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).

EFFICIENT EVALUATION OF RANKING PROCEDURES WHEN THE NUMBER OF UNITS IS LARGE WITH APPLICATION TO SNP IDENTIFICATION

Simulation-based assessment is a popular and frequently necessary approach to evaluation of statistical procedures. Sometimes overlooked is the ability to take advantage of underlying mathematical relations and we focus on this aspect. We show how to take advantage of large-sample theory when conducting a simulation using the analysis of genomic data as a motivating example. The approach uses convergence results to provide an approximation to smaller-sample results, results that are available only by simulation. We consider evaluating and comparing a variety of ranking-based methods for identifying the most highly associated SNPs in a genome-wide association study, derive integral equation representations of the pre-posterior distribution of percentiles produced by three ranking methods, and provide examples comparing performance. These results are of interest in their own right and set the framework for a more extensive set of comparisons.

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).

The role of the number of uninvolved lymph nodes in predicting locoregional recurrence in breast cancer

PURPOSE: To identify groups of early breast cancer patients with substantial risk (10-year risk > 20%) for locoregional failure (LRF) who might benefit from postmastectomy radiotherapy (RT). PATIENTS AND METHODS: Prognostic factors for LRF were evaluated among 6,660 patients (2,588 node-negative patients, 4,072 node-positive patients) in International Breast Cancer Study Group Trials I to IX treated with chemotherapy and/or endocrine therapy, and observed for a median of 14 years. In total, 1,251 LRFs were detected. All patients were treated with mastectomy without RT. RESULTS: No group with 10-year LRF risk exceeding 20% was found among patients with node-negative disease. Among patients with node-positive breast cancer, increasing numbers of uninvolved nodes were significantly associated with decreased risk of LRF, even after adjustment for other prognostic factors. The highest quartile of uninvolved nodes was compared with the lowest quartile. Among premenopausal patients, LRF risk was decreased by 35% (P = .0010); among postmenopausal patients, LRF risk was decreased by 46% (P < .0001). The 10-year cumulative incidence of LRF was 20% among patients with one to three involved lymph nodes and fewer than 10 uninvolved nodes. Age younger than 40 years and vessel invasion were also associated significantly with increased risk. Among patients with node-positive disease, overall survival was significantly greater in those with higher numbers of uninvolved nodes examined (P < .0001). CONCLUSION: Patients with one to three involved nodes and a low number of uninvolved nodes, vessel invasion, or young age have an increased risk of LRF and may be candidates for a similar treatment as those with at least four lymph node metastases.

Effect of voluntary exercise on number and volume of cardiomyocytes and their mitochondria in the mouse left ventricle

Voluntary exercise (VE) has a beneficial influence on the heart and mean lifespan. The present study evaluates structural adaptations of cardiomyocytes and their mitochondria due to VE by new, unbiased stereological methods. Female, 7-9-week-old mice were randomly assigned to a control (CG, n = 7) or VE group (EG, n = 7). EG animals were housed in cages with free access to a running wheel and had a mean running distance of 6.7 (1.8) km per day. After 4 weeks, the hearts of all mice were processed for light and electron microscopy. We estimated the number and volume of cardiomyocytes by the disector method and the number and volume of mitochondria by estimation of the Euler number. In comparison to CG, VE did not have an effect on the myocardial volume of the left ventricle (CG: 93 (10), EG: 103 (17) (mm(3))), the number of cardiomyocytes (CG: 2.81 (0.27), EG: 2.82 (0.43) (x10(6))) and their number-weighted mean volume. However, the composition of the cardiomyocytes changed due to VE. The total volume of mitochondria (CG: 21.8 (4.9), EG: 32.2 (4.3) (mm(3)), P < 0.01) and the total number (CG: 3.76 (0.44), EG: 7.02 (1.13) (x10(10)), P < 0.001) were significantly higher in EG than in CG. The mean number-weighted mitochondrial volume was smaller in EG than in CG (P < 0.05). In summary, VE does not alter ventricular volume nor cardiomyocyte volume or number but the oxidative capacity of cardiomyocytes by an increased mitochondrial number and total volume in the left ventricle. These structural changes may participate in the beneficial effects of VE.

Mothers adjust egg size to helper number in a cooperatively breeding cichlid

Mothers should adjust the size of propagules to the selective forces to which these offspring will be exposed. Usually, a larger propagule size is favored when young are exposed to high mortality risk or conspecific competition. Here we test 2 predictions on how egg size should vary with these selective agents. When offspring are cared for by parents and/or alloparents, protection may reduce the predation risk to young, which may allow mothers to invest less per single offspring. In the cooperatively breeding cichlid Neolamprologus pulcher, brood care helpers protect group offspring and reduce the latters' mortality rate. Therefore, females are expected to reduce their investment per egg when more helpers are present. In a first experiment, we tested this prediction by manipulating the helper number. In N. pulcher, helpers compete for dispersal opportunities with similar-sized individuals of neighboring groups. If the expected future competition pressure on young is high, females should increase their investment per offspring to give them a head start. In a second experiment, we tested whether females produce larger eggs when perceived neighbor density is high. Females indeed reduced egg size with increasing helper number. However, we did not detect an effect of local density on egg size, although females took longer to produce the next clutch when local density was high. We argue that females can use the energy saved by adjusting egg size to reduced predation risk to enhance future reproductive output. Adaptive adjustment of offspring size to helper number may be an important, as yet unrecognized, strategy of cooperative breeders.

Data-driven estimates of the number of clusters in multivariate time series

An important problem in unsupervised data clustering is how to determine the number of clusters. Here we investigate how this can be achieved in an automated way by using interrelation matrices of multivariate time series. Two nonparametric and purely data driven algorithms are expounded and compared. The first exploits the eigenvalue spectra of surrogate data, while the second employs the eigenvector components of the interrelation matrix. Compared to the first algorithm, the second approach is computationally faster and not limited to linear interrelation measures.

Comparison of multiplex ligation-dependent probe amplification and real-time PCR accuracy for gene copy number quantification using the beta-defensin locus

The reliable quantification of gene copy number variations is a precondition for future investigations regarding their functional relevance. To date, there is no generally accepted gold standard method for copy number quantification, and methods in current use have given inconsistent results in selected cohorts. In this study, we compare two methods for copy number quantification. beta-defensin gene copy numbers were determined in parallel in 80 genomic DNA samples by real-time PCR and multiplex ligation-dependent probe amplification (MLPA). The pyrosequencing-based paralog ratio test (PPRT) was used as a standard of comparison in 79 out of 80 samples. Realtime PCR and MPLA results confirmed concordant DEFB4, DEFB103A, and DEFB104A copy numbers within samples. These two methods showed identical results in 32 out of 80 samples; 29 of these 32 samples comprised four or fewer copies. The coefficient of variation of MLPA is lower compared with PCR. In addition, the consistency between MLPA and PPRT is higher than either PCR/MLPA or PCR/PPRT consistency. In summary, these results suggest that MLPA is superior to real-time PCR in beta-defensin copy number quantification.

Detection of cryptic pathogenic copy number variations and constitutional loss of heterozygosity using high resolution SNP microarray analysis in 117 patients referred for cytogenetic analysis and impact on clinical practice

BACKGROUND: Microarray genome analysis is realising its promise for improving detection of genetic abnormalities in individuals with mental retardation and congenital abnormality. Copy number variations (CNVs) are now readily detectable using a variety of platforms and a major challenge is the distinction of pathogenic from ubiquitous, benign polymorphic CNVs. The aim of this study was to investigate replacement of time consuming, locus specific testing for specific microdeletion and microduplication syndromes with microarray analysis, which theoretically should detect all known syndromes with CNV aetiologies as well as new ones. METHODS: Genome wide copy number analysis was performed on 117 patients using Affymetrix 250K microarrays. RESULTS: 434 CNVs (195 losses and 239 gains) were found, including 18 pathogenic CNVs and 9 identified as "potentially pathogenic". Almost all pathogenic CNVs were larger than 500 kb, significantly larger than the median size of all CNVs detected. Segmental regions of loss of heterozygosity larger than 5 Mb were found in 5 patients. CONCLUSIONS: Genome microarray analysis has improved diagnostic success in this group of patients. Several examples of recently discovered "new syndromes" were found suggesting they are more common than previously suspected and collectively are likely to be a major cause of mental retardation. The findings have several implications for clinical practice. The study revealed the potential to make genetic diagnoses that were not evident in the clinical presentation, with implications for pretest counselling and the consent process. The importance of contributing novel CNVs to high quality databases for genotype-phenotype analysis and review of guidelines for selection of individuals for microarray analysis is emphasised.