A censored-Poisson model based approach to the analysis of RNA-seq data



With the recent advance of sequencing technology, the collection of RNA expression (RNA-seq) data has been growing rapidly. RNA-seq data are statistically count-type measurements. Poisson distribution is a basic probability distribution for modeling count-type data. With Poisson regression models, various experimental factors, GC content as well as alternative splicing isoforms can be flexibly considered in RNA-seq data analysis. Due to the biochemical and technical limitations of sequencing technology, the biases among RNA-seq data have been recognized.


In this study, an artificial censoring approach has been proposed to an isoform-specific Poisson regression model for analyzing RNA-seq data. Low expression values can be grouped (censored) into one probability category, and high expression values can also be grouped (censored) into another probability category. We have implemented the related Newton-Raphson numeric computing procedure to achieve the maximum likelihood estimation for our censored-Poisson regression model. The related mathematical simplifications have been derived for the consideration of stable and convenient numerical computing.


The advantages of our artificial censoring approach have been demonstrated in both simulation studies and application analysis of experimental data.


Our proposed artificial censoring approach allows us to focus on the majority of data. As the extreme values (tails) of data are artificially censored, more efficient analysis results can be obtained, even from relatively simple Poisson regression models. Our proposed artificial censoring approach can certainly be considered for other well-developed models or methods for RNA-seq data analysis.


  1. 1.

    Trapnell, C., Roberts, A., Goff, L., Pertea, G., Kim, D., Kelley, D. R., Pimentel, H., Salzberg, S. L., Rinn, J. L., and Pachter, L. (2012) Differential gene and transcript expression analysis of RNA-seq experiments with TopHat and Cufflinks. Nat. Protoc., 7, 562–578

    CAS  Article  Google Scholar 

  2. 2.

    Alkhateeb, A., and Rueda, L. (2017) Zseq: An approach for preprocessing next-generation sequencing data. J. Comput. Biol., 24, 746–755

    CAS  Article  Google Scholar 

  3. 3.

    Pérez-Rubio, P., Lottaz, C., and Engelmann, J. C. (2019) FastqPuri: high-performance preprocessing of RNA-seq data. BMC Bioinformatics, 20, 226

    Article  Google Scholar 

  4. 4.

    Mortazavi, A., Williams, B. A., McCue, K., Schaeffer, L. and Wold, B. (2008) Mapping and quantifying mammalian transcriptomes by RNA-seq. Nat. Methods, 5, 621–628

    CAS  Article  Google Scholar 

  5. 5.

    Li, J., Jiang, H., and Wong, W. H. (2010) Modeling non-uniformity in short-read rates in RNA-seq data. Genome Biol., 11, R50

    Article  Google Scholar 

  6. 6.

    Li, B. and Dewey, C. N. (2011) RSEM: accurate transcript quantification from RNA-seq data with or without a reference genome. BMC Bioinformatics, 12, 323

    CAS  Article  Google Scholar 

  7. 7.

    Jiang, H. and Wong, W. H. (2009) Statistical inferences for isoform expression in RNA-seq. Bioinformatics, 25, 1026–1032

    CAS  Article  Google Scholar 

  8. 8.

    Salzman, J., Jiang, H. and Wong, W. H. (2011) Statistical modeling of RNA-seq data. Stat. Sci., 26, 62–83

    Article  Google Scholar 

  9. 9.

    Shi, Y. and Jiang, H. (2013) rSeqDiff: detecting differential isoform expression from RNA-seq data using hierarchical likelihood ratio test. PLoS One, 8, e79448

    Article  Google Scholar 

  10. 10.

    Dohm, J. C., Lottaz, C., Borodina, T. and Himmelbauer, H. (2008) Substantial biases in ultra-short read data sets from high-throughput DNA sequencing. Nucleic Acids Res., 36, e105

    Article  Google Scholar 

  11. 11.

    Aird, D., Ross, M. G., Chen, W. S., Danielsson, M., Fennell, T., Russ, C., Jaffe, D. B., Nusbaum, C. and Gnirke, A. (2011) Analyzing and minimizing PCR amplification bias in Illumina sequencing libraries. Genome Biol., 12, R18

    CAS  Article  Google Scholar 

  12. 12.

    Benjamini, Y. and Speed, T. P. (2012) Summarizing and correcting the GC content bias in high-throughput sequencing. Nucleic Acids Res., 40, e72

    CAS  Article  Google Scholar 

  13. 13.

    Hansen, K. D., Irizarry, R. A. and Wu, Z. (2012) Removing technical variability in RNA-seq data using conditional quantile normalization. Biostatistics, 13, 204–216

    Article  Google Scholar 

  14. 14.

    Robinson, M. D. and Smyth, G. K. (2007) Moderated statistical tests for assessing differences in tag abundance. Bioinformatics, 23, 2881–2887

    CAS  Article  Google Scholar 

  15. 15.

    Robinson, M. D. and Smyth, G. K. (2008) Small-sample estimation of negative binomial dispersion, with applications to SAGE data. Biostatistics, 9, 321–332

    Article  Google Scholar 

  16. 16.

    Anders, S. and Huber, W. (2010) Differential expression analysis for sequence count data. Genome Biol., 11, R106

    CAS  Article  Google Scholar 

  17. 17.

    Anders, S., McCarthy, D. J., Chen, Y., Okoniewski, M., Smyth G. K., Huber, W. and Robinson, M. D. (2013) Count-based differential expression analysis of RNA sequencing data using R and Bioconductor. Nat. Protoc., 8, 1765–1786

    Article  Google Scholar 

  18. 18.

    Rau, A., Maugis-Rabusseau, C., Martin-Magniette, M.-L. and Celeux G. (2015) Co-expression analysis of high-throughput transcriptome sequencing data with Poisson mixture models. Bioinformatics, 31, 1420–1427

    CAS  Article  Google Scholar 

  19. 19.

    Pertea, M., Kim, D., Pertea, G. M., Leek, J. T. and Salzberg, S. L. (2016) Transcript-level expression analysis of rna-seq experiments with hisat, stringtie and ballgown. Nat. Protoc., 11, 1650–1667

    CAS  Article  Google Scholar 

  20. 20.

    Kazakiewicz, D., Claesen, J., Görczak, K., Plewczynski, D. and Burzykowski, T. (2019) A multivariate negative-binomial model with random effects for differential gene-expression analysis of correlated mrna sequencing data. J. Comput. Biol., 26, 1339–1348

    CAS  Article  Google Scholar 

  21. 21.

    Li, B., Ruotti, V., Stewart, R. M., Thomson, J. A. and Dewey, C. N. (2010) RNA-seq gene expression estimation with read mapping uncertainty. Bioinformatics, 26, 493–500

    Article  Google Scholar 

  22. 22.

    Khoury, M. P. and Bourdon, J.-C. (2011) p53 isoforms: An intracellular microprocessor? Genes Cancer, 2, 453–465

    CAS  Article  Google Scholar 

  23. 23.

    Cancer Genome Atlas Network. (2012) Comprehensive molecular portraits of human breast tumours. Nature, 490, 61–70

    Article  Google Scholar 

  24. 24.

    Rosenbloom, K. R., Armstrong, J., Barber, G.P., Casper, J., Clawson, H., Diekhans, M., Dreszer, T.R., Fujita, P.A., Guruvadoo, L., Haeussler, M., et al. (2015) The UCSC Genome Browser database: 2015 update. Nucleic Acids Res., 43, D670–D681

    CAS  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Yinglei Lai.

Additional information

Author summary

RNA sequencing (RNA-seq) expression data have been increasingly collected for various biomedical studies. Due to the biochemical and technical limitations of sequencing technology, the biases among RNA-seq data have been recognized. We have developed an artificial censoring approach to the analysis of isoform-specific RNA-seq expression data. Low and high expression values can be grouped (censored) into the related probability categories. This approach allows us to focus on the majority of data and to obtain more efficient analysis results. Our proposed artificial censoring approach can also be considered in other RNA-seq data analysis scenarios.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chen, X., Lai, Y. A censored-Poisson model based approach to the analysis of RNA-seq data. Quant Biol (2020). https://doi.org/10.1007/s40484-020-0208-3

Download citation


  • RNA-seq
  • Poisson models
  • censored distribution