Wittenburg, D. | Search bioRxiv

bioRxiv2020

seagull: lasso, group lasso and sparse-group lasso regularisation for linear regression models via proximal gradient descent

Statistical analyses of biological problems in life sciences often lead to high-dimensional linear models. To solve the corresponding system of equations, penalisation approaches are often the methods of choice. They are especially useful in case of multicollinearity which appears if the number of explanatory variables exceeds the number of observations or for some biological reason. Then, the model goodness of fit is penalised by some suitable function of interest. Prominent examples are the lasso, group lasso and sparse-group lasso. Here, we offer a fast and numerically cheap implementation of these operators via proximal gradient descent. The grid search for the penalty parameter is realised by warm starts. The step size between consecutive iterations is determined with backtracking line search. Finally, the package produces complete regularisation paths. Availability and implementationseagull is an R package that is freely available on the Comprehensive R Archive Network (CRAN; https://CRAN.R-project.org/package=seagull; vignette included). The source code is available on https://github.com/jklosa/seagull. Contactwittenburg@fbn-dummerstorf.de

bioinformatics↗

bioRxiv2019

Design of Experiments for Fine-Mapping Quantitative Trait Loci in Livestock Populations

Single nucleotide polymorphisms (SNPs) which capture a significant impact on a trait can be identified with genome-wide association studies. High linkage disequilibrium (LD) among SNPs makes it difficult to identify causative variants correctly. Thus, often target regions instead of single SNPs are reported. Sample size has not only a crucial impact on the precision of parameter estimates, it also ensures that a desired level of statistical power can be reached. We study the design of experiments for fine-mapping of signals of a quantitative trait locus in such a target region. A multi-locus model allows to identify causative variants simultaneously, to state their positions more precisely and to account for existing dependencies. Based on the commonly applied SNP-BLUP approach, we determine the z-score statistic for locally testing non-zero SNP effects and investigate its distribution under the alternative hypothesis. This quantity employs the theoretical instead of observed dependence between SNPs; it can be set up as a function of paternal and maternal LD for any given population structure. We simulated multiple paternal half-sib families and considered a target region of 1 Mbp. A bimodal distribution of estimated sample size was observed, particularly if more than two causative variants were assumed. The median of estimates constituted the final proposal of optimal sample size; it was consistently less than sample size estimated from single-SNP investigations which was used as a baseline approach. The second mode pointed to inflated sample sizes and could be explained by blocks of varying linkage phases leading to negative correlations between SNPs. Optimal sample size increased almost linearly with number of signals to be identified but depended much stronger on the assumption on heritability. For instance, three times as many samples were required if heritability was 0.1 compared to 0.3. These results enable the resource-saving design of future experiments for fine-mapping of candidate variants in structured and unstructured populations.

genetics↗