The objective of the present paper is to develop a truly functional Bayesian method specifically designed for time series microarray data. The method allows one to identify differentially expressed genes in a time-course microarray experiment, to rank them and to estimate their expression profiles. Each gene expression profile is modeled as an expansion over some orthonormal basis, where the coefficients and the number of basis functions are estimated from the data. The proposed procedure deals successfully with various technical difficulties that arise in typical microarray experiments such as a small number of observations, non-uniform sampling intervals and missing or replicated data. The procedure allows one to account for various types of errors and offers a good compromise between nonparametric techniques and techniques based on normality assumptions. In addition, all evaluations are performed using analytic expressions, so the entire procedure requires very small computational effort. The procedure is studied using both simulated and real data, and is compared with competitive recent approaches. Finally, the procedure is applied to a case study of a human breast cancer cell line stimulated with estrogen. We succeeded in finding new significant genes that were not marked in an earlier work on the same dataset.

BackgroundGene expression levels in a given cell can be influenced by different factors, namely pharmacological or medical treatments. The response to a given stimulus is usually different for different genes and may depend on time. One of the goals of modern molecular biology is the high-throughput identification of genes associated with a particular treatment or a biological process of interest. From methodological and computational point of view, analyzing high-dimensional time course microarray data requires very specific set of tools which are usually not included in standard software packages. Recently, the authors of this paper developed a fully Bayesian approach which allows one to identify differentially expressed genes in a 'one-sample' time-course microarray experiment, to rank them and to estimate their expression profiles. The method is based on explicit expressions for calculations and, hence, very computationally efficient.ResultsThe software package BATS (Bayesian Analysis of Time Series) presented here implements the methodology described above. It allows an user to automatically identify and rank differentially expressed genes and to estimate their expression profiles when at least 5–6 time points are available. The package has a user-friendly interface. BATS successfully manages various technical difficulties which arise in time-course microarray experiments, such as a small number of observations, non-uniform sampling intervals and replicated or missing data.ConclusionBATS is a free user-friendly software for the analysis of both simulated and real microarray time course experiments. The software, the user manual and a brief illustrative example are freely available online at the BATS website:

The paper proposes a method of deconvolution in a periodic setting which combines two important ideas, the fast wavelet and Fourier transform-based estimation procedure of Johnstone "et al". ["J. Roy. Statist. Soc. Ser. B" 66 (2004) 547] and the multichannel system technique proposed by Casey and Walnut [ "SIAM Rev" . 36 (1994) 537]. An unknown function is estimated by a wavelet series where the empirical wavelet coefficients are filtered in an adapting non-linear fashion. It is shown theoretically that the estimator achieves optimal convergence rate in a wide range of Besov spaces. The procedure allows to reduce the ill-posedness of the problem especially in the case of non-smooth blurring functions such as boxcar functions: it is proved that additions of extra channels improve convergence rate of the estimator. Theoretical study is supplemented by an extensive set of small-sample simulation experiments demonstrating high-quality performance of the proposed method. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..

BackgroundThe main goal of the whole transcriptome analysis is to correctly identify all expressed transcripts within a specific cell/tissue - at a particular stage and condition - to determine their structures and to measure their abundances. RNA-seq data promise to allow identification and quantification of transcriptome at unprecedented level of resolution, accuracy and low cost. Several computational methods have been proposed to achieve such purposes. However, it is still not clear which promises are already met and which challenges are still open and require further methodological developments.ResultsWe carried out a simulation study to assess the performance of 5 widely used tools, such as: CEM, Cufflinks, iReckon, RSEM, and SLIDE. All of them have been used with default parameters. In particular, we considered the effect of the following three different scenarios: the availability of complete annotation, incomplete annotation, and no annotation at all. Moreover, comparisons were carried out using the methods in three different modes of action. In the first mode, the methods were forced to only deal with those isoforms that are present in the annotation; in the second mode, they were allowed to detect novel isoforms using the annotation as guide; in the third mode, they were operating in fully data driven way (although with the support of the alignment on the reference genome). In the latter modality, precision and recall are quite poor. On the contrary, results are better with the support of the annotation, even though it is not complete. Finally, abundance estimation error often shows a very skewed distribution. The performance strongly depends on the true real abundance of the isoforms. Lowly (and sometimes also moderately) expressed isoforms are poorly detected and estimated. In particular, lowly expressed isoforms are identified mainly if they are provided in the original annotation as potential isoforms.ConclusionsBoth detection and quantification of all isoforms from RNA-seq data are still hard problems and they are affected by many factors. Overall, the performance significantly changes since it depends on the modes of action and on the type of available annotation. Results obtained using complete or partial annotation are able to detect most of the expressed isoforms, even though the number of false positives is often high. Fully data driven approaches require more attention, at least for complex eucaryotic genomes. Improvements are desirable especially for isoform quantification and for isoform detection with low abundance.

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