Abstract
Microarray is a powerful tool for genome-wide gene expression analysis. In microarray expression data, often mean and variance have certain relationships. We present a non-parametric mean-variance smoothing method (NPMVS) to analyze differentially expressed genes. In this method, a nonlinear smoothing curve is fitted to estimate the relationship between mean and variance. Inference is then made upon shrinkage estimation of posterior means assuming variances are known. Different methods have been applied to simulated datasets, in which a variety of mean and variance relationships were imposed. The simulation study showed that NPMVS outperformed the other two popular shrinkage estimation methods in some mean-variance relationships; and NPMVS was competitive with the two methods in other relationships. A real biological dataset, in which a cold stress transcription factor gene, CBF2, was overexpressed, has also been analyzed with the three methods. Gene ontology and cis-element analysis showed that NPMVS identified more cold and stress responsive genes than the other two methods did. The good performance of NPMVS is mainly due to its shrinkage estimation for both means and variances. In addition, NPMVS exploits a non-parametric regression between mean and variance, instead of assuming a specific parametric relationship between mean and variance. The source code written in R is available from the authors on request.
Highlights
Microarray has become a powerful tool for biological and medical science to monitor transcriptome changes under different treatments
The simulation study showed that NPMSV performed better than limma in case 0, and the two methods were competitive in other mean-variance relationships
The gene set discovered by non-parametric mean-variance smoothing method (NPMVS) included all genes identified by the other two methods
Summary
Microarray has become a powerful tool for biological and medical science to monitor transcriptome changes under different treatments. The feature of small replicates and large gene numbers, e.g., about 6,000 in yeast and 23,000 in Arabidopsis, in microarray data usually results in poor estimation of gene-specific variances. Several methods have been suggested for modification of gene specific variances or covariances to improve the estimation. Efron et al [1] suggested modifying the denominator of the t-statistic to allow estimation less sensitive to gene-specific variances. Cui et al [3] and Tong and Wang [4] developed shrinkage estimators for gene specific variances using Stein-type estimation under squared error loss function which were used to construct traditional t- type and F - type statistics. In all the above estimators, gene specific means were assumed to be independent of variances. It has been observed that means are related to variances in microarray experiments; usually genes with high expression level show high variances, while genes with low expression level display small variances (Figure 1)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
