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PubMed2003

Generalized monotonic regression using random change points.

We introduce a procedure for generalized monotonic curve fitting that is based on a Bayesian analysis of the isotonic regression model. Conventional isotonic regression fits monotonically increasing step functions to data. In our approach we treat the number and location of the steps as random. For each step level we adopt the conjugate prior to the sampling distribution of the data as if the curve was unconstrained. We then propose to use Markov chain Monte Carlo simulation to draw samples from the unconstrained model space and retain only those samples for which the monotonic constraint holds. The proportion of the samples collected for which the constraint holds can be used to provide a value for the weight of evidence in terms of Bayes factors for monotonicity given the data. Using the samples, probability statements can be made about other quantities of interest such as the number of change points in the data and posterior distributions on the location of the change points can be provided. The method is illustrated throughout by a reanalysis of the leukaemia data studied by Schell and Singh.

Bayes Theorem↗
PubMed2005

Model inference or model selection: discussion of Klugkist, Laudy, and Hoijtink (2005).

I. Klugkist, O. Laudy, and H. Hoijtink (2005) presented a Bayesian approach to analysis of variance models with inequality constraints. Constraints may play 2 distinct roles in data analysis. They may represent prior information that allows more precise inferences regarding parameter values, or they may describe a theory to be judged against the data. In the latter case, the authors emphasized the use of Bayes factors and posterior model probabilities to select the best theory. One difficulty is that interpretation of the posterior model probabilities depends on which other theories are included in the comparison. The posterior distribution of the parameters under an unconstrained model allows one to quantify the support provided by the data for inequality constraints without requiring the model selection framework.

Analysis of Variance↗
PubMed2006

Phylogenetic systematics of the colorful, cyanide-producing millipedes of Appalachia (Polydesmida, Xystodesmidae, Apheloriini) using a total evidence Bayesian approach.

Here, we provide an exemplar-approach phylogeny of the xystodesmid millipede tribe Apheloriini with a focus on genus-group relationships-particularly of the genus Brachoria. Exemplars for the phylogenetic analysis were chosen to represent the maximum breadth of morphological diversity within all nominal genera in the tribe Apheloriini, and to broadly sample the genus Brachoria. In addition, three closely related tribes were used (Rhysodesmini, Nannariini, and Pachydesmini). Morphological and DNA sequence data were scored for Bayesian inference of phylogeny. Phylogenetic analysis resulted in polyphyletic genera Brachoria and Sigmoria, a monophyletic Apheloriini, and a "southern clade" that contains most of the tribal species diversity. We used this phylogeny to track morphological character histories and reconstruct ancestral states using stochastic character mapping. Based on the findings from the character mapping study, the diagnostic feature of the genus Brachoria, the cingulum, evolved independently in two lineages. We compared our phylogeny against prior classifications using Bayes factor hypothesis-testing and found that our phylogenetic hypothesis is inconsistent with the previous hypotheses underlying the most recent classification. With our preferred total-evidence phylogeny as a framework for taxonomic modifications, we describe a new genus, Appalachioria; supply phylogenetic diagnoses of monophyletic taxa; and provide a phylogeny-based classification for the tribe Apheloriini.

Animals↗
PubMed2004

A Bayesian mixture model for across-site heterogeneities in the amino-acid replacement process.

Most current models of sequence evolution assume that all sites of a protein evolve under the same substitution process, characterized by a 20 x 20 substitution matrix. Here, we propose to relax this assumption by developing a Bayesian mixture model that allows the amino-acid replacement pattern at different sites of a protein alignment to be described by distinct substitution processes. Our model, named CAT, assumes the existence of distinct processes (or classes) differing by their equilibrium frequencies over the 20 residues. Through the use of a Dirichlet process prior, the total number of classes and their respective amino-acid profiles, as well as the affiliations of each site to a given class, are all free variables of the model. In this way, the CAT model is able to adapt to the complexity actually present in the data, and it yields an estimate of the substitutional heterogeneity through the posterior mean number of classes. We show that a significant level of heterogeneity is present in the substitution patterns of proteins, and that the standard one-matrix model fails to account for this heterogeneity. By evaluating the Bayes factor, we demonstrate that the standard model is outperformed by CAT on all of the data sets which we analyzed. Altogether, these results suggest that the complexity of the pattern of substitution of real sequences is better captured by the CAT model, offering the possibility of studying its impact on phylogenetic reconstruction and its connections with structure-function determinants.

Amino Acid Sequence↗
PubMed2005

Exploratory Bayesian model selection for serial genetics data.

Characterizing the process by which molecular and cellular level changes occur over time will have broad implications for clinical decision making and help further our knowledge of disease etiology across many complex diseases. However, this presents an analytic challenge due to the large number of potentially relevant biomarkers and the complex, uncharacterized relationships among them. We propose an exploratory Bayesian model selection procedure that searches for model simplicity through independence testing of multiple discrete biomarkers measured over time. Bayes factor calculations are used to identify and compare models that are best supported by the data. For large model spaces, i.e., a large number of multi-leveled biomarkers, we propose a Markov chain Monte Carlo (MCMC) stochastic search algorithm for finding promising models. We apply our procedure to explore the extent to which HIV-1 genetic changes occur independently over time.

Algorithms↗
PubMed2006

Continued evolution in gp41 after interruption of enfuvirtide in subjects with advanced HIV type 1 disease.

Careful examination of viral dynamics during antiretroviral treatment can provide important insights into HIV pathogenesis. We examined viral evolution during and after enfuvirtide (T-20) treatment with an objective of defining the characteristics of viral evolution during advanced HIV immunodeficiency. Specifically, we examined the viral quasispecies from nine patients who experienced incomplete viral suppression on an enfuvirtide-based regimen, and who subsequently interrupted enfuvirtide while remaining on a stable optimized background regimen (enfuvirtide "partial treatment interruption"). On average, eight clones were sequenced from three time points: pre-enfuvirtide, post-enfuvirtide failure, and post-enfuvirtide interruption. We utilized a Bayesian hierarchical phylogenetic model to assess the evolutionary relatedness of the virus that emerged over time. In most subjects, interruption of enfuvirtide was associated with continued viral evolution as enfuvirtide mutations waned; in no subject did we find clear evidence supporting the reemergence of archived wild-type variants (Bayes factor=30.2, p=0.01). Evidence supporting ongoing viral evolution was particularly strong in subjects whose virus remained diverse or became more diverse during enfuvirtide therapy. In contrast to observations when all drugs are interrupted, loss of resistance during enfuvirtide interruption is most likely due to ongoing viral evolution (and back-mutation), rather than emergence of an archived virus.

Bayes Theorem↗
PubMed2004

Comparison of methods for handling censored records in beef fertility data: simulation study.

A simulation study was conducted to compare methods for handling censored records for days to calving in beef cattle data. Days to calving was defined as the time, in days, between when a bull is turned out in the pasture and the subsequent parturition. Simulated data were generated to have data structure and genetic relationships similar to an available field data set. Records were simulated for 33,176 daughters of 4,238 sires. Data were simulated using a mixed linear model that included the fixed effects of contemporary group and sex of calf, linear and quadratic covariates for age at mating, and random effects of animal and residual error. Two methods for handling censored records were evaluated, and two censoring rates of 12 and 20% were applied to assess the influence of higher censoring rates on inferences. Censored records were assigned penalty values on a within-contemporary group basis under the first method (DCPEN). Under the second method (DCSIM), censored records were drawn from their respective predictive distributions. A Bayesian approach via Gibbs sampling was used to estimate variance components and predict breeding values. Posterior means (PM) and standard deviations (SD) of additive genetic variance for DCPEN at 12 and 20% censoring were 23.2 (3.7) and 21.0 (3.6), respectively, whereas the same estimates for DCSIM at 12 and 20% censoring were 23.7(3.3) and 21.9 (3.4), respectively. In all cases, the true value of the genetic variance was within the high posterior density (HPD) interval (95%). The PM (SD) of residual variance for DCPEN at 12 and 20% censoring were 415.7 (4.7) and 440.0 (4.8) respectively, whereas the same estimates for DCSIM at 12 and 20% censoring were 371.0 (4.3) and 365.4 (4.4), respectively. The true value of the residual variance was within the HPD (95%) for DCSIM, but it was outside this interval for DCPEN at both censoring rates, indicating a systematic bias for this parameter. Bayes Factor and Deviance Information Criteria were used for model comparisons, and both criteria indicated the superiority of the DCSIM method. However, little difference was observed between the two methods for correlations between true breeding values and posterior means of animal effects for sires, indicating that no major reranking of sires would be expected. This finding suggests that either censored data handling technique can be successfully used in a genetic evaluation for days to calving.

Animals↗
PubMed2006

Major gene detection for fusiform rust resistance using Bayesian complex segregation analysis in loblolly pine.

The presence of major genes affecting rust resistance of loblolly pine was investigated in a progeny population that was generated with a half-diallel mating of six parents. A Bayesian complex segregation analysis was used to make inference about a mixed inheritance model (MIM) that included polygenic effects and a single major gene effect. Marginalizations were achieved by using Gibbs sampler. A parent block sampling by which genotypes of a parent and its offspring were sampled jointly was implemented to improve mixing. The MIM was compared with a pure polygenic model (PM) using Bayes factor. Results showed that the MIM was a better model to explain the inheritance of rust resistance than the pure PM in the diallel population. A large major gene variance component estimate (> 50% of total variance), indicated the existence of major genes for rust resistance in the studied loblolly pine population. Based on estimations of parental genotypes, it appears that there may be two or more major genes affecting disease phenotypes in this diallel population.

Basidiomycota↗
PubMed2005

Phylogeny and biogeography of the freshwater crayfish Euastacus (Decapoda: Parastacidae) based on nuclear and mitochondrial DNA.

Euastacus crayfish are endemic to freshwater ecosystems of the eastern coast of Australia. While recent evolutionary studies have focused on a few of these species, here we provide a comprehensive phylogenetic estimate of relationships among the species within the genus. We sequenced three mitochondrial gene regions (COI, 16S, and 12S) and one nuclear region (28S) from 40 species of the genus Euastacus, as well as one undescribed species. Using these data, we estimated the phylogenetic relationships within the genus using maximum-likelihood, parsimony, and Bayesian Markov Chain Monte Carlo analyses. Using Bayes factors to test different model hypotheses, we found that the best phylogeny supports monophyletic groupings of all but two recognized species and suggests a widespread ancestor that diverged by vicariance. We also show that Euastacus and Astacopsis are most likely monophyletic sister genera. We use the resulting phylogeny as a framework to test biogeographic hypotheses relating to the diversification of the genus.

Animals↗
PubMed2025

Exploiting pleiotropy to enhance variant discovery with functional false discovery rates.

The cost of recruiting participants for genome-wide association studies (GWASs) can limit sample sizes and hinder the discovery of genetic variants. Here we introduce the surrogate functional false discovery rate (sfFDR) framework that integrates summary statistics of related traits to increase power. The sfFDR framework provides estimates of FDR quantities such as the functional local FDR and q value, and uses these estimates to derive a functional P value for type I error rate control and a functional local Bayes' factor for post-GWAS analyses. Compared with a standard analysis, sfFDR substantially increased power (equivalent to a 52% increase in sample size) in a study of obesity-related traits from the UK Biobank and discovered eight additional lead SNPs near genes linked to immune-related responses in a rare disease GWAS of eosinophilic granulomatosis with polyangiitis. Collectively, these results highlight the utility of exploiting related traits in both small and large studies.

Humans↗
PubMed1999

On Bayesian calculations for mixture likelihoods and priors.

We present methodology for calculating Bayes factors between models as well as posterior probabilities of the models when the indicator variables of the models are integrated out of the posterior before Markov chain Monte Carlo (MCMC) computations. Standard methodology would include the indicator functions as part of the MCMC computations. We demonstrate that our methodology can give substantially greater accuracy than the traditional approach. We illustrate the methodology using the model selection prior of George and McCulloch applied to logistic regression and to a mixture model for observations in a hierarchical random effects model.

Bayes Theorem↗
PubMed2002

A Bayesian approach to the transmission/disequilibrium test for binary traits.

The transmission/disequilibrium test (TDT) for binary traits is a powerful method for detecting linkage between a marker locus and a trait locus in the presence of allelic association. The TDT uses information on the parent-to-offspring transmission status of the associated allele at the marker locus to assess linkage or association in the presence of the other, using one affected offspring from each set of parents. For testing for linkage in the presence of association, more than one offspring per family can be used. However, without incorporating the correlation structure among offspring, it is not possible to correctly assess the association in the presence of linkage. In this presentation, we propose a Bayesian TDT method as a complementary alternative to the classical approach. In the hypothesis testing setup, given two competing hypotheses, the Bayes factor can be used to weigh the evidence in favor of one of them, thus allowing us to decide between the two hypotheses using established criteria. We compare the proposed Bayesian TDT with a competing frequentist-testing method with respect to power and type I error validity. If we know the mode of inheritance of the disease, then the joint and marginal posterior distributions for the recombination fraction (theta) and disequilibrium coefficient (delta) can be obtained via standard MCMC methods, which lead naturally to Bayesian credible intervals for both parameters.

Alleles↗
PubMed2006

A Bayesian compound stochastic process for modeling nonstationary and nonhomogeneous sequence evolution.

Variations of nucleotidic composition affect phylogenetic inference conducted under stationary models of evolution. In particular, they may cause unrelated taxa sharing similar base composition to be grouped together in the resulting phylogeny. To address this problem, we developed a nonstationary and nonhomogeneous model accounting for compositional biases. Unlike previous nonstationary models, which are branchwise, that is, assume that base composition only changes at the nodes of the tree, in our model, the process of compositional drift is totally uncoupled from the speciation events. In addition, the total number of events of compositional drift distributed across the tree is directly inferred from the data. We implemented the method in a Bayesian framework, relying on Markov Chain Monte Carlo algorithms, and applied it to several nucleotidic data sets. In most cases, the stationarity assumption was rejected in favor of our nonstationary model. In addition, we show that our method is able to resolve a well-known artifact. By Bayes factor evaluation, we compared our model with 2 previously developed nonstationary models. We show that the coupling between speciations and compositional shifts inherent to branchwise models may lead to an overparameterization, resulting in a lesser fit. In some cases, this leads to incorrect conclusions, concerning the nature of the compositional biases. In contrast, our compound model more flexibly adapts its effective number of parameters to the data sets under investigation. Altogether, our results show that accounting for nonstationary sequence evolution may require more elaborate and more flexible models than those currently used.

Animals↗
PubMed2006

Short communication: Optimal random regression models for milk production in dairy cattle.

Legendre polynomials of orders 3 to 8 in random regression models (RRM) for first-lactation milk production in Canadian Holsteins were compared statistically to determine the best model. Twenty-six RRM were compared using LP of order 5 for the phenotypic age-season groupings. Variance components of RRM were estimated using Bayesian estimation via Gibbs sampling. Several statistical criteria for model comparison were used including the total residual variance, the log likelihood function, Akaike's information criterion, the Bayesian information criterion, Bayes factors, an information-theoretic measure of model complexity, and the percentage relative reduction in complexity. The residual variance always picks the model with the most parameters. The log likelihood and information-theoretic measure picked the model with order 5 for additive genetic effects and order 7 for permanent environmental effects. The currently used model in Canada (order 5 for both additive and permanent environmental effects) was not the best for any single criterion, but was optimal when considering all criteria.

Animals↗
PubMed2002

Bayesian analysis of overdispersed chromosome aberration data with the negative binomial model.

The usual assumption of a Poisson model for the number of chromosome aberrations in controlled calibration experiments implies variance equal to the mean. However, it is known that chromosome aberration data from experiments involving high linear energy transfer radiations can be overdispersed, i.e. the variance is greater than the mean. Present methods for dealing with overdispersed chromosome data rely on frequentist statistical techniques. In this paper. the problem of overdispersion is considered from a Bayesian standpoint. The Bayes Factor is used to compare Poisson and negative binomial models for two previously published calibration data sets describing the induction of dicentric chromosome aberrations by high doses of neutrons. Posterior densities for the model parameters, which characterise dose response and overdispersion are calculated and graphed. Calibrative densities are derived for unknown neutron doses from hypothetical radiation accident data to deterimine the impact of different model assumptions on dose estimates. The main conclusion is that an initial assumption of a negative binomial model is the conservative approach to chromosome dosimetry for high LET radiations.

Bayes Theorem↗
PubMed2004

Comparing alternative definitions of the contemporary group effect in Avilena Negra Iberica beef cattle using classical and Bayesian criteria.

Data on weaning weight from 12,740 animals were used to compare different definitions of contemporary groups (CG) for the genetic evaluation of the Avilena Negra Iberica beef cattle breed. Six alternative definitions for the CG effect were considered: herd-year-season of calving (HYS), with seasons defined according to the four natural seasons; herd-year-month of calving (HYM); herd clusters of 30 d (HC30-30) or 90 d (HC90-90); and adaptive herd clusters with two time limits, 30 and 90 d (HC30-90), and 30 and 180 d (HC30-180). A minimum of five observations in each CG class was required. This rendered substantial differences in loss of information, ranging from 0.7% of the total number of records for HC30-180 to 14% for HYM. Several classical statistics and Bayesian criteria for statistical model comparison were used. The use of classical criteria, such as the between- and within-CG variation and the accuracy of prediction, can be controversial because of their dependency on the unknown variance components. Residual variance decreased with the decrease in time span associated with the definition of CG. This was expected in this population because environmental conditions are highly variable throughout the year. However, estimates of the additive genetic variance for direct effects, which should not be affected by the definition of CG, were substantially larger for definitions involving larger time periods (HYS, HC90-90). When parameters used in the current evaluation procedure were used with all data sets, CG involving 30 d (HYM and HC30-30) were optimal in terms of providing the lowest/largest within-/between-CG variation. On the other hand, CG involving 90 d (HYS and HC90-90) yielded the poorest within-/between CG variation, with only a slight improvement of accuracy of prediction of direct genetic values over the other definitions. Bayes factors and cross-validation predictive densities allowed for improved discrimination among models. Models including CG spanning 30 d were more plausible and showed better predicting ability than models spanning 90 d. Adaptive CG showed intermediate results. Overall, it seems that average time span rendered by the different definitions had a major effect on the ranking of models. However, from the breeder's point of view, the loss of information associated with definitions involving shorter periods of time, such as HYM or HC30-30, might be unacceptable.

Animals↗
PubMed2006

Effect of misreported family history on Mendelian mutation prediction models.

People with familial history of disease often consult with genetic counselors about their chance of carrying mutations that increase disease risk. To aid them, genetic counselors use Mendelian models that predict whether the person carries deleterious mutations based on their reported family history. Such models rely on accurate reporting of each member's diagnosis and age of diagnosis, but this information may be inaccurate. Commonly encountered errors in family history can significantly distort predictions, and thus can alter the clinical management of people undergoing counseling, screening, or genetic testing. We derive general results about the distortion in the carrier probability estimate caused by misreported diagnoses in relatives. We show that the Bayes factor that channels all family history information has a convenient and intuitive interpretation. We focus on the ratio of the carrier odds given correct diagnosis versus given misreported diagnosis to measure the impact of errors. We derive the general form of this ratio and approximate it in realistic cases. Misreported age of diagnosis usually causes less distortion than misreported diagnosis. This is the first systematic quantitative assessment of the effect of misreported family history on mutation prediction. We apply the results to the BRCAPRO model, which predicts the risk of carrying a mutation in the breast and ovarian cancer genes BRCA1 and BRCA2.

Bayes Theorem↗
PubMed2004

Bayesian analysis of binary prediction tree models for retrospectively sampled outcomes.

Classification tree models are flexible analysis tools which have the ability to evaluate interactions among predictors as well as generate predictions for responses of interest. We describe Bayesian analysis of a specific class of tree models in which binary response data arise from a retrospective case-control design. We are also particularly interested in problems with potentially very many candidate predictors. This scenario is common in studies concerning gene expression data, which is a key motivating example context. Innovations here include the introduction of tree models that explicitly address and incorporate the retrospective design, and the use of nonparametric Bayesian models involving Dirichlet process priors on the distributions of predictor variables. The model specification influences the generation of trees through Bayes' factor based tests of association that determine significant binary partitions of nodes during a process of forward generation of trees. We describe this constructive process and discuss questions of generating and combining multiple trees via Bayesian model averaging for prediction. Additional discussion of parameter selection and sensitivity is given in the context of an example which concerns prediction of breast tumour status utilizing high-dimensional gene expression data; the example demonstrates the exploratory/explanatory uses of such models as well as their primary utility in prediction. Shortcomings of the approach and comparison with alternative tree modelling algorithms are also discussed, as are issues of modelling and computational extensions.

Algorithms↗