Open Access
June 2013 Refining genetically inferred relationships using treelet covariance smoothing
Andrew Crossett, Ann B. Lee, Lambertus Klei, Bernie Devlin, Kathryn Roeder
Ann. Appl. Stat. 7(2): 669-690 (June 2013). DOI: 10.1214/12-AOAS598


Recent technological advances coupled with large sample sets have uncovered many factors underlying the genetic basis of traits and the predisposition to complex disease, but much is left to discover. A common thread to most genetic investigations is familial relationships. Close relatives can be identified from family records, and more distant relatives can be inferred from large panels of genetic markers. Unfortunately these empirical estimates can be noisy, especially regarding distant relatives. We propose a new method for denoising genetically—inferred relationship matrices by exploiting the underlying structure due to hierarchical groupings of correlated individuals. The approach, which we call Treelet Covariance Smoothing, employs a multiscale decomposition of covariance matrices to improve estimates of pairwise relationships. On both simulated and real data, we show that smoothing leads to better estimates of the relatedness amongst distantly related individuals. We illustrate our method with a large genome-wide association study and estimate the “heritability” of body mass index quite accurately. Traditionally heritability, defined as the fraction of the total trait variance attributable to additive genetic effects, is estimated from samples of closely related individuals using random effects models. We show that by using smoothed relationship matrices we can estimate heritability using population-based samples. Finally, while our methods have been developed for refining genetic relationship matrices and improving estimates of heritability, they have much broader potential application in statistics. Most notably, for error-in-variables random effects models and settings that require regularization of matrices with block or hierarchical structure.


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Andrew Crossett. Ann B. Lee. Lambertus Klei. Bernie Devlin. Kathryn Roeder. "Refining genetically inferred relationships using treelet covariance smoothing." Ann. Appl. Stat. 7 (2) 669 - 690, June 2013.


Published: June 2013
First available in Project Euclid: 27 June 2013

zbMATH: 06279849
MathSciNet: MR3112913
Digital Object Identifier: 10.1214/12-AOAS598

Keywords: Covariance estimation , cryptic relatedness , genome-wide association , heritability , kinship

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.7 • No. 2 • June 2013
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