Adjacency-constrained hierarchical clustering of a band similarity matrix with application to genomics

BACKGROUND

Genomic data analyses such as Genome-Wide Association Studies (GWAS) or Hi-C studies are often faced with the problem of partitioning chromosomes into successive regions based on a similarity matrix of high-resolution, locus-level measurements. An intuitive way of doing this is to perform a modified Hierarchical Agglomerative Clustering (HAC), where only adjacent clusters (according to the ordering of positions within a chromosome) are allowed to be merged. But a major practical drawback of this method is its quadratic time and space complexity in the number of loci, which is typically of the order of 10 4 to 10 5 for each chromosome.

RESULTS

By assuming that the similarity between physically distant objects is negligible, we are able to propose an implementation of adjacency-constrained HAC with quasi-linear complexity. This is achieved by pre-calculating specific sums of similarities, and storing candidate fusions in a min-heap. Our illustrations on GWAS and Hi-C datasets demonstrate the relevance of this assumption, and show that this method highlights biologically meaningful signals. Thanks to its small time and memory footprint, the method can be run on a standard laptop in minutes or even seconds.

AVAILABILITY AND IMPLEMENTATION

Software and sample data are available as an R package, adjclust, that can be downloaded from the Comprehensive R Archive Network (CRAN).

Correction to: Assessment of the efficacy of firocoxib (Previcox®) and grapiprant (Galliprant®) in an induced model of acute arthritis in dogs

The original article [1] contains two mistaken instances of the molecule 'fipronil' in the results. These should instead have stated 'firocoxib'.

Assessment of the efficacy of firocoxib (Previcox®) and grapiprant (Galliprant®) in an induced model of acute arthritis in dogs

Background

Non-steroidal anti-inflammatory drugs (NSAIDs) are an important tool in the management of canine osteoarthritis, with the most recent introduction into the category being grapiprant, a piprant that selectively targets the EP4 prostaglandin receptor. To date there have been no efficacy studies comparing grapiprant with other NSAIDs. A randomized, two-sequence, assessor-blinded study involving two separate experiments was undertaken to measure the potency and persistence of acute pain control over 24 h resulting from a single oral dose of either firocoxib (Previcox®) or grapiprant (Galliprant®) in an acute arthritis model.

Results

Force-plate derived lameness ratios (0, no force recorded on the plate; 1, normal force) for the untreated group remained at 0 for most post-arthritis induction (PAI) assessments in both experiments. Throughout Experiment 1, mean PAI lameness ratios of the firocoxib-treated group remained at or above 0.80. In the grapiprant-treated group, ratios were 0 at 5 and 7 h PAI (7 and 9 h post-treatment), and 0.16 at 10 h PAI (12 h post-treatment). For lameness ratios, relative to the firocoxib group, the control and grapiprant group ratios were significantly lower at each PAI assessment (p ≤ 0.026 and p < 0.001, respectively), except at 1.5 h PAI at which acute pain was still not installed in untreated control dogs. In Experiment 2 the mean lameness ratios for the control group were 0 at 3, 5 and 7 h PAI, and in the grapiprant group at 5, 7 and 10 h PAI (i.e., 19, 21, and 24 h post-treatment). In the firocoxib group the lowest mean lameness ratio of 0.36 occurred at 3 h PAI (i.e. 17 h post-treatment). Except at 1.5 and 3 h PAI (i.e. 15.5 and 17 h post-treatment), due to the needed time for pain to install in the untreated control dogs, the lameness ratio differences between the firocoxib and both the control and grapiprant groups were significant at all assessments (p ≤ 0.033 for both groups). No significant differences were detected between the grapiprant and control groups in either experiment.

Conclusions

Firocoxib treatment prior to induction of arthritis in dogs resulted in a high level of analgesia from the first post-treatment assessment at 1.5 h through 24 h post-treatment. The reduction in lameness provided by firocoxib was consistently superior to that provided by grapiprant, which was not significantly different from untreated controls.

Performance of a blockwise approach in variable selection using linkage disequilibrium information

Background

Genome-wide association studies (GWAS) aim at finding genetic markers that are significantly associated with a phenotype of interest. Single nucleotide polymorphism (SNP) data from the entire genome are collected for many thousands of SNP markers, leading to high-dimensional regression problems where the number of predictors greatly exceeds the number of observations. Moreover, these predictors are statistically dependent, in particular due to linkage disequilibrium (LD).

We propose a three-step approach that explicitly takes advantage of the grouping structure induced by LD in order to identify common variants which may have been missed by single marker analyses (SMA). In the first step, we perform a hierarchical clustering of SNPs with an adjacency constraint using LD as a similarity measure. In the second step, we apply a model selection approach to the obtained hierarchy in order to define LD blocks. Finally, we perform Group Lasso regression on the inferred LD blocks. We investigate the efficiency of this approach compared to state-of-the art regression methods: haplotype association tests, SMA, and Lasso and Elastic-Net regressions.

Results

Our results on simulated data show that the proposed method performs better than state-of-the-art approaches as soon as the number of causal SNPs within an LD block exceeds 2. Our results on semi-simulated data and a previously published HIV data set illustrate the relevance of the proposed method and its robustness to a real LD structure. The method is implemented in the R package BALD (Blockwise Approach using Linkage Disequilibrium), available from http://www.math-evry.cnrs.fr/publications/logiciels.

Conclusions

Our results show that the proposed method is efficient not only at the level of LD blocks by inferring well the underlying block structure but also at the level of individual SNPs. Thus, this study demonstrates the importance of tailored integration of biological knowledge in high-dimensional genomic studies such as GWAS.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0556-6) contains supplementary material, which is available to authorized users.