IDEAS home Printed from https://ideas.repec.org/a/spr/stabio/v8y2016i2d10.1007_s12561-016-9143-2.html
   My bibliography  Save this article

Power and Effective Study Size in Heritability Studies

Author

Listed:
  • Jesse D. Raffa

    (University of Washington)

  • Elizabeth A. Thompson

    (University of Washington)

Abstract

Correlation between study units in quantitative genetics studies often makes it difficult to compare important inferential aspects of studies. Describing the relatedness between study units is critical to capture features of pedigree studies involving heritability, including power and precision of heritability estimates. Blangero et al. (Adv Genet 81:1–31, 2012) showed that in pedigree studies the power to detect heritability is a function of the true heritability and the eigenvalues of the kinship matrix. We extend this to a more general setting which allows statements about expected precision of heritability estimates. Using two different Taylor series approximations, we summarize the relatedness in a study design by one or two parameters. These relatedness summary parameters (RSPs) are functions of the eigenvalues or log-eigenvalues of the kinship matrix. Using the RSPs based on the log-eigenvalues, we accurately approximate the expectation of the likelihood ratio test and expected confidence interval widths. We define an effective sample size of a target study as one which has the equivalent power and precision to a reference design. Using unrelated sibpairs as the reference design provides very accurate assessments of power. RSPs and effective sample sizes provide new tools for comparing studies and communicating information about relatedness in heritability studies.

Suggested Citation

  • Jesse D. Raffa & Elizabeth A. Thompson, 2016. "Power and Effective Study Size in Heritability Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 8(2), pages 264-283, October.
    • Handle: RePEc:spr:stabio:v:8:y:2016:i:2:d:10.1007_s12561-016-9143-2
    DOI: 10.1007/s12561-016-9143-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12561-016-9143-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12561-016-9143-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Michael J. Daniels & Robert E. Kass, 2001. "Shrinkage Estimators for Covariance Matrices," Biometrics, The International Biometric Society, vol. 57(4), pages 1173-1184, December.
    2. Robert Makowsky & Nicholas M Pajewski & Yann C Klimentidis & Ana I Vazquez & Christine W Duarte & David B Allison & Gustavo de los Campos, 2011. "Beyond Missing Heritability: Prediction of Complex Traits," PLOS Genetics, Public Library of Science, vol. 7(4), pages 1-9, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hannart, Alexis & Naveau, Philippe, 2014. "Estimating high dimensional covariance matrices: A new look at the Gaussian conjugate framework," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 149-162.
    2. D. Gunzler & W. Tang & N. Lu & P. Wu & X. Tu, 2014. "A Class of Distribution-Free Models for Longitudinal Mediation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 543-568, October.
    3. Miao-Yu Tsai & Chuhsing Hsiao, 2008. "Computation of reference Bayesian inference for variance components in longitudinal studies," Computational Statistics, Springer, vol. 23(4), pages 587-604, October.
    4. Vaughn Gambeta & Roy Kwon, 2020. "Risk Return Trade-Off in Relaxed Risk Parity Portfolio Optimization," JRFM, MDPI, vol. 13(10), pages 1-28, October.
    5. Konno, Yoshihiko, 2009. "Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2237-2253, November.
    6. Joseph G. Ibrahim & Hongtu Zhu & Ramon I. Garcia & Ruixin Guo, 2011. "Fixed and Random Effects Selection in Mixed Effects Models," Biometrics, The International Biometric Society, vol. 67(2), pages 495-503, June.
    7. Tatsuya Kubokawa & Muni S. Srivastava, 2013. "Optimal Ridge-type Estimators of Covariance Matrix in High Dimension," CIRJE F-Series CIRJE-F-906, CIRJE, Faculty of Economics, University of Tokyo.
    8. Champion, Colin J., 2003. "Empirical Bayesian estimation of normal variances and covariances," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 60-79, October.
    9. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    10. Brett Naul & Bala Rajaratnam & Dario Vincenzi, 2016. "The role of the isotonizing algorithm in Stein’s covariance matrix estimator," Computational Statistics, Springer, vol. 31(4), pages 1453-1476, December.
    11. Berger, James O. & Sun, Dongchu & Song, Chengyuan, 2020. "An objective prior for hyperparameters in normal hierarchical models," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    12. Sverdlov, Serge & Thompson, Elizabeth A., 2013. "Correlation between relatives given complete genotypes: From identity by descent to identity by function," Theoretical Population Biology, Elsevier, vol. 88(C), pages 57-67.
    13. Matthew J. Heaton & Stephan R. Sain & Andrew J. Monaghan & Olga V. Wilhelmi & Mary H. Hayden, 2015. "An Analysis of an Incomplete Marked Point Pattern of Heat-Related 911 Calls," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 123-135, March.
    14. Daniels, Michael J., 2006. "Bayesian modeling of several covariance matrices and some results on propriety of the posterior for linear regression with correlated and/or heterogeneous errors," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1185-1207, May.
    15. Jie Yang & Rongling Wu & George Casella, 2009. "Nonparametric Functional Mapping of Quantitative Trait Loci," Biometrics, The International Biometric Society, vol. 65(1), pages 30-39, March.
    16. Monika Bours & Ansgar Steland, 2021. "Large‐sample approximations and change testing for high‐dimensional covariance matrices of multivariate linear time series and factor models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 610-654, June.
    17. Chi, Eric C. & Lange, Kenneth, 2014. "Stable estimation of a covariance matrix guided by nuclear norm penalties," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 117-128.
    18. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    19. Liusha Yang & Matthew R. Mckay & Romain Couillet, 2018. "High-Dimensional MVDR Beamforming: Optimized Solutions Based on Spiked Random Matrix Models," Post-Print hal-01957672, HAL.
    20. Wang, Y. & Daniels, M.J., 2013. "Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 130-140.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stabio:v:8:y:2016:i:2:d:10.1007_s12561-016-9143-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.