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

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 and integration of the marker-level estimates with complimentary Bioconductor software for inferring regions of copy number gain or loss. All analyses are performed in the statistical environment R.

Comparison of Haplotype-based and Tree-based SNP Imputation in Association Studies

Missing single nucleotide polymorphisms (SNPs) are quite common in genetic association studies. Subjects with missing SNPs are often discarded in analyses, which may seriously undermine the inference of SNP-disease association. In this article, we compare two haplotype-based imputation approaches and one regression tree-based imputation approach for association studies. The goal is to assess the imputation accuracy, and to evaluate the impact of imputation on parameter estimation. Haplotype-based approaches build on haplotype reconstruction by the expectation-maximization (EM) algorithm or a weighted EM (WEM) algorithm, depending on whether case-control status is taken into account. The tree-based approach uses a Gibbs sampler to iteratively sample from a full conditional distribution, which is obtained from the classification and regression tree (CART) algorithm. We employ a standard multiple imputation procedure to account for the uncertainty of imputation. We apply the methods to simulated data as well as a case-control study on developmental dyslexia. Our results suggest that imputation generally improves over the standard practice of ignoring missing data in terms of bias and efficiency. The haplotype-based approaches slightly outperform the tree-based approach when there are a small number of SNPs in linkage disequilibrium (LD), but the latter has a computational advantage. Finally, we demonstrate that utilizing the disease status in imputation helps to reduce the bias in the subsequent parameter estimation

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

Haplotype block partitioning as a tool for dimensionality reduction in SNP association studies

<p>Abstract</p> <p>Background</p> <p>Identification of disease-related genes in association studies is challenged by the large number of SNPs typed. To address the dilution of power caused by high dimensionality, and to generate results that are biologically interpretable, it is critical to take into consideration spatial correlation of SNPs along the genome. With the goal of identifying true genetic associations, partitioning the genome according to spatial correlation can be a powerful and meaningful way to address this dimensionality problem.</p> <p>Results</p> <p>We developed and validated an MCMC Algorithm To Identify blocks of Linkage DisEquilibrium (MATILDE) for clustering contiguous SNPs, and a statistical testing framework to detect association using partitions as units of analysis. We compared its ability to detect true SNP associations to that of the most commonly used algorithm for block partitioning, as implemented in the Haploview and HapBlock software. Simulations were based on artificially assigning phenotypes to individuals with SNPs corresponding to region 14q11 of the HapMap database. When block partitioning is performed using MATILDE, the ability to correctly identify a disease SNP is higher, especially for small effects, than it is with the alternatives considered.</p> <p>Advantages can be both in terms of true positive findings and limiting the number of false discoveries. Finer partitions provided by LD-based methods or by marker-by-marker analysis are efficient only for detecting big effects, or in presence of large sample sizes. The probabilistic approach we propose offers several additional advantages, including: a) adapting the estimation of blocks to the population, technology, and sample size of the study; b) probabilistic assessment of uncertainty about block boundaries and about whether any two SNPs are in the same block; c) user selection of the probability threshold for assigning SNPs to the same block.</p> <p>Conclusion</p> <p>We demonstrate that, in realistic scenarios, our adaptive, study-specific block partitioning approach is as or more efficient than currently available LD-based approaches in guiding the search for disease loci.</p

TRIO LOGIC REGRESSION - DETECTION OF SNP - SNP INTERACTIONS IN CASE-PARENT TRIOS

Statistical approaches to evaluate higher order SNP-SNP and SNP-environment interactions are critical in genetic association studies, as susceptibility to complex disease is likely to be related to the interaction of multiple SNPs and environmental factors. Logic regression (Kooperberg et al., 2001; Ruczinski et al., 2003) is one such approach, where interactions between SNPs and environmental variables are assessed in a regression framework, and interactions become part of the model search space. In this manuscript we extend the logic regression methodology, originally developed for cohort and case-control studies, for studies of trios with affected probands. Trio logic regression accounts for the linkage disequilibrium (LD) structure in the genotype data, and accommodates missing genotypes via haplotype-based imputation. We also derive an efficient algorithm to simulate case-parent trios where genetic risk is determined via epistatic interactions

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)

Analysis and visualization of chromosomal abnormalities in SNP data with SNPscan

BACKGROUND: A variety of diseases are caused by chromosomal abnormalities such as aneuploidies (having an abnormal number of chromosomes), microdeletions, microduplications, and uniparental disomy. High density single nucleotide polymorphism (SNP) microarrays provide information on chromosomal copy number changes, as well as genotype (heterozygosity and homozygosity). SNP array studies generate multiple types of data for each SNP site, some with more than 100,000 SNPs represented on each array. The identification of different classes of anomalies within SNP data has been challenging. RESULTS: We have developed SNPscan, a web-accessible tool to analyze and visualize high density SNP data. It enables researchers (1) to visually and quantitatively assess the quality of user-generated SNP data relative to a benchmark data set derived from a control population, (2) to display SNP intensity and allelic call data in order to detect chromosomal copy number anomalies (duplications and deletions), (3) to display uniparental isodisomy based on loss of heterozygosity (LOH) across genomic regions, (4) to compare paired samples (e.g. tumor and normal), and (5) to generate a file type for viewing SNP data in the University of California, Santa Cruz (UCSC) Human Genome Browser. SNPscan accepts data exported from Affymetrix Copy Number Analysis Tool as its input. We validated SNPscan using data generated from patients with known deletions, duplications, and uniparental disomy. We also inspected previously generated SNP data from 90 apparently normal individuals from the Centre d'Étude du Polymorphisme Humain (CEPH) collection, and identified three cases of uniparental isodisomy, four females having an apparently mosaic X chromosome, two mislabelled SNP data sets, and one microdeletion on chromosome 2 with mosaicism from an apparently normal female. These previously unrecognized abnormalities were all detected using SNPscan. The microdeletion was independently confirmed by fluorescence in situ hybridization, and a region of homozygosity in a UPD case was confirmed by sequencing of genomic DNA. CONCLUSION: SNPscan is useful to identify chromosomal abnormalities based on SNP intensity (such as chromosomal copy number changes) and heterozygosity data (including regions of LOH and some cases of UPD). The program and source code are available at the SNPscan website

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 and integration of the marker-level estimates with complimentary Bioconductor software for inferring regions of copy number gain or loss. All analyses are performed in the statistical environment R

A MULTILEVEL MODEL TO ADDRESS BATCH EFFECTS IN COPY NUMBER 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)