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Advances in Bioinformatics
Volume 2011 (2011), Article ID 261514, 6 pages
Research Article

A Growth Curve Model with Fractional Polynomials for Analysing Incomplete Time-Course Data in Microarray Gene Expression Studies

1Department of Clinical Genetics, Odense University Hospital, Sdr. Boulevard 29, 5000 Odense C, Denmark
2Epidemiology and Department of Biostatistics, Institute of Public Health, University of Southern Denmark, J. B. Winsløws Vej 9B, 5000 Odense C, Denmark
3Department of Dermatology and Allergy Center, Odense University Hospital, Sdr. Boulevard 29, 5000 Odense C, Denmark
4Discovery, LEO Pharma A/S, Industriparken 55, 2750 Ballerup, Denmark
5Department of Psychology, University of Minnesota, Minneapolis, MN 55455, USA

Received 11 April 2011; Revised 7 June 2011; Accepted 2 August 2011

Academic Editor: Rainer Spang

Copyright © 2011 Qihua Tan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Identifying the various gene expression response patterns is a challenging issue in expression microarray time-course experiments. Due to heterogeneity in the regulatory reaction among thousands of genes tested, it is impossible to manually characterize a parametric form for each of the time-course pattern in a gene by gene manner. We introduce a growth curve model with fractional polynomials to automatically capture the various time-dependent expression patterns and meanwhile efficiently handle missing values due to incomplete observations. For each gene, our procedure compares the performances among fractional polynomial models with power terms from a set of fixed values that offer a wide range of curve shapes and suggests a best fitting model. After a limited simulation study, the model has been applied to our human in vivo irritated epidermis data with missing observations to investigate time-dependent transcriptional responses to a chemical irritant. Our method was able to identify the various nonlinear time-course expression trajectories. The integration of growth curves with fractional polynomials provides a flexible way to model different time-course patterns together with model selection and significant gene identification strategies that can be applied in microarray-based time-course gene expression experiments with missing observations.