A Faster Circular Binary Segmentation Algorithm for the Analysis of Array CGH Data

Motivation: Array CGH technologies enable the simultaneous measurement of DNA copy number for thousands of sites on a genome. We developed the circular binary segmentation (CBS) algorithm to divide the genome into regions of equal copy number (Olshen {\it et~al}, 2004). The algorithm tests for change-points using a maximal $t$-statistic with a permutation reference distribution to obtain the corresponding $p$-value. The number of computations required for the maximal test statistic is $O(N^2),$ where $N$ is the number of markers. This makes the full permutation approach computationally prohibitive for the newer arrays that contain tens of thousands markers and highlights the need for a faster. algorithm. Results: We present a hybrid approach to obtain the $p$-value of the test statistic in linear time. We also introduce a rule for stopping early when there is strong evidence for the presence of a change. We show through simulations that the hybrid approach provides a substantial gain in speed with only a negligible loss in accuracy and that the stopping rule further increases speed. We also present the analysis of array CGH data from a breast cancer cell line to show the impact of the new approaches on the analysis of real data. Availability: An R (R Development Core Team, 2006) version of the CBS algorithm has been implemented in the ``DNAcopy'' package of the Bioconductor project (Gentleman {\it et~al}, 2004). The proposed hybrid method for the $p$-value is available in version 1.2.1 or higher and the stopping rule for declaring a change early is available in version 1.5.1 or higher.

An introduction to low-level analysis methods of DNA microarray data

This article gives an overview over the methods used in the low--level analysis of gene expression data generated using DNA microarrays. This type of experiment allows to determine relative levels of nucleic acid abundance in a set of tissues or cell populations for thousands of transcripts or loci simultaneously. Careful statistical design and analysis are essential to improve the efficiency and reliability of microarray experiments throughout the data acquisition and analysis process. This includes the design of probes, the experimental design, the image analysis of microarray scanned images, the normalization of fluorescence intensities, the assessment of the quality of microarray data and incorporation of quality information in subsequent analyses, the combination of information across arrays and across sets of experiments, the discovery and recognition of patterns in expression at the single gene and multiple gene levels, and the assessment of significance of these findings, considering the fact that there is a lot of noise and thus random features in the data. For all of these components, access to a flexible and efficient statistical computing environment is an essential aspect.

Differential Expression with the Bioconductor Project

A basic, yet challenging task in the analysis of microarray gene expression data is the identification of changes in gene expression that are associated with particular biological conditions. We discuss different approaches to this task and illustrate how they can be applied using software from the Bioconductor Project. A central problem is the high dimensionality of gene expression space, which prohibits a comprehensive statistical analysis without focusing on particular aspects of the joint distribution of the genes expression levels. Possible strategies are to do univariate gene-by-gene analysis, and to perform data-driven nonspecific filtering of genes before the actual statistical analysis. However, more focused strategies that make use of biologically relevant knowledge are more likely to increase our understanding of the data.