Statistics in Biosciences

, Volume 4, Issue 2, pp 282–299 | Cite as

Analysis for temporal gene expressions under multiple biological conditions

  • Hong-Bin Fang
  • Dianliang Deng
  • Guo-Liang Tian
  • Lixin Shen
  • Kangmin Duan
  • Jiuzhou Song


Temporal gene expression data are of particular interest to researchers as they contain rich information in characterization of gene function and have been widely used in biomedical studies and early cancer detection. However, the current temporal gene expressions usually have few measuring time series levels; extracting information and identifying efficient treatment effects without temporal information are still a problem. A dense temporal gene expression data set in bacteria shows that the gene expression has various patterns under different biological conditions. Instead of analyzing gene expression levels, in this paper we consider the relative change-rates of gene in the observation period. We propose a non-linear regression model to characterize the relative change-rates of genes, in which individual expression trajectory is modeled as longitudinal data with changeable variance and covariance structure. Then, based on the parameter estimates, a chi-square test is proposed to test the equality of gene expression change-rates. Furthermore, the Mahalanobis distance is used for the classification of genes. The proposed methods are applied to the data set of 18 genes in P. aeruginosa expressed in 24 biological conditions. The simulation studies show that our methods perform well for analysis of temporal gene expressions.


Chi-square test Classification Longitudinal data analysis Mahalanobis distance Non-linear regression analysis Temporal gene expression 


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Copyright information

© International Chinese Statistical Association 2012

Authors and Affiliations

  • Hong-Bin Fang
    • 1
  • Dianliang Deng
    • 2
  • Guo-Liang Tian
    • 3
  • Lixin Shen
    • 4
  • Kangmin Duan
    • 5
  • Jiuzhou Song
    • 6
  1. 1.Division of Biostatistics, Greenebaum Cancer Center, and Department of Epidemiology and Public HealthUniversity of Maryland School of MedicineBaltimoreUSA
  2. 2.Department of Mathematics and StatisticsUniversity of ReginaSaskatchewanCanada
  3. 3.Department of Statistics and Actuarial ScienceThe University of Hong KongHong KongChina
  4. 4.Molecular Microbiology Laboratory, Ministry of Education Key Laboratory of Resource Biology and Biotechnology in Western ChinaNorthwest UniversityXi’anChina
  5. 5.Department of Microbiology and Infectious Diseases, Health Sciences CenterUniversity of CalgaryCalgaryCanada
  6. 6.Department of Animal and Avian SciencesUniversity of MarylandCollege ParkUSA

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