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Sample size calculations for the differential expression analysis of RNA-seq data using a negative binomial regression model

Author

Listed:
  • Li Xiaohong

    (Department of Bioinformatics and Biostatistics, School of Public Health and Information Sciences, University of Louisville, Louisville, KY 40202, USA)

  • Wu Dongfeng

    (Department of Bioinformatics and Biostatistics, School of Public Health and Information Sciences, University of Louisville, Louisville, KY 40202, USA)

  • Cooper Nigel G.F.

    (Department of Anatomical Sciences and Neurobiology, School of Medicine, University of Louisville, Louisville, KY, USA)

  • Rai Shesh N.

    (Department of Bioinformatics and Biostatistics, School of Public Health and Information Sciences, University of Louisville, Louisville, KY 40202, USA)

Abstract

High throughput RNA sequencing (RNA-seq) technology is increasingly used in disease-related biomarker studies. A negative binomial distribution has become the popular choice for modeling read counts of genes in RNA-seq data due to over-dispersed read counts. In this study, we propose two explicit sample size calculation methods for RNA-seq data using a negative binomial regression model. To derive these new sample size formulas, the common dispersion parameter and the size factor as an offset via a natural logarithm link function are incorporated. A two-sided Wald test statistic derived from the coefficient parameter is used for testing a single gene at a nominal significance level 0.05 and multiple genes at a false discovery rate 0.05. The variance for the Wald test is computed from the variance-covariance matrix with the parameters estimated from the maximum likelihood estimates under the unrestricted and constrained scenarios. The performance and a side-by-side comparison of our new formulas with three existing methods with a Wald test, a likelihood ratio test or an exact test are evaluated via simulation studies. Since other methods are much computationally extensive, we recommend our M1 method for quick and direct estimation of sample sizes in an experimental design. Finally, we illustrate sample sizes estimation using an existing breast cancer RNA-seq data.

Suggested Citation

  • Li Xiaohong & Wu Dongfeng & Cooper Nigel G.F. & Rai Shesh N., 2019. "Sample size calculations for the differential expression analysis of RNA-seq data using a negative binomial regression model," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(1), pages 1-17, February.
    • Handle: RePEc:bpj:sagmbi:v:18:y:2019:i:1:p:17:n:2
    DOI: 10.1515/sagmb-2018-0021
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    References listed on IDEAS

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    1. Molenberghs, Geert & Verbeke, Geert, 2007. "Likelihood Ratio, Score, and Wald Tests in a Constrained Parameter Space," The American Statistician, American Statistical Association, vol. 61, pages 22-27, February.
    2. Gu Mi & Yanming Di & Daniel W Schafer, 2015. "Goodness-of-Fit Tests and Model Diagnostics for Negative Binomial Regression of RNA Sequencing Data," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-16, March.
    3. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498, August.
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