Diverse correlation structures in gene expression data and their utility in improving statistical inference

It is well known that correlations in microarray data represent a serious nuisance deteriorating the performance of gene selection procedures. This paper is intended to demonstrate that the correlation structure of microarray data provides a rich source of useful information. We discuss distinct correlation substructures revealed in microarray gene expression data by an appropriate ordering of genes. These substructures include stochastic proportionality of expression signals in a large percentage of all gene pairs, negative correlations hidden in ordered gene triples, and a long sequence of weakly dependent random variables associated with ordered pairs of genes. The reported striking regularities are of general biological interest and they also have far-reaching implications for theory and practice of statistical methods of microarray data analysis. We illustrate the latter point with a method for testing differential expression of nonoverlapping gene pairs. While designed for testing a different null hypothesis, this method provides an order of magnitude more accurate control of type 1 error rate compared to conventional methods of individual gene expression profiling. In addition, this method is robust to the technical noise. Quantitative inference of the correlation structure has the potential to extend the analysis of microarray data far beyond currently practiced methods.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS120 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Application of Volcano Plots in Analyses of mRNA Differential Expressions with Microarrays

Volcano plot displays unstandardized signal (e.g. log-fold-change) against noise-adjusted/standardized signal (e.g. t-statistic or -log10(p-value) from the t test). We review the basic and an interactive use of the volcano plot, and its crucial role in understanding the regularized t-statistic. The joint filtering gene selection criterion based on regularized statistics has a curved discriminant line in the volcano plot, as compared to the two perpendicular lines for the "double filtering" criterion. This review attempts to provide an unifying framework for discussions on alternative measures of differential expression, improved methods for estimating variance, and visual display of a microarray analysis result. We also discuss the possibility to apply volcano plots to other fields beyond microarray.Comment: 8 figure

GaGa: A parsimonious and flexible model for differential expression analysis

Hierarchical models are a powerful tool for high-throughput data with a small to moderate number of replicates, as they allow sharing information across units of information, for example, genes. We propose two such models and show its increased sensitivity in microarray differential expression applications. We build on the gamma--gamma hierarchical model introduced by Kendziorski et al. [Statist. Med. 22 (2003) 3899--3914] and Newton et al. [Biostatistics 5 (2004) 155--176], by addressing important limitations that may have hampered its performance and its more widespread use. The models parsimoniously describe the expression of thousands of genes with a small number of hyper-parameters. This makes them easy to interpret and analytically tractable. The first model is a simple extension that improves the fit substantially with almost no increase in complexity. We propose a second extension that uses a mixture of gamma distributions to further improve the fit, at the expense of increased computational burden. We derive several approximations that significantly reduce the computational cost. We find that our models outperform the original formulation of the model, as well as some other popular methods for differential expression analysis. The improved performance is specially noticeable for the small sample sizes commonly encountered in high-throughput experiments. Our methods are implemented in the freely available Bioconductor gaga package.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS244 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Reproducibility of Lists of Differentially Expressed Genes in Microarray Studies

Reproducibility is a fundamental requirement in scientific experiments and clinical contexts. Recent publications raise concerns about the reliability of microarray technology because of the apparent lack of agreement between lists of differentially expressed genes (DEGs). In this study we demonstrate that (1) such discordance may stem from ranking and selecting DEGs solely by statistical significance (P) derived from widely used simple t-tests; (2) when fold change (FC) is used as the ranking criterion, the lists become much more reproducible, especially when fewer genes are selected; and (3) the instability of short DEG lists based on P cutoffs is an expected mathematical consequence of the high variability of the t-values. We recommend the use of FC ranking plus a non-stringent P cutoff as a baseline practice in order to generate more reproducible DEG lists. The FC criterion enhances reproducibility while the P criterion balances sensitivity and specificity

Previously Unidentified Changes in Renal Cell Carcinoma Gene Expression Identified by Parametric Analysis of Microarray Data

BACKGROUND. Renal cell carcinoma is a common malignancy that often presents as a metastatic-disease for which there are no effective treatments. To gain insights into the mechanism of renal cell carcinogenesis, a number of genome-wide expression profiling studies have been performed. Surprisingly, there is very poor agreement among these studies as to which genes are differentially regulated. To better understand this lack of agreement we profiled renal cell tumor gene expression using genome-wide microarrays (45,000 probe sets) and compare our analysis to previous microarray studies. METHODS. We hybridized total RNA isolated from renal cell tumors and adjacent normal tissue to Affymetrix U133A and U133B arrays. We removed samples with technical defects and removed probesets that failed to exhibit sequence-specific hybridization in any of the samples. We detected differential gene expression in the resulting dataset with parametric methods and identified keywords that are overrepresented in the differentially expressed genes with the Fisher-exact test. RESULTS. We identify 1,234 genes that are more than three-fold changed in renal tumors by t-test, 800 of which have not been previously reported to be altered in renal cell tumors. Of the only 37 genes that have been identified as being differentially expressed in three or more of five previous microarray studies of renal tumor gene expression, our analysis finds 33 of these genes (89%). A key to the sensitivity and power of our analysis is filtering out defective samples and genes that are not reliably detected. CONCLUSIONS. The widespread use of sample-wise voting schemes for detecting differential expression that do not control for false positives likely account for the poor overlap among previous studies. Among the many genes we identified using parametric methods that were not previously reported as being differentially expressed in renal cell tumors are several oncogenes and tumor suppressor genes that likely play important roles in renal cell carcinogenesis. This highlights the need for rigorous statistical approaches in microarray studies.National Institutes of Healt