Penalized-regression-based multimarker genotype analysis of Genetic Analysis Workshop 17 data

Abstract

Testing for association between multiple markers and a phenotype can not only capture untyped causal variants in weak linkage disequilibrium with nearby typed markers but also identify the effect of a combination of markers. We propose a sliding window approach that uses multimarker genotypes as variables in a penalized regression. We investigate a penalty with three separate components: (1) a group least absolute shrinkage and selection operator (LASSO) that selects multimarker genotypes in a gene to be included in or excluded from the model, (2) an allele-sharing penalty that encourages multimarker genotypes with similar alleles to have similar coefficients, and (3) a penalty that shrinks the size of coefficients while performing model selection. The penalized likelihood is minimized with a cyclic coordinate descent algorithm, allowing quick coefficient estimation for a large number of markers. We compare our method to single-marker analysis and a gene-based sparse group LASSO on the Genetic Analysis Workshop 17 data for quantitative trait Q2. We found that all of the methods were underpowered to detect the simulated rare causal variants at the low false-positive rates desired in association studies. However, the sparse group LASSO on multi-marker genotypes seems to provide some advantage over the sparse group LASSO applied to single SNPs within genes, giving further evidence that there may be an advantage to modeling combinations of rare variant alleles over modeling them individually.

Multiple Regression Methods Show Great Potential for Rare Variant Association Tests

“…Others addressed the question of simultaneous modelling across multiple regions or genes, combining methods such as LASSO or PLS first at the gene level, and then across genes [13] , [15] . A few publications described innovative approaches specifically developed for the sequencing context: Ayers et al [17] built a LASSO with three custom penalties encouraging different aspects of shrinkage; Luo et al [20] combined LASSO with local linear embedding. Each of these papers featured a different multiple regression method.…”

Fine‐Mapping Additive and Dominant SNP Effects Using Group‐LASSO and Fractional Resample Model Averaging

“…[], Ayers et al. [], Ayers and Cordell [], or Larson and Schaid []. In this case, a given procedure would be applied in full to multiple independent fractional resamples, with each such resample defined through a reweighting of the likelihood component (as in Equation ); the results of each application would then be aggregated in the manner described for Equation .…”

“…Our association model focuses on grouped effects for single SNPs but it could be extended to consider different types of grouped effects, such as differential effects of local haplotype combinations, structural variants, or combinations of rare variants within a gene or LD block. For the last of these, our FReMA framework could also be used to provide model-averaged inference for existing single-solution rare variant selection procedures such as those of Zhou et al [2010], Ayers et al [2011], Ayers and Cordell [2013], or Larson and Schaid [2014]. In this case, a given procedure would be applied in full to multiple independent fractional resamples, with each such resample defined through a reweighting of the likelihood component (as in Equation (2)); the results of each application would then be aggregated in the manner described for Equation (7).…”

Correction: Multiple Regression Methods Show Great Potential for Rare Variant Association Tests

“…However, for the analysis of rare genetic variation, such approaches have only recently been explored. There were several groups at the GAW17 workshop in 2010 who implemented feature extraction or penalization methods, using a wide variety of different approaches [13][14][15][16][17][18], and a few other publications have appeared recently using such methods (e.g. [19][20][21]).…”