2019/11/22 by Bingxin Zhao, Hongtu Zhu, Zhao, Bingxin +1 · 6 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Biology #Combinatorics #Estimator #FOS: Computer and information sciences #Genetic Associations and Epidemiology #Genetic Mapping and Diversity in Plants and Animals #Genetic and phenotypic traits in livestock #Genetics #Genome-wide association study #Lambda #Mathematics #Methodology (stat.ME) #Omega #Physics #Sample size determination #Statistics #stat.ME
paper · pdf · doi:10.48550/arxiv.1911.10142
published in arXiv (Cornell University) (Cornell University)
arxiv created 2019/11/22 · openalex publication_date 2019/11/22 · arxiv updated 2019/11/25 · openalex created_date 2019/12/05 · openalex updated_date 2026/08/06
Marginal association summary statistics have attracted great attention in statistical genetics, mainly because the primary results of most genome-wide association studies (GWAS) are produced by marginal screening. In this paper, we study the prediction accuracy of marginal estimator in dense (or sparsity free) high-dimensional settings with (n,p,m) → ∞, m/n → γ∈ (0,∞), and p/n → ω∈ (0,∞). We consider a general correlation structure among the p features and allow an unknown subset m of them to be signals. As the marginal estimator can be viewed as a ridge estimator with regularization parameter λ→ ∞, we further investigate a class of ridge-type estimators in a unifying framework, including the popular best linear unbiased prediction (BLUP) in genetics. We find that the influence of λ on out-of-sample prediction accuracy heavily depends on ω. Though selecting an optimal λ can be important when p and n are comparable, it turns out that the out-of-sample R2 of ridge-type estimators becomes near-optimal for any λ∈ (0,∞) as ω increases. For example, when features are independent, the out-of-sample R2 is always bounded by 1/ω from above and is largely invariant to λ given large ω (say, ω>5). We also find that in-sample R2 has completely different patterns and depends much more on λ than out-of-sample R2. In practice, our analysis delivers useful messages for genome-wide polygenic risk prediction and computation-accuracy trade-off in dense high-dimensions. We numerically illustrate our results in simulation studies and a real data example.