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Using Stochastic Approximation Techniques to Efficiently Construct Confidence Intervals for Heritability

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Research in Computational Molecular Biology (RECOMB 2017)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 10229))

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Abstract

Estimation of heritability is an important task in genetics. The use of linear mixed models (LMMs) to determine narrow-sense SNP-heritability and related quantities has received much recent attention, due of its ability to account for variants with small effect sizes. Typically, heritability estimation under LMMs uses the restricted maximum likelihood (REML) approach. The common way to report the uncertainty in REML estimation uses standard errors (SE), which rely on asymptotic properties. However, these assumptions are often violated because of the bounded parameter space, statistical dependencies, and limited sample size, leading to biased estimates and inflated or deflated confidence intervals. In addition, for larger datasets (e.g., tens of thousands of individuals), the construction of SEs itself may require considerable time, as it requires expensive matrix inversions and multiplications.

Here, we present FIESTA (Fast confidence IntErvals using STochastic Approximation), a method for constructing accurate confidence intervals (CIs). FIESTA is based on parametric bootstrap sampling, and therefore avoids unjustified assumptions on the distribution of the heritability estimator. FIESTA uses stochastic approximation techniques, which accelerate the construction of CIs by several orders of magnitude, compared to previous approaches as well as to the analytical approximation used by SEs. FIESTA builds accurate CIs rapidly, e.g., requiring only several seconds for datasets of tens of thousands of individuals, making FIESTA a very fast solution to the problem of building accurate CIs for heritability for all dataset sizes.

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Acknowledgements

The authors would like to thank David Steinberg. R.S. is supported by the Colton Family Foundation. This study was supported in part by a fellowship from the Edmond J. Safra Center for Bioinformatics at Tel Aviv University to R.S. The Northern Finland Birth Cohort data were obtained from dbGaP: phs000276.v2.p1. This study makes use of data generated by the Wellcome Trust Case Control Consortium. A full list of the investigators who contributed to the generation of the data is available from www.wtccc.org.uk. Funding for the project was provided by the Wellcome Trust under award 076113.

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Authors and Affiliations

  1. Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Regev Schweiger & Elior Rahmani

  2. School of Mathematical Sciences, Department of Statistics, Tel Aviv University, Tel Aviv, Israel

    Eyal Fisher, Liat Shenhav & Saharon Rosset

  3. Department of Computer Science, University of California, Los Angeles, California, USA

    Eran Halperin

  4. Department of Anesthesiology and Perioperative Medicine, University of California, Los Angeles, California, USA

    Eran Halperin

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  1. Regev Schweiger
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  2. Eyal Fisher
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  3. Elior Rahmani
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  4. Liat Shenhav
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  5. Saharon Rosset
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  6. Eran Halperin
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Correspondence to Regev Schweiger .

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Editors and Affiliations

  1. Indiana University Bloomington, Bloomington, Indiana, USA

    S. Cenk Sahinalp

Appendix

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The supplementary material, including additional figures, are located at https://github.com/cozygene/albi.

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Schweiger, R., Fisher, E., Rahmani, E., Shenhav, L., Rosset, S., Halperin, E. (2017). Using Stochastic Approximation Techniques to Efficiently Construct Confidence Intervals for Heritability. In: Sahinalp, S. (eds) Research in Computational Molecular Biology. RECOMB 2017. Lecture Notes in Computer Science(), vol 10229. Springer, Cham. https://doi.org/10.1007/978-3-319-56970-3_15

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  • DOI: https://doi.org/10.1007/978-3-319-56970-3_15

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