# A statistical framework for GWAS of high dimensional phenotypes using summary statistics, with application to metabolite GWAS

arXiv: https://arxiv.org/abs/2303.10221 · HTML: https://mlsanity.com/paper/2303.10221/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 65 references that are in the map.
- First posted on arXiv 17 Mar 2023.

## Builds on (most cited first, 14 of 14)

- [Estimation of the number of spiked eigenvalues in a covariance matrix by bulk eigenvalue matching analysis](https://mlsanity.com/paper/2006.00436/) (2020)
- [Robust high dimensional factor models with applications to statistical machine learning](https://mlsanity.com/paper/1808.03889/) (2018)
- [Empirical Bayes PCA in high dimensions](https://mlsanity.com/paper/2012.11676/) (2020)
- [Permutation methods for factor analysis and PCA](https://mlsanity.com/paper/1710.00479/) (2017)
- [Empirical Bayes Matrix Factorization](https://mlsanity.com/paper/1802.06931/) (2018)
- [Confounder Adjustment in Multiple Hypothesis Testing](https://mlsanity.com/paper/1508.04178/) (2015)
- [Deterministic parallel analysis: An improved method for selecting factors and principal components](https://mlsanity.com/paper/1711.04155/) (2017)
- [Bi-cross-validation for factor analysis](https://mlsanity.com/paper/1503.03515/) (2015)
- [Accounting for unobserved covariates with varying degrees of estimability in high dimensional biological data](https://mlsanity.com/paper/1801.00865/) (2018)
- [Estimation and inference in metabolomics with non-random missing data and latent factors](https://mlsanity.com/paper/1909.02644/) (2019)
- [Fast Bayesian whole-brain fMRI analysis with spatial 3D priors](https://mlsanity.com/paper/1606.00980/) (2016)
- [Estimating and accounting for unobserved covariates in high dimensional correlated data](https://mlsanity.com/paper/1808.05895/) (2018)
- [Joint Analysis of Individual-level and Summary-level GWAS Data by Leveraging Pleiotropy](https://mlsanity.com/paper/1804.11011/) (2018)
- [Factor analysis in high dimensional biological data with dependent observations](https://mlsanity.com/paper/2009.11134/) (2020)

## Abstract (arXiv)

The recent explosion of genetic and high dimensional biobank and 'omic' data has provided researchers with the opportunity to investigate the shared genetic origin (pleiotropy) of hundreds to thousands of related phenotypes. However, existing methods for multi-phenotype genome-wide association studies (GWAS) do not model pleiotropy, are only applicable to a small number of phenotypes, or provide no way to perform inference. To add further complication, raw genetic and phenotype data are rarely observed, meaning analyses must be performed on GWAS summary statistics whose statistical properties in high dimensions are poorly understood. We therefore developed a novel model, theoretical framework, and set of methods to perform Bayesian inference in GWAS of high dimensional phenotypes using summary statistics that explicitly model pleiotropy, beget fast computation, and facilitate the use of biologically informed priors. We demonstrate the utility of our procedure by applying it to metabolite GWAS, where we develop new nonparametric priors for genetic effects on metabolite levels that use known metabolic pathway information and foster interpretable inference at the pathway level.