Bias in genetic variance estimates due to spatial autocorrelation

Summary A central problem in the analysis of genetic field trials is the dichotomy of genetic and environmental effects because one cannot be defined without the other. Results from 768,000 simulated family trials in complete randomized block designs demonstrated a serious upward bias in estimates of family variance components from multi-unit plot designs when the phenotypic observations were compatible with a first-order autoregressive (AR1) process. The inflation of family variances and, thus, additive genetic variance and narrow sense individual heritabilities progressed exponentially with an increase in the nearest neighbor correlation () in the AR1 process. Significant differences in inflation rates persisted among various plot configurations. At = 0.2 the inflation of family variances reached 48–73%. Inflation rates were independent of the level of heritability. Modified Papadakis nearest neighbor (NN) adjustment procedures were tested for their ability to remove the bias in family variances. A NN-adjustment based on Mead's coefficient of interplant interaction and one derived from Bartlett's simultaneous autoregressive scheme removed up to 97% of the bias introduced by the phenotypic correlations. NN-adjusted estimates had slightly (5–8%) higher relative errors than did unadjusted estimates.     

A Bayesian approach to jointly modeling toxicity and biomarker expression in a phase I/II dose-finding trial

In this article, we propose a Bayesian approach to phase I/II dose-finding oncology trials by jointly modeling a binary toxicity outcome and a continuous biomarker expression outcome. We apply our method to a clinical trial of a new gene therapy for bladder cancer patients. In this trial, the biomarker expression indicates biological activity of the new therapy. For ethical reasons, the trial is conducted sequentially, with the dose for each successive patient chosen using both toxicity and activity data from patients previously treated in the trial. The modeling framework that we use naturally incorporates correlation between the binary toxicity and continuous activity outcome via a latent Gaussian variable. The dose-escalation/de-escalation decision rules are based on the posterior distributions of both toxicity and activity. A flexible state-space model is used to relate the activity outcome and dose. Extensive simulation studies show that the design reliably chooses the preferred dose using both toxicity and expression outcomes under various clinical scenarios.     

Bayesian detection and modeling of spatial disease clustering

Many current statistical methods for disease clustering studies are based on a hypothesis testing paradigm. These methods typically do not produce useful estimates of disease rates or cluster risks. In this paper, we develop a Bayesian procedure for drawing inferences about specific models for spatial clustering. The proposed methodology incorporates ideas from image analysis, from Bayesian model averaging, and from model selection. With our approach, we obtain estimates for disease rates and allow for greater flexibility in both the type of clusters and the number of clusters that may be considered. We illustrate the proposed procedure through simulation studies and an analysis of the well-known New York leukemia data.     

Bayesian Inference for the Spatio-Temporal Invasion of Alien Species

In this paper we develop a Bayesian approach to parameter estimation in a stochastic spatio-temporal model of the spread of invasive species across a landscape. To date, statistical techniques, such as logistic and autologistic regression, have outstripped stochastic spatio-temporal models in their ability to handle large numbers of covariates. Here we seek to address this problem by making use of a range of covariates describing the bio-geographical features of the landscape. Relative to regression techniques, stochastic spatio-temporal models are more transparent in their representation of biological processes. They also explicitly model temporal change, and therefore do not require the assumption that the species' distribution (or other spatial pattern) has already reached equilibrium as is often the case with standard statistical approaches. In order to illustrate the use of such techniques we apply them to the analysis of data detailing the spread of an invasive plant, Heracleum mantegazzianum, across Britain in the 20th Century using geo-referenced covariate information describing local temperature, elevation and habitat type. The use of Markov chain Monte Carlo sampling within a Bayesian framework facilitates statistical assessments of differences in the suitability of different habitat classes for H. mantegazzianum, and enables predictions of future spread to account for parametric uncertainty and system variability. Our results show that ignoring such covariate information may lead to biased estimates of key processes and implausible predictions of future distributions.     

Hierarchical Bayesian modeling in dichotomous processes in the presence of nonresponse

Sampling units that do not answer a survey may dramatically affect the estimation results of interest. The response may even be conditional on the outcome of interest in the survey. If estimates are found using only those who responded, the estimate may be biased, known as nonresponse bias. We are interested in finding estimates of success rates from a survey. We begin by looking at two current Bayesian approaches to treating nonresponse in a hierarchical model. However, these approaches do not consider possible spatial correlations between domains for either success rate or response rate. We build a Bayesian hierarchical spatial model to explicitly estimate the success rate, response rate given success, and response rate given failure. The success rates in the domains of the survey are allowed to be spatially correlated. We also allow spatial dependence between domains in both response rate given success and response rate given failure. Spatial dependence is induced by a common latent spatial structure between the two conditional response rates. We use the 1998 Missouri Turkey Hunting Survey to illustrate this methodology. We find significant spatial correlation in the success rates and incorporating nonrespondents has an impact on the success rate estimates.     

bgc: Software for Bayesian estimation of genomic clines

Introgression in admixed populations can be used to identify candidate loci that might underlie adaptation or reproductive isolation. The Bayesian genomic cline model provides a framework for quantifying variable introgression in admixed populations and identifying regions of the genome with extreme introgression that are potentially associated with variation in fitness. Here we describe the bgc software, which uses Markov chain Monte Carlo to estimate the joint posterior probability distribution of the parameters in the Bayesian genomic cline model and designate outlier loci. This software can be used with next‐generation sequence data, accounts for uncertainty in genotypic state, and can incorporate information from linked loci on a genetic map. Output from the analysis is written to an HDF5 file for efficient storage and manipulation. This software is written in C++ . The source code, software manual, compilation instructions and example data sets are available under the GNU Public License at http://sites.google.com/site/bgcsoftware/ .     

Hierarchical proportional hazards regression models for highly stratified data

In clinical trials conducted over several data collection centers, the most common statistically defensible analytic method, a stratified Cox model analysis, suffers from two important defects. First, identification of units that are outlying with respect to the baseline hazard is awkward since this hazard is implicit (rather than explicit) in the Cox partial likelihood. Second (and more seriously), identification of modest treatment effects is often difficult since the model fails to acknowledge any similarity across the strata. We consider a number of hierarchical modeling approaches that preserve the integrity of the stratified design while offering a middle ground between traditional stratified and unstratified analyses. We investigate both fully parametric (Weibull) and semiparametric models, the latter based not on the Cox model but on an extension of an idea by Gelfand and Mallick (1995, Biometrics 51, 843-852), which models the integrated baseline hazard as a mixture of monotone functions. We illustrate the methods using data from a recent multicenter AIDS clinical trial, comparing their ease of use, interpretation, and degree of robustness with respect to estimates of both the unit-specific baseline hazards and the treatment effect.     

Estimation of amino acid residue substitution rates at local spatial regions and application in protein function inference: a Bayesian Monte Carlo approach

The amino acid sequences of proteins provide rich information for inferring distant phylogenetic relationships and for predicting protein functions. Estimating the rate matrix of residue substitutions from amino acid sequences is also important because the rate matrix can be used to develop scoring matrices for sequence alignment. Here we use a continuous time Markov process to model the substitution rates of residues and develop a Bayesian Markov chain Monte Carlo method for rate estimation. We validate our method using simulated artificial protein sequences. Because different local regions such as binding surfaces and the protein interior core experience different selection pressures due to functional or stability constraints, we use our method to estimate the substitution rates of local regions. Our results show that the substitution rates are very different for residues in the buried core and residues on the solvent-exposed surfaces. In addition, the rest of the proteins on the binding surfaces also have very different substitution rates from residues. Based on these findings, we further develop a method for protein function prediction by surface matching using scoring matrices derived from estimated substitution rates for residues located on the binding surfaces. We show with examples that our method is effective in identifying functionally related proteins that have overall low sequence identity, a task known to be very challenging.     

A genetic and spatial Bayesian analysis of mastitis resistance

A nationwide health card recording system for dairy cattle was introduced in Norway in 1975 (the Norwegian Cattle Health Services). The data base holds information on mastitis occurrences on an individual cow basis. A reduction in mastitis frequency across the population is desired, and for this purpose risk factors are investigated. In this paper a Bayesian proportional hazards model is used for modelling the time to first veterinary treatment of clinical mastitis, including both genetic and environmental covariates. Sire effects were modelled as shared random components, and veterinary district was included as an environmental effect with prior spatial smoothing. A non-informative smoothing prior was assumed for the baseline hazard, and Markov chain Monte Carlo methods (MCMC) were used for inference. We propose a new measure of quality for sires, in terms of their posterior probability of being among the, say 10% best sires. The probability is an easily interpretable measure that can be directly used to rank sires. Estimating these complex probabilities is straightforward in an MCMC setting. The results indicate considerable differences between sires with regards to their daughters disease resistance. A regional effect was also discovered with the lowest risk of disease in the south-eastern parts of Norway.     

Bayesian inference for kappa from single and multiple studies

Cohen's kappa coefficient is a widely popular measure for chance-corrected nominal scale agreement between two raters. This article describes Bayesian analysis for kappa that can be routinely implemented using Markov chain Monte Carlo (MCMC) methodology. We consider the case of m > or = 2 independent samples of measured agreement, where in each sample a given subject is rated by two rating protocols on a binary scale. A major focus here is on testing the homogeneity of the kappa coefficient across the different samples. The existing frequentist tests for this case assume exchangeability of rating protocols, whereas our proposed Bayesian test does not make any such assumption. Extensive simulation is carried out to compare the performances of the Bayesian and the frequentist tests. The developed methodology is illustrated using data from a clinical trial in ophthalmology.     

Alternative implementations of Monte Carlo EM algorithms for likelihood inferences

Two methods of computing Monte Carlo estimators of variance components using restricted maximum likelihood via the expectation-maximisation algorithm are reviewed. A third approach is suggested and the performance of the methods is compared using simulated data.     

Hierarchical Bayesian modeling of spatially correlated health service outcome and utilization rates

We present Bayesian hierarchical spatial models for spatially correlated small-area health service outcome and utilization rates, with a particular emphasis on the estimation of both measured and unmeasured or unknown covariate effects. This Bayesian hierarchical model framework enables simultaneous modeling of fixed covariate effects and random residual effects. The random effects are modeled via Bayesian prior specifications reflecting spatial heterogeneity globally and relative homogeneity among neighboring areas. The model inference is implemented using Markov chain Monte Carlo methods. Specifically, a hybrid Markov chain Monte Carlo algorithm (Neal, 1995, Bayesian Learning for Neural Networks; Gustafson, MacNab, and Wen, 2003, Statistics and Computing, to appear) is used for posterior sampling of the random effects. To illustrate relevant problems, methods, and techniques, we present an analysis of regional variation in intraventricular hemorrhage incidence rates among neonatal intensive care unit patients across Canada.     

Dissecting total genetic variance into additive and dominance components of purebred and crossbred pig traits

The partition of the total genetic variance into its additive and non-additive components can differ from trait to trait, and between purebred and crossbred populations. A quantification of these genetic variance components will determine the extent to which it would be of interest to account for dominance in genomic evaluations or to establish mate allocation strategies along different populations and traits. This study aims at assessing the contribution of the additive and dominance genomic variances to the phenotype expression of several purebred Piétrain and crossbred (Piétrain × Large White) pig performances. A total of 636 purebred and 720 crossbred male piglets were phenotyped for 22 traits that can be classified into six groups of traits: growth rate and feed efficiency, carcass composition, meat quality, behaviour, boar taint and puberty. Additive and dominance variances estimated in univariate genotypic models, including additive and dominance genotypic effects, and a genomic inbreeding covariate allowed to retrieve the additive and dominance single nucleotide polymorphism variances for purebred and crossbred performances. These estimated variances were used, together with the allelic frequencies of the parental populations, to obtain additive and dominance variances in terms of genetic breeding values and dominance deviations. Estimates of the Piétrain and Large White allelic contributions to the crossbred variance were of about the same magnitude in all the traits. Estimates of additive genetic variances were similar regardless of the inclusion of dominance. Some traits showed relevant amount of dominance genetic variance with respect to phenotypic variance in both populations (i.e. growth rate 8%, feed conversion ratio 9% to 12%, backfat thickness 14% to 12%, purebreds-crossbreds). Other traits showed higher amount in crossbreds (i.e. ham cut 8% to 13%, loin 7% to 16%, pH semimembranosus 13% to 18%, pH longissimus dorsi 9% to 14%, androstenone 5% to 13% and estradiol 6% to 11%, purebreds-crossbreds). It was not encountered a clear common pattern of dominance expression between groups of analysed traits and between populations. These estimates give initial hints regarding which traits could benefit from accounting for dominance for example to improve genomic estimated breeding value accuracy in genetic evaluations or to boost the total genetic value of progeny by means of assortative mating.     

Bayesian inference for stochastic kinetic models using a diffusion approximation

This article is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white noise term models stochastic behavior and the model is identified using equispaced time course data. The estimation framework involves the introduction of m- 1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters. The methodology is applied to the estimation of parameters in a prokaryotic autoregulatory gene network.     

Bayesian analysis of amino acid substitution models

Models of amino acid substitution present challenges beyond those often faced with the analysis of DNA sequences. The alignments of amino acid sequences are often small, whereas the number of parameters to be estimated is potentially large when compared with the number of free parameters for nucleotide substitution models. Most approaches to the analysis of amino acid alignments have focused on the use of fixed amino acid models in which all of the potentially free parameters are fixed to values estimated from a large number of sequences. Often, these fixed amino acid models are specific to a gene or taxonomic group (e.g. the Mtmam model, which has parameters that are specific to mammalian mitochondrial gene sequences). Although the fixed amino acid models succeed in reducing the number of free parameters to be estimated--indeed, they reduce the number of free parameters from approximately 200 to 0--it is possible that none of the currently available fixed amino acid models is appropriate for a specific alignment. Here, we present four approaches to the analysis of amino acid sequences. First, we explore the use of a general time reversible model of amino acid substitution using a Dirichlet prior probability distribution on the 190 exchangeability parameters. Second, we then explore the behaviour of prior probability distributions that are'centred' on the rates specified by the fixed amino acid model. Third, we consider a mixture of fixed amino acid models. Finally, we consider constraints on the exchangeability parameters as partitions,similar to how nucleotide substitution models are specified, and place a Dirichlet process prior model on all the possible partitioning schemes.