IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v42y2015i3p477-491.html
   My bibliography  Save this article

Application of skew-normal distribution for detecting differential expression to microRNA data

Author

Listed:
  • Ahmed Hossain
  • Joseph Beyene

Abstract

Traditional statistical modeling of continuous outcome variables relies heavily on the assumption of a normal distribution. However, in some applications, such as analysis of microRNA (miRNA) data, normality may not hold. Skewed distributions play an important role in such studies and might lead to robust results in the presence of extreme outliers. We apply a skew-normal (SN) distribution, which is indexed by three parameters (location, scale and shape), in the context of miRNA studies. We developed a test statistic for comparing means of two conditions replacing the normal assumption with SN distribution. We compared the performance of the statistic with other Wald-type statistics through simulations. Two real miRNA datasets are analyzed to illustrate the methods. Our simulation findings showed that the use of a SN distribution can result in improved identification of differentially expressed miRNAs, especially with markedly skewed data and when the two groups have different variances. It also appeared that the statistic with SN assumption performs comparably with other Wald-type statistics irrespective of the sample size or distribution. Moreover, the real dataset analyses suggest that the statistic with SN assumption can be used effectively for identification of important miRNAs. Overall, the statistic with SN distribution is useful when data are asymmetric and when the samples have different variances for the two groups.

Suggested Citation

  • Ahmed Hossain & Joseph Beyene, 2015. "Application of skew-normal distribution for detecting differential expression to microRNA data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 477-491, March.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:3:p:477-491
    DOI: 10.1080/02664763.2014.962490
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2014.962490
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2014.962490?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. Hossain, Ahmed & Beyene, Joseph & Willan, Andrew R. & Hu, Pingzhao, 2009. "A flexible approximate likelihood ratio test for detecting differential expression in microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3685-3695, August.
    2. Henry T Robertson & David B Allison, 2012. "A Novel Generalized Normal Distribution for Human Longevity and other Negatively Skewed Data," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-7, May.
    3. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    4. Margaret Sullivan Pepe & Gary Longton & Garnet L. Anderson & Michel Schummer, 2003. "Selecting Differentially Expressed Genes from Microarray Experiments," Biometrics, The International Biometric Society, vol. 59(1), pages 133-142, March.
    5. A. Capitanio & A. Azzalini & E. Stanghellini, 2003. "Graphical models for skew‐normal variates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 129-144, March.
    6. Liseo, Brunero & Loperfido, Nicola, 2003. "A Bayesian interpretation of the multivariate skew-normal distribution," Statistics & Probability Letters, Elsevier, vol. 61(4), pages 395-401, February.
    7. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
    8. Arthur Pewsey, 2000. "Problems of inference for Azzalini's skewnormal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(7), pages 859-870.
    9. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    10. Victor Ambros, 2004. "The functions of animal microRNAs," Nature, Nature, vol. 431(7006), pages 350-355, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wenhao Gui & Lei Guo, 2018. "Statistical Inference for the Location and Scale Parameters of the Skew Normal Distribution," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(4), pages 633-650, December.

    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. Angela Montanari & Cinzia Viroli, 2010. "A skew-normal factor model for the analysis of student satisfaction towards university courses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 473-487.
    2. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Young, Phil D. & Kahle, David J. & Young, Dean M., 2017. "On the independence of singular multivariate skew-normal sub-vectors," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 58-62.
    4. Jamalizadeh, A. & Balakrishnan, N., 2010. "Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1412-1427, July.
    5. David Mayston, 2015. "Analysing the effectiveness of public service producers with endogenous resourcing," Journal of Productivity Analysis, Springer, vol. 44(1), pages 115-126, August.
    6. Zareifard, Hamid & Rue, Håvard & Khaledi, Majid Jafari & Lindgren, Finn, 2016. "A skew Gaussian decomposable graphical model," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 58-72.
    7. Sharon Lee & Geoffrey McLachlan, 2013. "On mixtures of skew normal and skew $$t$$ -distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(3), pages 241-266, September.
    8. Young, Phil D. & Harvill, Jane L. & Young, Dean M., 2016. "A derivation of the multivariate singular skew-normal density function," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 40-45.
    9. Taras Bodnar & Stepan Mazur & Nestor Parolya, 2019. "Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix‐variate location mixture of normal distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(2), pages 636-660, June.
    10. Jorge M. Arevalillo & Hilario Navarro, 2019. "A stochastic ordering based on the canonical transformation of skew-normal vectors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 475-498, June.
    11. Kahrari, F. & Rezaei, M. & Yousefzadeh, F. & Arellano-Valle, R.B., 2016. "On the multivariate skew-normal-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 80-88.
    12. Jorge M. Arevalillo & Hilario Navarro, 2020. "Data projections by skewness maximization under scale mixtures of skew-normal vectors," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 435-461, June.
    13. Kim, Hyoung-Moon & Ryu, Duchwan & Mallick, Bani K. & Genton, Marc G., 2014. "Mixtures of skewed Kalman filters," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 228-251.
    14. Corrado Crocetta & Nicola Loperfido, 2009. "Maximum likelihood estimation of correlation between maximal oxygen consumption and the 6-min walk test in patients with chronic heart failure," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(10), pages 1101-1108.
    15. Kozubowski, Tomasz J. & Nolan, John P., 2008. "Infinite divisibility of skew Gaussian and Laplace laws," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 654-660, April.
    16. Clécio S. Ferreira & Gilberto A. Paula, 2017. "Estimation and diagnostic for skew-normal partially linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 3033-3053, December.
    17. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    18. Reinaldo B. Arellano-Valle & Marc G. Genton, 2010. "Multivariate extended skew-t distributions and related families," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 201-234.
    19. Fang, B.Q., 2006. "Sample mean, covariance and T2 statistic of the skew elliptical model," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1675-1690, August.
    20. Ye, Rendao & Wang, Tonghui & Gupta, Arjun K., 2014. "Distribution of matrix quadratic forms under skew-normal settings," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 229-239.

    More about this item

    Statistics

    Access and download statistics

    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:taf:japsta:v:42:y:2015:i:3:p:477-491. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.