Eigenvalue significance testing for genetic association

A SIMPLE AND FLEXIBLE TEST OF SAMPLE EXCHANGEABILITY WITH APPLICATIONS TO STATISTICAL GENOMICS

In scientific studies involving analyses of multivariate data, basic but important questions often arise for the researcher: Is the sample exchangeable, meaning that the joint distribution of the sample is invariant to the ordering of the units? Are the features independent of one another, or perhaps the features can be grouped so that the groups are mutually independent? In statistical genomics, these considerations are fundamental to downstream tasks such as demographic inference and the construction of polygenic risk scores. We propose a non-parametric approach, which we call the V test, to address these two questions, namely, a test of sample exchangeability given dependency structure of features, and a test of feature independence given sample exchangeability. Our test is conceptually simple, yet fast and flexible. It controls the Type I error across realistic scenarios, and handles data of arbitrary dimensions by leveraging large-sample asymptotics. Through extensive simulations and a comparison against unsupervised tests of stratification based on random matrix theory, we find that our test compares favorably in various scenarios of interest. We apply the test to data from the 1000 Genomes Project, demonstrating how it can be employed to assess exchangeability of the genetic sample, or find optimal linkage disequilibrium (LD) splits for downstream analysis. For exchangeability assessment, we find that removing rare variants can substantially increase the p -value of the test statistic. For optimal LD splitting, the V test reports different optimal splits than previous approaches not relying on hypothesis testing. Software for our methods is available in R (CRAN: flintyR) and Python (PyPI: flintyPy).

An eigenvalue ratio approach to inferring population structure from whole genome sequencing data

Inference of population structure from genetic data plays an important role in population and medical genetics studies. With the advancement and decreasing cost of sequencing technology, the increasingly available whole genome sequencing data provide much richer information about the underlying population structure. The traditional method (Patterson et al., 2006) originally developed for array-based genotype data for computing and selecting top principal components that capture population structure may not perform well on sequencing data for two reasons. First, the number of genetic variants p is much larger than the sample size n in sequencing data such that the sample-to-marker ratio n/p is nearly zero, violating the assumption of the Tracy-Widom test used in their method. Second, their method might not be able to handle the linkage disequilibrium well in sequencing data. To resolve those two practical issues, we propose a new method called ERStruct to determine the number of top informative principal components based on sequencing data. More specifically, we propose to use the ratio of consecutive eigenvalues as a more robust test statistic, and then we approximate its null distribution using modern random matrix theory. Both simulation studies and applications to two public data sets from the HapMap 3 and the 1000 Genomes Projects demonstrate the empirical performance of our ERStruct method. This article is protected by copyright. All rights reserved.