A high-resolution comparative radiation hybrid map of equine chromosome 4q12-q22

In this study, we present a comprehensive 5000-rad radiation hybrid map of a 40-cM region on equine chromosome 4 (ECA4) that contains quantitative trait loci for equine osteochondrosis. We mapped 29 gene-associated sequence tagged site markers using primers designed from equine expressed sequence tags or BAC clones in the ECA4q12-q22 region. Three blocks of conserved synteny, showing two chromosomal breakpoints, were identified in the segment of ECA4q12-q22. Markers from other segments of HSA7q mapped to ECA13p and ECA4p, and a region of HSA7p was homologous to ECA13p. Therefore, we have improved the resolution of the human-equine comparative map, which allows the identification of candidate genes underlying traits of interest.

A human-horse comparative map based on equine BAC end sequences

In an effort to increase the density of sequence-based markers for the horse genome we generated 9473 BAC end sequences (BESs) from the CHORI-241 BAC library with an average read length of 677 bp. BLASTN searches with the BESs revealed 4036 meaningful hits (E map. The 4036 BLASTN hits allowed the anchoring of 3079 BAC clones to the human genome, on average one corresponding equine BAC clone per megabase of human DNA. We used the BLASTN anchored BESs for an in silico prediction of the gene content and chromosome assignment of comparatively mapped equine BAC clones. As a first verification of our in silico mapping strategy we placed 19 equine BESs with matches to HSA6 onto the RH map. All markers were assigned to the predicted localizations on ECA10, ECA20, and ECA31, respectively.

Single linkage group per chromosome genetic linkage map for the horse, based on two three-generation, full-sibling, crossbred horse reference families

A genetic linkage map of the horse consisting of 742 markers, which comprises a single linkage group for each of the autosomes and the X chromosome, is presented. The map has been generated from two three-generation full-sibling reference families, sired by the same stallion, in which there are 61 individuals in the F2 generation. Each linkage group has been assigned to a chromosome and oriented with reference to markers mapped by fluorescence in situ hybridization. The average interval between markers is 3.7 cM and the linkage groups collectively span 2772 cM. The 742 markers comprise 734 microsatellite and 8 gene-based markers. The utility of the microsatellite markers for comparative mapping has been significantly enhanced by comparing their flanking sequences with the human genome sequence; this enabled conserved segments between human and horse to be identified. The new map provides a valuable resource for genetically mapping traits of interest in the horse.

A second generation radiation hybrid map to aid the assembly of the bovine genome sequence

BACKGROUND: Several approaches can be used to determine the order of loci on chromosomes and hence develop maps of the genome. However, all mapping approaches are prone to errors either arising from technical deficiencies or lack of statistical support to distinguish between alternative orders of loci. The accuracy of the genome maps could be improved, in principle, if information from different sources was combined to produce integrated maps. The publicly available bovine genomic sequence assembly with 6x coverage (Btau_2.0) is based on whole genome shotgun sequence data and limited mapping data however, it is recognised that this assembly is a draft that contains errors. Correcting the sequence assembly requires extensive additional mapping information to improve the reliability of the ordering of sequence scaffolds on chromosomes. The radiation hybrid (RH) map described here has been contributed to the international sequencing project to aid this process. RESULTS: An RH map for the 30 bovine chromosomes is presented. The map was built using the Roslin 3000-rad RH panel (BovGen RH map) and contains 3966 markers including 2473 new loci in addition to 262 amplified fragment-length polymorphisms (AFLP) and 1231 markers previously published with the first generation RH map. Sequences of the mapped loci were aligned with published bovine genome maps to identify inconsistencies. In addition to differences in the order of loci, several cases were observed where the chromosomal assignment of loci differed between maps. All the chromosome maps were aligned with the current 6x bovine assembly (Btau_2.0) and 2898 loci were unambiguously located in the bovine sequence. The order of loci on the RH map for BTA 5, 7, 16, 22, 25 and 29 differed substantially from the assembled bovine sequence. From the 2898 loci unambiguously identified in the bovine sequence assembly, 131 mapped to different chromosomes in the BovGen RH map. CONCLUSION: Alignment of the BovGen RH map with other published RH and genetic maps showed higher consistency in marker order and chromosome assignment than with the current 6x sequence assembly. This suggests that the bovine sequence assembly could be significantly improved by incorporating additional independent mapping information.

Distribution Map

Understanding large software systems is a challenging task, and to support it many approaches have been developed. Often, the result of these approaches categorize existing entities into new groups or associates them with mutually exclusive properties. In this paper we present the Distribution Map as a generic technique to visualize and analyze this type of result. Our technique is based on the notion of focus, which shows whether a property is well-encapsulated or cross-cutting, and the notion of spread, which shows whether the property is present in several parts of the system. We present a basic visualization and complement it with measurements that quantify focus and spread. To validate our technique we show evidence of applying it on the result sets of different analysis approaches. As a conclusion we propose that the Distribution Map technique should belong to any reverse engineering toolkit.

USE OF HIDDEN MARKOV MODELS FOR QTL MAPPING

An important aspect of the QTL mapping problem is the treatment of missing genotype data. If complete genotype data were available, QTL mapping would reduce to the problem of model selection in linear regression. However, in the consideration of loci in the intervals between the available genetic markers, genotype data is inherently missing. Even at the typed genetic markers, genotype data is seldom complete, as a result of failures in the genotyping assays or for the sake of economy (for example, in the case of selective genotyping, where only individuals with extreme phenotypes are genotyped). We discuss the use of algorithms developed for hidden Markov models (HMMs) to deal with the missing genotype data problem.

A Note on the Asymptotic Variance of Survival Function in the Semi-Markov Model

In Malani and Neilsen (1992) we have proposed alternative estimates of survival function (for time to disease) using a simple marker that describes time to some intermediate stage in a disease process. In this paper we derive the asymptotic variance of one such proposed estimator using two different methods and compare terms of order 1/n when there is no censoring. In the absence of censoring the asymptotic variance obtained using the Greenwood type approach converges to exact variance up to terms involving 1/n. But the asymptotic variance obtained using the theory of the counting process and results from Voelkel and Crowley (1984) on semi-Markov processes has a different term of order 1/n. It is not clear to us at this point why the variance formulae using the latter approach give different results.

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.

Checking Assumptions in Latent Class Regression Models via a Markov Chain Monte Carlo Estimation Approach: An Application to Depression and Socio-Economic Status

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to calculate posterior distributions and point estimates of any functions of parameters. It is this convenience that allows us to provide the diagnostic methods that we introduce. As a motivating example we present an analysis focusing on the association between depression and socioeconomic status, using data from the Epidemiologic Catchment Area study. We consider a latent class regression analysis investigating the association between depression and socioeconomic status measures, where the latent variable depression is regressed on education and income indicators, in addition to age, gender, and marital status variables. While the fitted latent class regression model yields interesting results, the model parameters are found to be invalid due to the violation of model assumptions. The violation of these assumptions is clearly identified by the presented diagnostic plots. These methods can be applied to standard latent class and latent class regression models, and the general principle can be extended to evaluate model assumptions in other types of models.

Fixed-Width Output Analysis for Markov Chain Monte Carlo

Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a complicated target distribution via simple ergodic averages. A fundamental question in MCMC applications is when should the sampling stop? That is, when are the ergodic averages good estimates of the desired quantities? We consider a method that stops the MCMC sampling the first time the width of a confidence interval based on the ergodic averages is less than a user-specified value. Hence calculating Monte Carlo standard errors is a critical step in assessing the output of the simulation. In particular, we consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We describe sufficient conditions for the strong consistency and asymptotic normality of both methods and investigate their finite sample properties in a variety of examples.

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.

COVARIATE-ADJUSTED NONPARAMETRIC ANALYSIS OF MAGNETIC RESONANCE IMAGES USING MARKOV CHAIN MONTE CARLO

Permutation tests are useful for drawing inferences from imaging data because of their flexibility and ability to capture features of the brain that are difficult to capture parametrically. However, most implementations of permutation tests ignore important confounding covariates. To employ covariate control in a nonparametric setting we have developed a Markov chain Monte Carlo (MCMC) algorithm for conditional permutation testing using propensity scores. We present the first use of this methodology for imaging data. Our MCMC algorithm is an extension of algorithms developed to approximate exact conditional probabilities in contingency tables, logit, and log-linear models. An application of our non-parametric method to remove potential bias due to the observed covariates is presented.