "subset")
obj.svd2 <- bed_autoSVD(obj.bed, ind.row = ind.row,
                        ind.col = ind.col, thr.r2 = NA,
                        k = 20, ncores = nb_cores())

##
## Skipping clumping.
## Discarding 0 variant with MAC < 10.
##
## Iteration 1:
## Computing SVD..
## 22 outlier variants detected..
## 1 long-range LD region detected..
##
## Iteration 2:
## Computing SVD..
## 0 outlier variant detected..
##
## Converged!

Verification

plot(obj.svd2)

plot(obj.svd2, type = "loadings", loadings = 1:20, coeff = 0.4)

plot(obj.svd2, type = "scores", scores = 1:20, coeff = 0.4)

Project remaining individuals

PCs <- matrix(NA, nrow(obj.bed), ncol(obj.svd2$u))
PCs[ind.row, ] <- predict(obj.svd2)

proj <- bed_projectSelfPCA(obj.svd2, obj.bed,
                           ind.row = rows_along(obj.bed)[-ind.row],
                           ncores = 1) # useless -> too few individuals
PCs[-ind.row, ] <- proj$OADP_proj

plot(PCs[ind.row, 7:8], pch = 20, xlab = "PC7", ylab = "PC8")
points(PCs[-ind.row, 7:8], pch = 20, col = "blue")

References