Estimating linkage disequilibrium from genotypes under Hardy-Weinberg equilibrium
File(s)
Published version
Author(s)
Hui, Tin-Yu J
Burt, Austin
Type
Journal Article
Abstract
BACKGROUND: Measures of linkage disequilibrium (LD) play a key role in a wide range of applications from disease association to demographic history estimation. The true population LD cannot be measured directly and instead can only be inferred from genetic samples, which are unavoidably subject to measurement error. Previous studies of r2 (a measure of LD), such as the bias due to finite sample size and its variance, were based on the special case that the true population-wise LD is zero. These results generally do not hold for non-zero [Formula: see text] values, which are more common in real genetic data. RESULTS: This work generalises the estimation of r2 to all levels of LD, and for both phased and unphased data. First, we provide new formulae for the effect of finite sample size on the observed r2 values. Second, we find a new empirical formula for the variance of the observed r2, equals to 2E[r2](1 - E[r2])/n, where n is the diploid sample size. Third, we propose a new routine, Constrained ML, a likelihood-based method to directly estimate haplotype frequencies and r2 from diploid genotypes under Hardy-Weinberg Equilibrium. While serving the same purpose as the pre-existing Expectation-Maximisation algorithm, the new routine can have better convergence and is simpler to use. A new likelihood-ratio test is also introduced to test for the absence of a particular haplotype. Extensive simulations are run to support these findings. CONCLUSION: Most inferences on LD will benefit from our new findings, from point and interval estimation to hypothesis testing. Genetic analyses utilising r2 information will become more accurate as a result.
Date Issued
2020-02-26
Date Acceptance
2020-01-29
Citation
BMC Genetics, 2020, 21 (1)
ISSN
1471-2156
Publisher
BioMed Central
Journal / Book Title
BMC Genetics
Volume
21
Issue
1
Copyright Statement
© 2020 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Sponsor
Bill & Melinda Gates Foundation
Silicon Valley Community Foundation
Identifier
https://www.ncbi.nlm.nih.gov/pubmed/32102657
PII: 10.1186/s12863-020-0818-9
Grant Number
OPP1141988
N/A
Subjects
Linkage disequilibrium
Maximum likelihood estimation
Sampling error
Publication Status
Published
Coverage Spatial
England
Article Number
21
Date Publish Online
2020-02-26