A MULTILEVEL MODEL TO ADDRESS BATCH EFFECTS IN COPY NUMBER ESTIMATION USING SNP ARRAYS

Submicroscopic changes in chromosomal DNA copy number dosage are common and have been implicated in many heritable diseases and cancers. Recent high-throughput technologies have a resolution that permits the detection of segmental changes in DNA copy number that span thousands of basepairs across the genome. Genome-wide association studies (GWAS) may simultaneously screen for copy number-phenotype and SNP-phenotype associations as part of the analytic strategy. However, genome-wide array analyses are particularly susceptible to batch effects as the logistics of preparing DNA and processing thousands of arrays often involves multiple laboratories and technicians, or changes over calendar time to the reagents and laboratory equipment. Failure to adjust for batch effects can lead to incorrect inference and requires inefficient post-hoc quality control procedures that exclude regions that are associated with batch. Our work extends previous model-based approaches for copy number estimation by explicitly modeling batch effects and using shrinkage to improve locus-specific estimates of copy number uncertainty. Key features of this approach include the use of diallelic genotype calls from experimental data to estimate batch- and locus-specific parameters of background and signal without the requirement of training data. We illustrate these ideas using a study of bipolar disease and a study of chromosome 21 trisomy. The former has batch effects that dominate much of the observed variation in quantile-normalized intensities, while the latter illustrates the robustness of our approach to datasets where as many as 25% of the samples have altered copy number. Locus-specific estimates of copy number can be plotted on the copy-number scale to investigate mosaicism and guide the choice of appropriate downstream approaches for smoothing the copy number as a function of physical position. The software is open source and implemented in the R package CRLMM available at Bioconductor (http:www.bioconductor.org).

A HIDDEN MARKOV MODEL FOR JOINT ESTIMATION OF GENOTYPE AND COPY NUMBER IN HIGH-THROUGHPUT SNP CHIPS

Amplifications and deletions of chromosomal DNA, as well as copy-neutral loss of heterozygosity have been associated with diseases processes. High-throughput single nucleotide polymorphism (SNP) arrays are useful for making genome-wide estimates of copy number and genotype calls. Because neighboring SNPs in high throughput SNP arrays are likely to have dependent copy number and genotype due to the underlying haplotype structure and linkage disequilibrium, hidden Markov models (HMM) may be useful for improving genotype calls and copy number estimates that do not incorporate information from nearby SNPs. We improve previous approaches that utilize a HMM framework for inference in high throughput SNP arrays by integrating copy number, genotype calls, and the corresponding confidence scores when available. Using simulated data, we demonstrate how confidence scores control smoothing in a probabilistic framework. Software for fitting HMMs to SNP array data is available in the R package ICE.

USING THE R PACKAGE crlmm FOR GENOTYPING AND COPY NUMBER ESTIMATION

Genotyping platforms such as Affymetrix can be used to assess genotype-phenotype as well as copy number-phenotype associations at millions of markers. While genotyping algorithms are largely concordant when assessed on HapMap samples, tools to assess copy number changes are more variable and often discordant. One explanation for the discordance is that copy number estimates are susceptible to systematic differences between groups of samples that were processed at different times or by different labs. Analysis algorithms that do not adjust for batch effects are prone to spurious measures of association. The R package crlmm implements a multilevel model that adjusts for batch effects and provides allele-specific estimates of copy number. This paper illustrates a workflow for the estimation of allele-specific copy number, develops markerand study-level summaries of batch effects, and demonstrates how the marker-level estimates can be integrated with complimentary Bioconductor software for inferring regions of copy number gain or loss. All analyses are performed in the statistical environment R. A compendium for reproducing the analysis is available from the author’s website (http://www.biostat.jhsph.edu/~rscharpf/crlmmCompendium/index.html).

A Pseudolikelihood Approach for Simultaneous Analysis of Array Comparative Genomic Hybridizations (aCGH)

DNA sequence copy number has been shown to be associated with cancer development and progression. Array-based Comparative Genomic Hybridization (aCGH) is a recent development that seeks to identify the copy number ratio at large numbers of markers across the genome. Due to experimental and biological variations across chromosomes and across hybridizations, current methods are limited to analyses of single chromosomes. We propose a more powerful approach that borrows strength across chromosomes and across hybridizations. We assume a Gaussian mixture model, with a hidden Markov dependence structure, and with random effects to allow for intertumoral variation, as well as intratumoral clonal variation. For ease of computation, we base estimation on a pseudolikelihood function. The method produces quantitative assessments of the likelihood of genetic alterations at each clone, along with a graphical display for simple visual interpretation. We assess the characteristics of the method through simulation studies and through analysis of a brain tumor aCGH data set. We show that the pseudolikelihood approach is superior to existing methods both in detecting small regions of copy number alteration and in accurately classifying regions of change when intratumoral clonal variation is present.

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.

Bayesian Hidden Markov Modeling of Array CGH Data

Genomic alterations have been linked to the development and progression of cancer. The technique of Comparative Genomic Hybridization (CGH) yields data consisting of fluorescence intensity ratios of test and reference DNA samples. The intensity ratios provide information about the number of copies in DNA. Practical issues such as the contamination of tumor cells in tissue specimens and normalization errors necessitate the use of statistics for learning about the genomic alterations from array-CGH data. As increasing amounts of array CGH data become available, there is a growing need for automated algorithms for characterizing genomic profiles. Specifically, there is a need for algorithms that can identify gains and losses in the number of copies based on statistical considerations, rather than merely detect trends in the data. We adopt a Bayesian approach, relying on the hidden Markov model to account for the inherent dependence in the intensity ratios. Posterior inferences are made about gains and losses in copy number. Localized amplifications (associated with oncogene mutations) and deletions (associated with mutations of tumor suppressors) are identified using posterior probabilities. Global trends such as extended regions of altered copy number are detected. Since the posterior distribution is analytically intractable, we implement a Metropolis-within-Gibbs algorithm for efficient simulation-based inference. Publicly available data on pancreatic adenocarcinoma, glioblastoma multiforme and breast cancer are analyzed, and comparisons are made with some widely-used algorithms to illustrate the reliability and success of the technique.