IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2009i10p3685-3695.html
   My bibliography  Save this article

A flexible approximate likelihood ratio test for detecting differential expression in microarray data

Author

Listed:
  • Hossain, Ahmed
  • Beyene, Joseph
  • Willan, Andrew R.
  • Hu, Pingzhao

Abstract

Identifying differentially expressed genes in microarray data has been studied extensively and several methods have been proposed. Most popular methods in the study of gene expression microarray data analysis rely on normal distribution assumption and are based on a Wald statistic. These methods may be inefficient when expression levels follow a skewed distribution. To deal with possible violations of the normality assumption, we propose a method based on Generalized Logistic Distribution of Type II (GLDII). The motivation behind this distributional assumption is to allow longer tails than normal distribution. This is important in analyzing gene expression data since extreme values are common in such experiments. The shape parameter for GLDII allows flexibility in modeling a wide range of distributions. To simplify the computational complexity involved in carrying out Likelihood Ratio (LR) tests for several thousands of genes, an Approximate LR Test (ALRT) is proposed. We also generalize the two-class ALRT method to multi-class microarray data. The performance of the ALRT method under the GLDII assumption is compared to methods based on Wald-type statistics using simulation. The results from the simulations show that our method performs quite well compared to the significance analysis of microarrays (SAM) approach using standardized Wilcoxon rank statistics and the empirical Bayes (E-B) t-statistics. Our method is also less sensitive to extreme values. We illustrate our method using two publicly available gene expression data sets.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:10:p:3685-3695
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(09)00121-2
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Dudoit Sandrine & van der Laan Mark J. & Pollard Katherine S., 2004. "Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-71, June.
    2. Efron B. & Tibshirani R. & Storey J.D. & Tusher V., 2001. "Empirical Bayes Analysis of a Microarray Experiment," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1151-1160, December.
    3. Sandrine Dudoit & Mark van der Laan & Katherine Pollard, 2004. "Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates," U.C. Berkeley Division of Biostatistics Working Paper Series 1137, Berkeley Electronic Press.
    4. Geman Donald & d'Avignon Christian & Naiman Daniel Q. & Winslow Raimond L., 2004. "Classifying Gene Expression Profiles from Pairwise mRNA Comparisons," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-22, August.
    5. 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.
    6. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
    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. 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.

    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. Miecznikowski, Jeffrey C. & Gold, David & Shepherd, Lori & Liu, Song, 2011. "Deriving and comparing the distribution for the number of false positives in single step methods to control k-FWER," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1695-1705, November.
    2. Rossell David & Guerra Rudy & Scott Clayton, 2008. "Semi-Parametric Differential Expression Analysis via Partial Mixture Estimation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-29, April.
    3. Bickel David R., 2008. "Correcting the Estimated Level of Differential Expression for Gene Selection Bias: Application to a Microarray Study," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-27, March.
    4. van der Laan Mark J. & Hubbard Alan E., 2006. "Quantile-Function Based Null Distribution in Resampling Based Multiple Testing," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-30, May.
    5. Yu Lianbo & Gulati Parul & Fernandez Soledad & Pennell Michael & Kirschner Lawrence & Jarjoura David, 2011. "Fully Moderated T-statistic for Small Sample Size Gene Expression Arrays," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-22, September.
    6. Ahmed Hossain & Hafiz T.A. Khan, 2016. "Identification of genomic markers correlated with sensitivity in solid tumors to Dasatinib using sparse principal components," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2538-2549, October.
    7. Hirakawa, Akihiro & Hamada, Chikuma & Yoshimura, Isao, 2011. "Sample size calculation for a regularized t-statistic in microarray experiments," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 870-875, July.
    8. Christina C. Bartenschlager & Michael Krapp, 2015. "Theorie und Methoden multipler statistischer Vergleiche," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 9(2), pages 107-129, November.
    9. Dazard, Jean-Eudes & Sunil Rao, J., 2012. "Joint adaptive mean–variance regularization and variance stabilization of high dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2317-2333.
    10. Montazeri Zahra & Yanofsky Corey M. & Bickel David R., 2010. "Shrinkage Estimation of Effect Sizes as an Alternative to Hypothesis Testing Followed by Estimation in High-Dimensional Biology: Applications to Differential Gene Expression," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-33, June.
    11. Merrill Birkner & Sandra Sinisi & Mark van der Laan, 2004. "Multiple Testing and Data Adaptive Regression: An Application to HIV-1 Sequence Data," U.C. Berkeley Division of Biostatistics Working Paper Series 1161, Berkeley Electronic Press.
    12. Leek Jeffrey T & Storey John D., 2011. "The Joint Null Criterion for Multiple Hypothesis Tests," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-22, June.
    13. Xu, Ping & Brock, Guy N. & Parrish, Rudolph S., 2009. "Modified linear discriminant analysis approaches for classification of high-dimensional microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1674-1687, March.
    14. Khalili, Abbas & Huang, Tim & Lin, Shili, 2009. "A robust unified approach to analyzing methylation and gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1701-1710, March.
    15. Yoshiyuki Ninomiya & Hironori Fujisawa, 2007. "A Conservative Test for Multiple Comparison Based on Highly Correlated Test Statistics," Biometrics, The International Biometric Society, vol. 63(4), pages 1135-1142, December.
    16. Li, Chin-Shang & Cheng, Cheng, 2004. "Stable classification with applications to microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 599-609, October.
    17. Hwang J.T. Gene & Liu Peng, 2010. "Optimal Tests Shrinking Both Means and Variances Applicable to Microarray Data Analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-35, October.
    18. Giuseppe Jurman & Samantha Riccadonna & Roberto Visintainer & Cesare Furlanello, 2012. "Algebraic Comparison of Partial Lists in Bioinformatics," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-20, May.
    19. Yang, Tae Young, 2009. "Simple Bayesian binary framework for discovering significant genes and classifying cancer diagnosis," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1743-1754, March.
    20. Rubin Daniel & Dudoit Sandrine & van der Laan Mark, 2006. "A Method to Increase the Power of Multiple Testing Procedures Through Sample Splitting," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-20, August.

    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:eee:csdana:v:53:y:2009:i:10:p:3685-3695. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.