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.

A CASE STUDY IN PHARMACOLOGIC IMAGING USING PRINCIPAL CURVES IN SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY

In this manuscript we are concerned with functional imaging of the colon to assess the kinetics of a microbicide lubricant. The overarching goal is to understand the distribution of the lubricant in the colon. Such information is crucial for understanding the potential impact of the microbicide on HIV viral transmission. The experiment was conducted by imaging a radiolabeled lubricant distributed in the subject’s colon. The tracer imaging was conducted via single photon emission computed tomography (SPECT), a non-invasive, in-vivo functional imaging technique. We develop a novel principal curve algorithm to construct a three dimensional curve through the colon images. The developed algorithm is tested and debugged on several difficult two dimensional images of familiar curves where the original principal curve algorithm does not apply. The final curve fit to the colon data is compared with experimental sigmoidoscope collection.