Inferring Linkage Disequilibrium blocks from genotypes

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

## Loading required package: snpStats

## Loading required package: survival

## Loading required package: Matrix

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

## A SnpMatrix with  90 rows and  602 columns
## Row names:  NA06985 ... NA12892 
## Col names:  rs5993821 ... rs5747302

These data are drawn from the International HapMap Project and concern 602 SNPs¹ over a 1Mb region of chromosome 22 in sample of 90 Europeans.

We can compute and display the LD between these SNPs.

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")

## Warning in run.snpClust(x, h = h, stats = stats): Forcing the LD similarity to
## be smaller than or equal to 1

## Note: 135 merges with non increasing heights.

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")

## Warning in run.snpClust(x, h = h, stats = stats): Forcing the LD similarity to
## be smaller than or equal to 1

## Note: 133 merges with non increasing heights.

fitH

## 
## Call:
## snpClust(geno, h = 100, stats = "R.squared")
## 
## Cluster method   : snpClust 
## Number of objects: 602

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")

## Warning: 
## Detected reversals in dendrogram: mode = 'corrected', 'within-disp' or 'total-disp' might be more relevant.

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))

##      [,1] [,2]
## [1,]   -1   -2
## [2,] -255 -256
## [3,] -488 -489
## [4,] -487    3
## [5,] -486    4
## [6,] -234 -235

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)

## Note: forcing the diagonal of the LD similarity matrix to be 1

## Warning in run.snpClust(x, h = h, stats = stats): Forcing the LD similarity to
## be smaller than or equal to 1

## Note: 133 merges with non increasing heights.

snpClust also handles inputs of class base::matrix:

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

## Note: 133 merges with non increasing heights.

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.

Session information

sessionInfo()

## R version 4.4.1 (2024-06-14)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 22.04.5 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so;  LAPACK version 3.10.0
## 
## locale:
##  [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
##  [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
##  [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
## [10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   
## 
## time zone: UTC
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] adjclust_0.6.10 snpStats_1.54.0 Matrix_1.7-0    survival_3.6-4 
## 
## loaded via a namespace (and not attached):
##  [1] viridis_0.6.5            sass_0.4.9               utf8_1.2.4              
##  [4] lattice_0.22-6           digest_0.6.37            magrittr_2.0.3          
##  [7] evaluate_1.0.0           sparseMatrixStats_1.16.0 grid_4.4.1              
## [10] fastmap_1.2.0            jsonlite_1.8.9           gridExtra_2.3           
## [13] fansi_1.0.6              capushe_1.1.2            viridisLite_0.4.2       
## [16] scales_1.3.0             textshaping_0.4.0        jquerylib_0.1.4         
## [19] cli_3.6.3                rlang_1.1.4              munsell_0.5.1           
## [22] splines_4.4.1            cachem_1.1.0             yaml_2.3.10             
## [25] tools_4.4.1              colorspace_2.1-1         ggplot2_3.5.1           
## [28] BiocGenerics_0.50.0      vctrs_0.6.5              R6_2.5.1                
## [31] matrixStats_1.4.1        lifecycle_1.0.4          zlibbioc_1.50.0         
## [34] fs_1.6.4                 MASS_7.3-60.2            ragg_1.3.3              
## [37] pkgconfig_2.0.3          desc_1.4.3               dendextend_1.18.0       
## [40] pkgdown_2.1.1            pillar_1.9.0             bslib_0.8.0             
## [43] gtable_0.3.5             glue_1.8.0               Rcpp_1.0.13             
## [46] systemfonts_1.1.0        highr_0.11               xfun_0.48               
## [49] tibble_3.2.1             MatrixGenerics_1.16.0    knitr_1.48              
## [52] htmltools_0.5.8.1        rmarkdown_2.28           compiler_4.4.1

Shubham Chaturvedi, Pierre Neuvial, Nathalie Vialaneix