Objective Bayes model selection in probit models.

We describe a new variable selection procedure for categorical responses where the candidate models are all probit regression models. The procedure uses objective intrinsic priors for the model parameters, which do not depend on tuning parameters, and ranks the models for the different subsets of covariates according to their model posterior probabilities. When the number of covariates is moderate or large, the number of potential models can be very large, and for those cases, we derive a new stochastic search algorithm that explores the potential sets of models driven by their model posterior probabilities. The algorithm allows the user to control the dimension of the candidate models and thus can handle situations when the number of covariates exceed the number of observations. We assess, through simulations, the performance of the procedure and apply the variable selector to a gene expression data set, where the response is whether a patient exhibits pneumonia. Software needed to run the procedures is available in the R package varselectIP.

A regionalised strategy for improving motor vehicle-related highway driver deaths using a weighted averages method.

OBJECTIVE: The state of Florida has some of the most dangerous highways in the USA. In 2006, Florida averaged 1.65 fatalities per 100 million vehicle miles travelled (VMT) compared with the national average of 1.42. A study was undertaken to find a method of identifying counties that contributed to the most driver fatalities after a motor vehicle collision (MVC). By regionalising interventions unique to this subset of counties, the use of resources would have the greatest potential of improving statewide driver death. METHODS: The Florida Highway Safety Motor Vehicle database 2000-2006 was used to calculate driver VMT-weighted deaths by county. A total of 3,468,326 motor vehicle crashes were evaluated. Counties that had driver death rates higher than the state average were sorted by a weighted averages method. Multivariate regression was used to calculate the likelihood of death for various risk factors. RESULTS: VMT-weighted death rates identified 12 out of 67 counties that contributed up to 50% of overall driver fatalities. These counties were primarily clustered in central and south Florida. The strongest independent risk factors for driver death attributable to MVC in these high-risk counties were alcohol/drug use, rural roads, speed limit ≥45 mph, adverse weather conditions, divided highways, vehicle type, vehicle defects and roadway location. CONCLUSIONS: Using the weighted averages method, a small subset of counties contributing to the majority of statewide driver fatalities was identified. Regionalised interventions on specific risk factors in these counties may have the greatest impact on reducing driver-related MVC fatalities.

Generalized shrinkage F-like statistics for testing an interaction term in gene expression analysis in the presence of heteroscedasticity.

BACKGROUND: Many analyses of gene expression data involve hypothesis tests of an interaction term between two fixed effects, typically tested using a residual variance. In expression studies, the issue of variance heteroscedasticity has received much attention, and previous work has focused on either between-gene or within-gene heteroscedasticity. However, in a single experiment, heteroscedasticity may exist both within and between genes. Here we develop flexible shrinkage error estimators considering both between-gene and within-gene heteroscedasticity and use them to construct F-like test statistics for testing interactions, with cutoff values obtained by permutation. These permutation tests are complicated, and several permutation tests are investigated here. RESULTS: Our proposed test statistics are compared with other existing shrinkage-type test statistics through extensive simulation studies and a real data example. The results show that the choice of permutation procedures has dramatically more influence on detection power than the choice of F or F-like test statistics. When both types of gene heteroscedasticity exist, our proposed test statistics can control preselected type-I errors and are more powerful. Raw data permutation is not valid in this setting. Whether unrestricted or restricted residual permutation should be used depends on the specific type of test statistic. CONCLUSIONS: The F-like test statistic that uses the proposed flexible shrinkage error estimator considering both types of gene heteroscedasticity and unrestricted residual permutation can provide a statistically valid and powerful test. Therefore, we recommended that it should always applied in the analysis of real gene expression data analysis to test an interaction term.

Interval estimation in two-stage, drop-the-losers clinical trials with flexible treatment selection.

In a two-stage, drop-the-losers clinical trial, researchers choose the 'best' among a number of treatments at an interim analysis after the first stage. The selected treatment continues to the second stage for confirmation of efficacy, and the remaining treatments (the 'losers') are dropped from the study. Wu et al. (Biometrika 2010; 97:405-418) showed how to construct confidence limits for the mean difference between the selected treatment and the control when the treatment is chosen after the first stage based on the highest efficacy in the primary clinical endpoint. In this article, we show how to construct a lower confidence limit for the mean difference when the treatment is chosen based on first-stage safety data, early endpoint efficacy data, a combination of safety and efficacy data or any other prespecified selection rule. The result extends the applicability of drop-the-losers designs, for in practice, the 'best' treatment often is not chosen for efficacy alone.

Score statistics for mapping quantitative trait loci.

We propose a method to detect the existence of quantitative trait loci (QTL) in a backcross population using a score test. Since the score test only uses the MLEs of parameters under the null hypothesis, it is computationally simpler than the likelihood ratio test (LRT). Moreover, because the location parameter of the QTL is unidentifiable under the null hypothesis, the distribution of the maximum of the LRT statistics, typically the statistic of choice for testing H0: no QTL, does not have the standard chi-square distribution asymptotically under the null hypothesis. From the simple structure of the score test statistics, the asymptotic null distribution can be derived for the maximum of the square of score test statistics. Numerical methods are proposed to compute the asymptotic null distribution and the critical thresholds can be obtained accordingly. We show that the maximum of the LR test statistics and the maximum of the square of score statistics are asymptotically equivalent. Therefore, the critical threshold for the score test can be used for the LR test also. A simple backcross design is used to demonstrate the application of the score test to QTL mapping.

Model-based Bayesian clustering (MBBC).

MOTIVATION: The program MBBC 2.0 clusters time-course microarray data using a Bayesian product partition model. RESULTS: The Bayesian product partition model in Booth et al. (2007) simultaneously searches for the optimal number of clusters, and assigns cluster memberships based on temporal changes of gene expressions. MBBC 2.0 to makes this method easily available for statisticians and scientists, and is built with three free computer language software packages: Ox, R and C++, taking advantage of the strengths of each language. Within MBBC, the search algorithm is implemented with Ox and resulting graphs are drawn with R. A user-friendly graphical interface is built with C++ to run the Ox and R programs internally. Thus, MBBC users are not required to know how to use Ox, R or C++, but they must be pre-installed. AVAILABILITY: A self-extractable zip file, MBBC20zip.exe, is available at the MBBC webpage www.stat.ufl.edu/~casella/mbbc/, which contains MBBC.exe, source files, and all other related files. The current version works only in the Windows operating system. A free installation program and overview for Ox is available at www.doornik.com. A detailed installation guide for Ox is provided by MBBC, and is accessible without installing Ox. R is available at www.r-project.org/.

Nonparametric functional mapping of quantitative trait loci.

Functional mapping is a useful tool for mapping quantitative trait loci (QTL) that control dynamic traits. It incorporates mathematical aspects of biological processes into the mixture model-based likelihood setting for QTL mapping, thus increasing the power of QTL detection and the precision of parameter estimation. However, in many situations there is no obvious functional form and, in such cases, this strategy will not be optimal. Here we propose to use nonparametric function estimation, typically implemented with B-splines, to estimate the underlying functional form of phenotypic trajectories, and then construct a nonparametric test to find evidence of existing QTL. Using the representation of a nonparametric regression as a mixed model, the final test statistic is a likelihood ratio test. We consider two types of genetic maps: dense maps and general maps, and the power of nonparametric functional mapping is investigated through simulation studies and demonstrated by examples.

Nonparametric functional mapping of quantitative trait loci underlying programmed cell death.

The development of an organism represents a complex dynamic process, which is controlled by a network of genes and multiple environmental factors. Programmed cell death (PCD), a physiological cell suicide process, occurs during the development of most organisms and is, typically, a complex dynamic trait. Understanding how genes control this complex developmental process has been a long-standing topic in PCD studies. In this article, we propose a nonparametric model, based on orthogonal Legendre polynomials, to map genes or quantitative trait loci (QTLs) that govern the dynamic features of the PCD process. The model is built under the maximum likelihood-based functional mapping framework and is implemented with the EM algorithm. A general information criterion is proposed for selecting the optimal Legendre order that best fits the dynamic pattern of the PCD process. The consistency of the order selection criterion is established. A nonstationary structured antedependence model (SAD) is applied to model the covariance structure among the phenotypes measured at different time points. The developed model generates a number of hypothesis tests regarding the genetic control mechanism of the PCD process. Extensive simulation studies are conducted to investigate the statistical behavior of the model. Finally, we apply the model to a rice tiller number data set in which several QTLs are identified. The developed model provides a quantitative and testable framework for assessing the interplay between genes and the developmental PCD process, and will have great implications for elucidating the genetic architecture of the PCD process.

Testing for the existence of clusters.

Detecting and determining clusters present in a certain sample has been an important concern, among researchers from different fields, for a long time. In particular, assessing whether the clusters are statistically significant, is a question that has been asked by a number of experimenters. Recently, this question arose again in a study in maize genetics, where determining the significance of clusters is crucial as a primary step in the identification of a genome-wide collection of mutants that may affect the kernel composition.Although several efforts have been made in this direction, not much has been done with the aim of developing an actual hypothesis test in order to assess the significance of clusters. In this paper, we propose a new methodology that allows the examination of the hypothesis test H(0) : κ=1 vs. H(1) : κ=k, where κ denotes the number of clusters present in a certain population. Our procedure, based on Bayesian tools, permits us to obtain closed form expressions for the posterior probabilities corresponding to the null hypothesis. From here, we calibrate our results by estimating the frequentist null distribution of the posterior probabilities in order to obtain the p-values associated with the observed posterior probabilities. In most cases, actual evaluation of the posterior probabilities is computationally intensive and several algorithms have been discussed in the literature. Here, we propose a simple estimation procedure, based on MCMC techniques, that permits an efficient and easily implementable evaluation of the test. Finally, we present simulation studies that support our conclusions, and we apply our method to the analysis of NIR spectroscopy data coming from the genetic study that motivated this work.

Comparative analysis of the transcriptomes of Populus trichocarpa and Arabidopsis thaliana suggests extensive evolution of gene expression regulation in angiosperms.

Sequencing of the Populus trichocarpa genome creates an opportunity to describe the transcriptome of a woody perennial species and establish an atlas of gene expression. A comparison with the transcriptomes of other species can also define genes that are conserved or diverging in plant species. Here, the transcriptome in vegetative organs of the P. trichocarpa reference genotype Nisqually-1 was characterized. A comparison with Arabidopsis thaliana orthologs was used to distinguish gene functional categories that may be evolving differently in a woody perennial and an annual herbaceous species. A core set of genes expressed in common among vegetative organs was detected, as well as organ-specific genes. Statistical tests identified chromatin domains, where adjacent genes were expressed more frequently than expected by chance. Extensive divergence was detected in the expression patterns of A. thaliana and P. trichocarpa orthologs, but transcription of a small number of genes appeared to have remained conserved in the two species. Despite separation of lineages for over 100 million yr, these results suggest that selection has limited transcriptional divergence of genes associated with some essential functions in A. thaliana and P. trichocarpa. However, extensive remodeling of transcriptional networks indicates that expression regulation may be a key determinant of plant diversity.

A preliminary gene expression profile of acute graft-versus-host disease.

Allogeneic hematopoietic stem cell transplantation (HSCT) is the treatment of choice for high-risk hematological malignancies, yet a major complication associated with this therapy is acute graft-versus-host disease (GVHD). Despite a well-defined pathophysiological mechanism, there are no definitive markers for predicting acute GVHD development or progression to advanced stages. In the current study, we enrolled four acute GVHD and four acute GVHD-free recipients of allogeneic HSCT and collected peripheral blood just prior to onset of clinical acute GVHD for analysis on Affymetrix GeneChip Human Genome U133 Plus 2.0 microarrays. We noted significant differences in expression of 1,658 genes between control and acute GVHD patients, based on an analysis of covariance (ANCOVA) by type of transplant, a pooled error estimate, and a false discovery rate (FDR) of 10%. In conclusion, we offer the first report of a preliminary molecular signature of acute GVHD in allogeneic HSCT patients.

Normalization of dye bias in microarray data using the mixture of splines model.

This paper discusses characteristics of dye biases in microarray data that the conventional normalization methods do not handle, and proposes a new normalization method involving a mixture of splines model. We also develop a test for between-group comparisons of each gene that is designed to be used with our proposed method.

Hematopoietic stem cell mobilization with G-CSF induces innate inflammation yet suppresses adaptive immune gene expression as revealed by microarray analysis.

OBJECTIVE: Granulocyte colony-stimulating factor (G-CSF) is used to boost granulocyte counts in immunocompromised patients, but its effects on the immune system may be counterproductive. We tested the hypothesis that G-CSF-mobilized peripheral blood stem cell (PBSC) products are immunologically downregulated based on gene microarray analysis. METHODS: Ten peripheral blood samples from normal donors for allogeneic PBSC transplantation were obtained before and after administration of G-CSF and tested on Affymetrix Human U133 Plus 2.0 GeneChip microarrays and by flow cytometry. Significant changes in gene expression after G-CSF were reported by controlling the false discovery rate at 5%. The quantitative real-time polymerase chain reaction method was used to validate expression of representative genes. RESULTS: All immune cells measured, including neutrophils, monocytes, lymphocytes, and dendritic cells, were significantly increased after G-CSF. In terms of gene expression, inflammatory and neutrophil activation pathways were upregulated after G-CSF. However, adaptive immune-related gene expression, such as antigen presentation, co-stimulation, T-cell activation and cytolytic effector responses, were downregulated. CONCLUSION: Despite significant increases in lymphocytes and antigen-presenting cells, G-CSF-mobilized PBSC allografts exhibit a suppressive adaptive immune-related gene-expression profile. However, innate and inflammatory responses are elevated. Our data provides an explanation for the potentially immunosuppressive effects observed after G-CSF administration.

Dose verification after topical treatment of alligator (Alligator mississippiensis) eggs.

Numerous studies have used temperature-dependent sex determination in reptilian eggs to investigate potential developmental effects of exogenously applied substances. However, few studies have measured the dose carried across the eggshell. We report embryonic mortality and internal egg concentrations determined by gas chromatography-mass spectrometry two weeks after exposure of American alligator (Alligator mississippiensis) eggs to chlorinated organic pesticides via injection or topical application. Puncturing the eggshell for injection produced high mortality compared with unpunctured controls; therefore, further evaluation of this method was abandoned. Although higher than controls, mortality was much lower in eggs treated topically than in those injected. Transfer of chemicals across the eggshell was very low, highly variable, and did not correlate with the applied dose after topical application. These results are consistent with previous reports in the literature, casting doubt on whether a reproducible internal dose can be achieved in reptilian eggs by topical treatment.

Skeletal muscle protein synthesis after active or passive ascent to high altitude.

INTRODUCTION: The effects of acute exposure to high altitude on muscle protein synthesis rates in human volunteers were examined after active and passive ascent. METHODS: Measurements were made initially at low altitude (550 m) and again after ascent to high altitude (4,559 m). To be able to separate the contribution of physical exercise, one group was flown by helicopter (air group, N=8), whereas the other group climbed to high altitude (foot group, N=9). Fractional rates of muscle protein synthesis rates (FSR) were determined from the incorporation of isotope into protein after injection of [H5ring] phenylalanine. RESULTS: In the air group, there was no change in FSR at high altitude, whereas in the foot group, there was a 35% increase in FSR (P<0.05 for interaction) measured 19-23 h after the end of climbing. At high altitude, the degree of hypoxia and alkalosis were not different between the groups. The plasma concentration of insulin-like growth factor-1, free thyroxin, free triiodothyronine, and thyroid-stimulating hormone were not different between the groups. Urinary 24-h cortisol excretion increased significantly in both groups after ascent, but the increase in the foot group was significantly higher compared with the air group. CONCLUSION: Physical exercise appeared to be responsible for the observed increase in muscle FSR. The significantly higher increase of 24-h cortisol excretion in the foot group suggests that the increase in FSR occurred despite higher levels of glucocorticoids, which generally affect muscle protein turnover by inhibiting protein synthesis.

Mapping quantitative trait Loci interactions from the maternal and offspring genomes.

The expression of most developmental or behavioral traits involves complex interactions between quantitative trait loci (QTL) from the maternal and offspring genomes. The maternal-offspring interactions play a pivotal role in shaping the direction and rate of evolution in terms of their substantial contribution to quantitative genetic (co)variation. To study the genetics and evolution of maternal-offspring interactions, a unifying statistical framework that embraces both the direct and indirect genetic effects of maternal and offspring QTL on any complex trait is developed. This model is derived for a simple backcross design within the maximum-likelihood context, implemented with the EM algorithm. Results from extensive simulations suggest that this model can provide reasonable estimation of additive and dominant effects of the QTL at different generations and their interaction effects derived from the maternal and offspring genomes. Although our model is framed to characterize the actions and interactions of maternal and offspring QTL affecting offspring traits, the idea can be readily extended to decipher the genetic machinery of maternal traits, such as maternal care. Our model provides a powerful means for studying the evolutionary significance of indirect genetic effects in any sexually reproductive organisms.

A bivalent polyploid model for mapping quantitative trait loci in outcrossing tetraploids.

Two major aspects have made the genetic and genomic study of polyploids extremely difficult. First, increased allelic or nonallelic combinations due to multiple alleles result in complex gene actions and interactions for quantitative trait loci (QTL) in polyploids. Second, meiotic configurations in polyploids undergo a complex biological process including either bivalent or multivalent formation, or both. For bivalent polyploids, different degrees of preferential chromosome pairings may occur during meiosis. In this article, we develop a maximum-likelihood-based model for mapping QTL in tetraploids by considering the quantitative inheritance and meiotic mechanism of bivalent polyploids. This bivalent polyploid model is implemented with the EM algorithm to simultaneously estimate QTL position, QTL effects, and QTL-marker linkage phases by incorporating the impact of a cytological parameter determining bivalent chromosome pairings (the preferential pairing factor). Simulation studies are performed to investigate the performance and robustness of our statistical method for parameter estimation. The implication and extension of the bivalent polyploid model are discussed.

Joint linkage and linkage disequilibrium mapping of quantitative trait loci in natural populations.

Linkage analysis and allelic association (also referred to as linkage disequilibrium) studies are two major approaches for mapping genes that control simple or complex traits in plants, animals, and humans. But these two approaches have limited utility when used alone, because they use only part of the information that is available for a mapping population. More recently, a new mapping strategy has been designed to integrate the advantages of linkage analysis and linkage disequilibrium analysis for genome mapping in outcrossing populations. The new strategy makes use of a random sample from a panmictic population and the open-pollinated progeny of the sample. In this article, we extend the new strategy to map quantitative trait loci (QTL), using molecular markers within the EM-implemented maximum-likelihood framework. The most significant advantage of this extension is that both linkage and linkage disequilibrium between a marker and QTL can be estimated simultaneously, thus increasing the efficiency and effectiveness of genome mapping for recalcitrant outcrossing species. Simulation studies are performed to test the statistical properties of the MLEs of genetic and genomic parameters including QTL allele frequency, QTL effects, QTL position, and the linkage disequilibrium of the QTL and a marker. The potential utility of our mapping strategy is discussed.

Functional mapping of quantitative trait loci underlying the character process: a theoretical framework.

Unlike a character measured at a finite set of landmark points, function-valued traits are those that change as a function of some independent and continuous variable. These traits, also called infinite-dimensional characters, can be described as the character process and include a number of biologically, economically, or biomedically important features, such as growth trajectories, allometric scalings, and norms of reaction. Here we present a new statistical infrastructure for mapping quantitative trait loci (QTL) underlying the character process. This strategy, termed functional mapping, integrates mathematical relationships of different traits or variables within the genetic mapping framework. Logistic mapping proposed in this article can be viewed as an example of functional mapping. Logistic mapping is based on a universal biological law that for each and every living organism growth over time follows an exponential growth curve (e.g., logistic or S-shaped). A maximum-likelihood approach based on a logistic-mixture model, implemented with the EM algorithm, is developed to provide the estimates of QTL positions, QTL effects, and other model parameters responsible for growth trajectories. Logistic mapping displays a tremendous potential to increase the power of QTL detection, the precision of parameter estimation, and the resolution of QTL localization due to the small number of parameters to be estimated, the pleiotropic effect of a QTL on growth, and/or residual correlations of growth at different ages. More importantly, logistic mapping allows for testing numerous biologically important hypotheses concerning the genetic basis of quantitative variation, thus gaining an insight into the critical role of development in shaping plant and animal evolution and domestication. The power of logistic mapping is demonstrated by an example of a forest tree, in which one QTL affecting stem growth processes is detected on a linkage group using our method, whereas it cannot be detected using current methods. The advantages of functional mapping are also discussed.

A general framework for analyzing the genetic architecture of developmental characteristics.

The genetic architecture of growth traits plays a central role in shaping the growth, development, and evolution of organisms. While a limited number of models have been devised to estimate genetic effects on complex phenotypes, no model has been available to examine how gene actions and interactions alter the ontogenetic development of an organism and transform the altered ontogeny into descendants. In this article, we present a novel statistical model for mapping quantitative trait loci (QTL) determining the developmental process of complex traits. Our model is constructed within the traditional maximum-likelihood framework implemented with the EM algorithm. We employ biologically meaningful growth curve equations to model time-specific expected genetic values and the AR(1) model to structure the residual variance-covariance matrix among different time points. Because of a reduced number of parameters being estimated and the incorporation of biological principles, the new model displays increased statistical power to detect QTL exerting an effect on the shape of ontogenetic growth and development. The model allows for the tests of a number of biological hypotheses regarding the role of epistasis in determining biological growth, form, and shape and for the resolution of developmental problems at the interface with evolution. Using our newly developed model, we have successfully detected significant additive x additive epistatic effects on stem height growth trajectories in a forest tree.