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In the era of big data, univariate models have widely been used as a workhorse tool for quickly producing marginal estimators; and this is true even when in a high‐dimensional dense setting, in which many features are "true," but weak signals. Genome‐wide association studies (GWAS) epitomize this type of setting. Although the GWAS marginal estimator is popular, it has long been criticized for ignoring the correlation structure of genetic variants (i.e., the linkage disequilibrium [LD] pattern). In this paper, we study the effects of LD pattern on the GWAS marginal estimator and investigate whether or not additionally accounting for the LD can improve the prediction accuracy of complex traits. We consider a general high‐dimensional dense setting for GWAS and study a class of ridge‐type estimators, including the popular marginal estimator and the best linear unbiased prediction (BLUP) estimator as two special cases. We show that the performance of GWAS marginal estimator depends on the LD pattern through the first three moments of its eigenvalue distribution. Furthermore, we uncover that the relative performance of GWAS marginal and BLUP estimators highly depends on the ratio of GWAS sample size over the number of genetic variants. Particularly, our finding reveals that the marginal estimator can easily become near‐optimal within this class when the sample size is relatively small, even though it ignores the LD pattern. On the other hand, BLUP estimator has substantially better performance than the marginal estimator as the sample size increases toward the number of genetic variants, which is typically in millions. Therefore, adjusting for the LD (such as in the BLUP) is most needed when GWAS sample size is large. We illustrate the importance of our results by using the simulated data and real GWAS. [ABSTRACT FROM AUTHOR]

Polygenic risk scores (PRS) have gained substantial attention for complex traits prediction in genome‐wide association studies (GWAS). Motivated by the polygenic model of complex traits, we study the statistical properties of PRS under the high‐dimensional but sparsity free setting where the triplet (n,p,m)→(∞,∞,∞)$(n,p,m) \rightarrow (\infty , \infty , \infty)$ with n,p,m$n, p, m$ being the sample size, the number of assayed single‐nucleotide polymorphisms (SNPs), and the number of assayed causal SNPs, respectively. First, we derive asymptotic results on the out‐of‐sample (prediction) R‐squared for PRS. These results help understand the widespread observed gap between the in‐sample heritability (or partial R‐squared due to the genetic features) estimate and the out‐of‐sample R‐squared for most complex traits. Next, we investigate how features should be selected (e.g., by a p‐value threshold) for constructing optimal PRS. We reveal that the optimal threshold depends largely on the genetic architecture underlying the complex trait and the sample size of the training GWAS, or the m/n$m/n$ ratio. For highly polygenic traits with a large m/n$m/n$ ratio, it is difficult to separate causal and null SNPs and stringent feature selection in principle often leads to poor PRS prediction. We numerically illustrate the theoretical results with intensive simulation studies and real data analysis on 33 complex traits with a wide range of genetic architectures in the UK Biobank database. [ABSTRACT FROM AUTHOR]