Inferring Linkage Disequilibrium blocks from genotypes
In adjclust: Adjacency-Constrained Clustering of a Block-Diagonal Similarity Matrix

# IMPORTANT: this vignette is not created if snpStats is not installed
if (!require("snpStats")) {
  knitr::opts_chunk$set(eval = FALSE)
}

Introduction

In this vignette we demonstrate the use of snpClust function in the adjclust package. snpClust performs adjacency-constrained hierarchical clustering of single nucleotide polymorphisms (SNPs), where the similarity between SNPs is defined by linkage disequilibrium (LD).

This function implements the algorithm described in [1]. It is an extension of the algorithm described in [3,4]. Denoting by $p$ the number of SNPs to cluster and assuming that the similarity between SNPs whose indices are more distant than $h$, its time complexity is $O(p (\log(p) + h))$, and its space complexity is $O(hp)$.

library("adjclust")

Loading and displaying genotype data

The beginning of this vignette closely follows the "LD vignette" of the SnpStats package [2]. First, we load genotype data.

data("ld.example", package = "snpStats")

We focus on the ceph.1mb data.

geno <- ceph.1mb[, -316]  ## drop one SNP leading to one missing LD value
p <- ncol(geno)
nSamples <- nrow(geno)
geno

These data are drawn from the International HapMap Project and concern 602 SNPs[^1] over a 1Mb region of chromosome 22 in sample of 90 Europeans.

We can compute and display the LD between these SNPs.

[^1]: We have dropped SNP rs2401075 because it produced a missing value due to the lack of genetic diversity in the considered sample.

ld.ceph <- snpStats::ld(geno, stats = "R.squared", depth = p-1)
image(ld.ceph, lwd = 0)

Adjacency-constrained Hierarchical Agglomerative Clustering

The snpClust function can handle genotype data as an input:

fit <- snpClust(geno, stats = "R.squared")

Note that due to numerical errors in the LD estimation, some of the estimated LD values may be slightly larger than 1. These values are rounded to 1 internally.

The above figure suggests that the LD signal is concentrated close to the diagonal. We can focus on a diagonal band with the bandwidth parameter h:

fitH <- snpClust(geno, h = 100, stats = "R.squared")
fitH

Output

The output of the snpClust is of class chac. In particular, it can be plotted as a dendrogram silently relying on the function plot.dendrogram:

plot(fitH, type = "rectangle", leaflab = "perpendicular")

Moreover, the output contains an element named merge which describes the successive merges of the clustering, and an element gains which gives the improvement in the criterion optimized by the clustering at each successive merge.

head(cbind(fitH$merge, fitH$gains))

Other types of input

In this section we show how the snpClust function can also be applied directly to LD values.

h <- 100
ld.ceph <- snpStats::ld(geno, stats = "R.squared", depth = h, symmetric = TRUE)
image(ld.ceph, lwd = 0)

Note that we have forced the snpStats::ld function to return a symmetric matrix. We can apply snpClust directly to this LD matrix (of class Matrix::dsCMatrix):

fitL <- snpClust(ld.ceph, h)

snpClust also handles inputs of class base::matrix:

gmat <- as(geno, "matrix")
fitM <- snpClust(geno, h, stats = "R.squared")

References

[1] Ambroise C., Dehman A., Neuvial P., Rigaill G., and Vialaneix N. (2019). Adjacency-constrained hierarchical clustering of a band similarity matrix with application to genomics. Algorithms for Molecular Biology, 14, 22.

[2] Clayton D. (2015). snpStats: SnpMatrix and XSnpMatrix classes and methods. R package version 1.20.0

[3] Dehman A., Ambroise C., Neuvial P. (2015). Performance of a blockwise approach in variable selection using linkage disequilibrium information. BMC Bioinformatics, 16, 148.

[4] Randriamihamison N., Vialaneix N., and Neuvial P. (2021). Applicability and interpretability of Ward's hierarchical agglomerative clustering with or without contiguity constraints. Journal of Classification, 38, 363–389.