Expression level of genes in a given cell can be influenced by a pharmacological or
medical treatment. The response to a given stimulus is usually different for
different genes and may depend on the time. Microarray experiments allow one to
simultaneously monitor the level of expression of thousands of genes. Suitable
statistical methods are required to automatically detect those genes that can be
associated with the biological condition under investigation. In what follows we
consider microarray experiments involving comparisons between two biological
conditions like control and treatment made in the course of time. Special statistical
algorithms are necessary for efficient analysis of this type of experiments.
BATS is a user-friendly software for the Bayesian Analysis of Time Series microarray
experiments based on the novel statistical approach proposed in Angelini et al.
(2006). BATS can carry out analysis with both simulated and real experimental data,
also it handles data from different platforms.
BATS implements a truly functional fully Bayesian method which allows the user to
automatically identify and rank differentially expressed genes and estimate their
profiles on the basis of time series microarray data. The arrays are taken at n
different not necessarily uniformly spaced time points on the interval [0,T] with
possible replicates at some or all time points. For each gene, we assume that
evolution in time of its expression level is governed by a regular function, true
gene expression profile, which is observed with some additive noise. According to
Angelini et al. (2006) each gene expression profile is modeled as an expansion over
some orthonormal basis, with unknown number of terms and coefficients. Then a fully
Bayesian model for the data is developed by eliciting prior distributions on the
number of terms, the coefficients and the level of the noise. In particular, all
parameters in the model are treated either as random variables or as nuisance
parameters which are recovered from the data. Three different Bayesian models, which
vary by the way the noise is treated, are considered. All evaluations are based on
The proposed procedure manages successfully various technical difficulties which
arise in microarray time-course experiments such as a small number of observations
available, non-uniform sampling intervals, presence of missing or multiple data as
well as temporal dependence between observations for each gene.
BATS is a user-friendly software written in Matlab which is freely available upon
request. It allows a user to analyze time series microarray experiments using three
different models to account for various types of errors thus offering a good
compromise between nonparametric and normality assumption based techniques. It allows
a user to specify hyper-parameters of the model or estimate them from the data. The
method accounts for multiplicity, selects and ranks differentially expressed genes
and estimates their expression profiles. Since all evaluations are performed using
analytic expressions, the entire procedure requires very small computational effort.
In the talk, we describe statistical model used in BATS, the main features of the
software interface and an application of BATS to a case study of a human breast
cancer cell stimulated with estrogen. The latter led to the discovery of some new
differentially expressed genes which were not marked earlier due to the high
variability in the raw data.
Although originally designed for cDNA time series microarray experiments, BATS
supports different platforms, such as Affimetrix and Illumina. Future work will focus
on the development of a method for clustering time series genes expression profiles
which is designed for the data described above.
F. Abramovich and C. Angelini (2006), Bayesian Maximum a Posteriori Multiple Testing
Procedure, Sankhya, 68, 436--460. (2006)
C. Angelini, D. De Canditiis, M. Mutarelli, M. Pensky. (2006) Bayesian approach to
estimation and testing in time course microarray experiments, Tech. Rep. IAC-CNR n.
317/06. Available http://www.na.iac.cnr.it/rapporti/anno2006.htm
Cicatiello, L., Scarfoglio, C., Altucci, L., Cancemi, M., Natoli, G., Facchiano, A.,
Iazzetti G., Calogero, R., Biglia, N., De Bortoli, M., Sfiligol, C., Sismondi, P.,
Bresciani, F. and Weisz, A., (2004). A genomic view of estrogen actions in human
breast cancer cells by expression profiling of the hormone-responsive trascriptome.
Journal of Molecular Endocrinology, 32, 719--775.