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High dimensional extension of the growth curve model and its application in genetics

Author

Listed:
  • Sayantee Jana

    (McMaster University)

  • Narayanaswamy Balakrishnan

    (McMaster University)

  • Dietrich Rosen

    (Swedish Agricultural University
    Linköping University)

  • Jemila Seid Hamid

    (McMaster University
    St. Michael’s Hospital
    McMaster University)

Abstract

Recent advances in technology have allowed researchers to collect large scale complex biological data, simultaneously, often in matrix format. In genomic studies, for instance, measurements from tens to hundreds of thousands of genes are taken from individuals across several experimental groups. In time course microarray experiments, gene expression is measured at several time points for each individual across the whole genome resulting in a high-dimensional matrix for each gene. In such experiments, researchers are faced with high-dimensional longitudinal data. Unfortunately, traditional methods for longitudinal data are not appropriate for high-dimensional situations. In this paper, we use the growth curve model and introduce test useful for high-dimensional longitudinal data and evaluate its performance using simulations. We also show how our approach can be used to filter genes in time course genomic experiments. We illustrate this using publicly available genomic data, involving experiments comparing normal human lung tissue with vanadium pentoxide treated human lung tissue, designed with the aim of understanding the susceptibility of individuals working in petro-chemical factories to airway re-modelling. Using our method, we were able to filter out 1053 (about 5 %) genes as non-noise genes from a pool of 22,277. Although our focus is on hypothesis testing, we also provided modified maximum likelihood estimator for the mean parameter of the growth curve model and assessed its performance through bias and mean squared error.

Suggested Citation

  • Sayantee Jana & Narayanaswamy Balakrishnan & Dietrich Rosen & Jemila Seid Hamid, 2017. "High dimensional extension of the growth curve model and its application in genetics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(2), pages 273-292, June.
    • Handle: RePEc:spr:stmapp:v:26:y:2017:i:2:d:10.1007_s10260-016-0369-4
    DOI: 10.1007/s10260-016-0369-4
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    References listed on IDEAS

    as
    1. Yu Chuan Tai & Terence P. Speed, 2009. "On Gene Ranking Using Replicated Microarray Time Course Data," Biometrics, The International Biometric Society, vol. 65(1), pages 40-51, March.
    2. Yuan, Ming & Kendziorski, Christina, 2006. "Hidden Markov Models for Microarray Time Course Data in Multiple Biological Conditions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1323-1332, December.
    3. Hamid, Jemila S. & Beyene, Joseph & von Rosen, Dietrich, 2011. "A novel trace test for the mean parameters in a multivariate growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 238-251, February.
    4. Hamid Jemila S & Beyene Joseph, 2009. "A Multivariate Growth Curve Model for Ranking Genes in Replicated Time Course Microarray Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-28, July.
    5. von Rosen, Dietrich, 1989. "Maximum likelihood estimators in multivariate linear normal models," Journal of Multivariate Analysis, Elsevier, vol. 31(2), pages 187-200, November.
    6. Smyth Gordon K, 2004. "Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-28, February.
    7. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
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    1. Jana, Sayantee & Balakrishnan, Narayanaswamy & Hamid, Jemila S., 2018. "Estimation of the parameters of the extended growth curve model under multivariate skew normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 111-128.

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