A clustering procedure for three-way RNA sequencing data using data transformations and matrix-variate Gaussian mixture models.

RNA sequencing of time-course experiments results in three-way count data where the dimensions are the genes, the time points and the biological units. Clustering RNA-seq data allows to extract groups of co-expressed genes over time. After standardisation, the normalised counts of individual genes across time points and biological units have similar properties as compositional data. We propose the following procedure to suitably cluster three-way RNA-seq data: (1) pre-process the RNA-seq data by calculating the normalised expression profiles, (2) transform the data using the additive log ratio transform to map the composition in the D-part Aitchison simplex to a D - 1 -dimensional Euclidean vector, (3) cluster the transformed RNA-seq data using matrix-variate Gaussian mixture models and (4) assess the quality of the overall cluster solution and of individual clusters based on cluster separation in the transformed space using density-based silhouette information and on compactness of the cluster in the original space using cluster maps as a suitable visualisation. The proposed procedure is illustrated on RNA-seq data from fission yeast and results are also compared to an analogous two-way approach after flattening out the biological units.

Multiparametric Analysis Combining DSC-MR Perfusion and [18F]FET-PET is Superior to a Single Parameter Approach for Differentiation of Progressive Glioma from Radiation Necrosis.

PURPOSE: Perfusion-weighted (PWI) magnetic resonance imaging (MRI) and O­(2-[18F]fluoroethyl-)-l-tyrosine ([18F]FET) positron emission tomography (PET) are both useful for discrimination of progressive disease (PD) from radiation necrosis (RN) in patients with gliomas. Previous literature showed that the combined use of FET-PET and MRI-PWI is advantageous; hhowever the increased diagnostic performances were only modest compared to the use of a single modality. Hence, the goal of this study was to further explore the benefit of combining MRI-PWI and [18F]FET-PET for differentiation of PD from RN. Secondarily, we evaluated the usefulness of cerebral blood flow (CBF), mean transit time (MTT) and time to peak (TTP) as previous studies mainly examined cerebral blood volume (CBV). METHODS: In this single center study, we retrospectively identified patients with WHO grades II-IV gliomas with suspected tumor recurrence, presenting with ambiguous findings on structural MRI. For differentiation of PD from RN we used both MRI-PWI and [18F]FET-PET. Dynamic susceptibility contrast MRI-PWI provided normalized parameters derived from perfusion maps (r(relative)CBV, rCBF, rMTT, rTTP). Static [18F]FET-PET parameters including mean and maximum tumor to brain ratios (TBRmean, TBRmax) were calculated. Based on histopathology and radioclinical follow-up we diagnosed PD in 27 and RN in 10 cases. Using the receiver operating characteristic (ROC) analysis, area under the curve (AUC) values were calculated for single and multiparametric models. The performances of single and multiparametric approaches were assessed with analysis of variance and cross-validation. RESULTS: After application of inclusion and exclusion criteria, we included 37 patients in this study. Regarding the in-sample based approach, in single parameter analysis rTBRmean (AUC = 0.91, p < 0.001), rTBRmax (AUC = 0.89, p < 0.001), rTTP (AUC = 0.87, p < 0.001) and rCBVmean (AUC = 0.84, p < 0.001) were efficacious for discrimination of PD from RN. The rCBFmean and rMTT did not reach statistical significance. A classification model consisting of TBRmean, rCBVmean and rTTP achieved an AUC of 0.98 (p < 0.001), outperforming the use of rTBRmean alone, which was the single parametric approach with the highest AUC. Analysis of variance confirmed the superiority of the multiparametric approach over the single parameter one (p = 0.002). While cross-validation attributed the highest AUC value to the model consisting of TBRmean and rCBVmean, it also suggested that the addition of rTTP resulted in the highest accuracy. Overall, multiparametric models performed better than single parameter ones. CONCLUSION: A multiparametric MRI-PWI and [18F]FET-PET model consisting of TBRmean, rCBVmean and PWI rTTP significantly outperformed the use of rTBRmean alone, which was the best single parameter approach. Secondarily, we firstly report the potential usefulness of PWI rTTP for discrimination of PD from RN in patients with glioma; however, for validation of our findings the prospective studies with larger patient samples are necessary.

How many data clusters are in the Galaxy data set?: Bayesian cluster analysis in action.

In model-based clustering, the Galaxy data set is often used as a benchmark data set to study the performance of different modeling approaches. Aitkin (Stat Model 1:287-304) compares maximum likelihood and Bayesian analyses of the Galaxy data set and expresses reservations about the Bayesian approach due to the fact that the prior assumptions imposed remain rather obscure while playing a major role in the results obtained and conclusions drawn. The aim of the paper is to address Aitkin's concerns about the Bayesian approach by shedding light on how the specified priors influence the number of estimated clusters. We perform a sensitivity analysis of different prior specifications for the mixtures of finite mixture model, i.e., the mixture model where a prior on the number of components is included. We use an extensive set of different prior specifications in a full factorial design and assess their impact on the estimated number of clusters for the Galaxy data set. Results highlight the interaction effects of the prior specifications and provide insights into which prior specifications are recommended to obtain a sparse clustering solution. A simulation study with artificial data provides further empirical evidence to support the recommendations. A clear understanding of the impact of the prior specifications removes restraints preventing the use of Bayesian methods due to the complexity of selecting suitable priors. Also, the regularizing properties of the priors may be intentionally exploited to obtain a suitable clustering solution meeting prior expectations and needs of the application.

Lack of association between cortical amyloid deposition and glucose metabolism in early stage Alzheimer´s disease patients.

BACKGROUND: Beta amyloid (Aß) causes synaptic dysfunction leading to neuronal death. It is still controversial if the magnitude of Aß deposition correlates with the degree of cognitive impairment. Diagnostic imaging may lead to a better understanding the role of Aß in development of cognitive deficits. The aim of the present study was to investigate if Aß deposition in the corresponding brain region of early stage Alzheimer´s disease (AD) patients, directly correlates to neuronal dysfunction and cognitive impairment indicated by reduced glucose metabolism. PATIENTS AND METHODS: In 30 patients with a clinical phenotype of AD and amyloid positive brain imaging, 2-[18F] fluoro-2-deoxy-d-glucose (FDG) PET/CT was performed. We extracted the average [18F] flutemetamol (Vizamyl) uptake for each of the 16 regions of interest in both hemispheres and computed the standardized uptake value ratio (SUVR) by dividing the Vimazyl intensities by the mean signal of positive and negative control regions. Data were analysed using the R environment for statistical computing and graphics. RESULTS: Any negative correlation between Aß deposition and glucose metabolism in 32 dementia related and corresponding brain regions in AD patients was not found. None of the correlation coefficient values were statistically significant different from zero based on two-sided p- value. CONCLUSIONS: Regional Aß deposition did not correlate negatively with local glucose metabolism in early stage AD patients. Our findings support the role of Aß as a valid biomarker, but does not permit to conclude that Aß is a direct cause for an aberrant brain glucose metabolism and neuronal dysfunction.

Semi-parametric Regression under Model Uncertainty: Economic Applications.

Economic theory does not always specify the functional relationship between dependent and explanatory variables, or even isolate a particular set of covariates. This means that model uncertainty is pervasive in empirical economics. In this paper, we indicate how Bayesian semi-parametric regression methods in combination with stochastic search variable selection can be used to address two model uncertainties simultaneously: (i) the uncertainty with respect to the variables which should be included in the model and (ii) the uncertainty with respect to the functional form of their effects. The presented approach enables the simultaneous identification of robust linear and nonlinear effects. The additional insights gained are illustrated on applications in empirical economics, namely willingness to pay for housing, and cross-country growth regression.

A Sharing-Based Approach to Enticing Tourists to Behave More Environmentally Friendly.

Tourist behavior has a critical impact on the environmental sustainability of tourism. The hedonic nature of tourism and lack of an economic incentive make tourist behavior particularly hard to change. Making tourists behave more environmentally friendly would have substantial environmental benefits. This is the aim of the present study. Three alternative approaches are tested. The most successful approach-based on sharing monetary savings with guests-leads to a 42 percent change in one specific tourist behavior with negative environmental consequences. This new sharing-based approach significantly outperforms current approaches of increasing awareness of environmental consequences and of tourist ability to make a change. Tourism businesses should consider replacing current appeals with sharing-based schemes.

Identifying Mixtures of Mixtures Using Bayesian Estimation.

The use of a finite mixture of normal distributions in model-based clustering allows us to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by imposing constraints on the model or by using post-processing procedures. Within the Bayesian framework, we propose a different approach based on sparse finite mixtures to achieve identifiability. We specify a hierarchical prior, where the hyperparameters are carefully selected such that they are reflective of the cluster structure aimed at. In addition, this prior allows us to estimate the model using standard MCMC sampling methods. In combination with a post-processing approach which resolves the label switching issue and results in an identified model, our approach allows us to simultaneously (1) determine the number of clusters, (2) flexibly approximate the cluster distributions in a semiparametric way using finite mixtures of normals and (3) identify cluster-specific parameters and classify observations. The proposed approach is illustrated in two simulation studies and on benchmark datasets. Supplementary materials for this article are available online.

Model-based clustering based on sparse finite Gaussian mixtures.

In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well as to obtain an identified model. Our approach consists in specifying sparse hierarchical priors on the mixture weights and component means. In a deliberately overfitting mixture model the sparse prior on the weights empties superfluous components during MCMC. A straightforward estimator for the true number of components is given by the most frequent number of non-empty components visited during MCMC sampling. Specifying a shrinkage prior, namely the normal gamma prior, on the component means leads to improved parameter estimates as well as identification of cluster-relevant variables. After estimating the mixture model using MCMC methods based on data augmentation and Gibbs sampling, an identified model is obtained by relabeling the MCMC output in the point process representation of the draws. This is performed using [Formula: see text]-centroids cluster analysis based on the Mahalanobis distance. We evaluate our proposed strategy in a simulation setup with artificial data and by applying it to benchmark data sets.

Statistical approaches for the determination of cut points in anti-drug antibody bioassays.

Cut points in immunogenicity assays are used to classify future specimens into anti-drug antibody (ADA) positive or negative. To determine a cut point during pre-study validation, drug-naive specimens are often analyzed on multiple microtiter plates taking sources of future variability into account, such as runs, days, analysts, gender, drug-spiked and the biological variability of un-spiked specimens themselves. Five phenomena may complicate the statistical cut point estimation: i) drug-naive specimens may contain already ADA-positives or lead to signals that erroneously appear to be ADA-positive, ii) mean differences between plates may remain after normalization of observations by negative control means, iii) experimental designs may contain several factors in a crossed or hierarchical structure, iv) low sample sizes in such complex designs lead to low power for pre-tests on distribution, outliers and variance structure, and v) the choice between normal and log-normal distribution has a serious impact on the cut point. We discuss statistical approaches to account for these complex data: i) mixture models, which can be used to analyze sets of specimens containing an unknown, possibly larger proportion of ADA-positive specimens, ii) random effects models, followed by the estimation of prediction intervals, which provide cut points while accounting for several factors, and iii) diagnostic plots, which allow the post hoc assessment of model assumptions. All methods discussed are available in the corresponding R add-on package mixADA.

On maximum likelihood estimation of the concentration parameter of von Mises-Fisher distributions.

Maximum likelihood estimation of the concentration parameter of von Mises-Fisher distributions involves inverting the ratio [Formula: see text] of modified Bessel functions and computational methods are required to invert these functions using approximative or iterative algorithms. In this paper we use Amos-type bounds for [Formula: see text] to deduce sharper bounds for the inverse function, determine the approximation error of these bounds, and use these to propose a new approximation for which the error tends to zero when the inverse of [Formula: see text] is evaluated at values tending to [Formula: see text] (from the left). We show that previously introduced rational bounds for [Formula: see text] which are invertible using quadratic equations cannot be used to improve these bounds.

On standard conjugate families for natural exponential families with bounded natural parameter space.

Diaconis and Ylvisaker (1979) give necessary conditions for conjugate priors for distributions from the natural exponential family to be proper as well as to have the property of linear posterior expectation of the mean parameter of the family. Their conditions for propriety and linear posterior expectation are also sufficient if the natural parameter space is equal to the set of all [Formula: see text]-dimensional real numbers. In this paper their results are extended to characterize when conjugate priors are proper if the natural parameter space is bounded. For the special case where the natural exponential family is through a spherical probability distribution  [Formula: see text], we show that the proper conjugate priors can be characterized by the behavior of the moment generating function of [Formula: see text] at the boundary of the natural parameter space, or the second-order tail behavior of [Formula: see text]. In addition, we show that if these families are non-regular, then linear posterior expectation never holds. The results for this special case are also extended to natural exponential families through elliptical probability distributions.

Branding water.

Branding is a key strategy widely used in commercial marketing to make products more attractive to consumers. With the exception of bottled water, branding has largely not been adopted in the water context although public acceptance is critical to the implementation of water augmentation projects. Based on responses from 6247 study participants collected between 2009 and 2012, this study shows that (1) different kinds of water - specifically recycled water, desalinated water, tap water and rainwater from personal rainwater tanks - are each perceived very differently by the public, (2) external events out of the control of water managers, such as serious droughts or floods, had a minimal effect on people's perceptions of water, (3) perceptions of water were stable over time, and (4) certain water attributes are anticipated to be more effective to use in public communication campaigns aiming at increasing public acceptance for drinking purposes. The results from this study can be used by a diverse range of water stakeholders to increase public acceptance and adoption of water from alternative sources.

On conjugate families and Jeffreys priors for von Mises-Fisher distributions.

This paper discusses characteristics of standard conjugate priors and their induced posteriors in Bayesian inference for von Mises-Fisher distributions, using either the canonical natural exponential family or the more commonly employed polar coordinate parameterizations. We analyze when standard conjugate priors as well as posteriors are proper, and investigate the Jeffreys prior for the von Mises-Fisher family. Finally, we characterize the proper distributions in the standard conjugate family of the (matrix-valued) von Mises-Fisher distributions on Stiefel manifolds.

Amos-type bounds for modified Bessel function ratios.

We systematically investigate lower and upper bounds for the modified Bessel function ratio [Formula: see text] by functions of the form [Formula: see text] in case [Formula: see text] is positive for all [Formula: see text], or equivalently, where [Formula: see text] or [Formula: see text] is a negative integer. For [Formula: see text], we give an explicit description of the set of lower bounds and show that it has a greatest element. We also characterize the set of upper bounds and its minimal elements. If [Formula: see text], the minimal elements are tangent to [Formula: see text] in exactly one point [Formula: see text], and have [Formula: see text] as their lower envelope. We also provide a new family of explicitly computable upper bounds. Finally, if [Formula: see text] is a negative integer, we explicitly describe the sets of lower and upper bounds, and give their greatest and least elements, respectively.

"Translating" between survey answer formats.

Survey research remains the most popular source of market knowledge, yet researchers have not yet established one consistent technique for measuring responses. Some market research companies offer respondents two answer options; others five or seven. Some answer formats use middle points on the answer scales, others do not. Some formats verbalize all answer options, some only the endpoints. The wide variety of answer formats that market research companies and academic researchers use makes comparing results across studies virtually impossible. This study offers guidance for market researchers by presenting empirical translations for the answer formats they most commonly use, thus enabling easier comparisons of results.

Modelling human immunodeficiency virus ribonucleic acid levels with finite mixtures for censored longitudinal data.

The measurement of human immunodeficiency virus ribonucleic acid levels over time leads to censored longitudinal data. Suitable models for dynamic modelling of these levels need to take this data characteristic into account. If groups of patients with different developments of the levels over time are suspected the model class of finite mixtures of mixed effects models with censored data is required. We describe the model specification and derive the estimation with a suitable expectation-maximization algorithm. We propose a convenient implementation using closed form formulae for the expected mean and variance of the truncated multivariate distribution. Only efficient evaluation of the cumulative multivariate normal distribution function is required. Model selection as well as methods for inference are discussed. The application is demonstrated on the clinical trial ACTG 315 data.

Water conservation behavior in Australia.

Ensuring a nation's long term water supply requires the use of both supply-sided approaches such as water augmentation through water recycling, and demand-sided approaches such as water conservation. Conservation behavior can only be increased if the key drivers of such behavior are understood. The aim of this study is to reveal the main drivers from a comprehensive pool of hypothesized factors. An empirical study was conducted with 3094 Australians. Data was analyzed using multivariate linear regression analysis and decision trees to determine which factors best predict self-reported water conservation behavior. Two key factors emerge: high level of pro-environmental behavior; and pro-actively seeking out information about water. A number of less influential factors are also revealed. Public communication strategy implications are derived.

Modelling time course gene expression data with finite mixtures of linear additive models.

UNLABELLED: A model class of finite mixtures of linear additive models is presented. The component-specific parameters in the regression models are estimated using regularized likelihood methods. The advantages of the regularization are that (i) the pre-specified maximum degrees of freedom for the splines is less crucial than for unregularized estimation and that (ii) for each component individually a suitable degree of freedom is selected in an automatic way. The performance is evaluated in a simulation study with artificial data as well as on a yeast cell cycle dataset of gene expression levels over time. AVAILABILITY: The latest release version of the R package flexmix is available from CRAN (http://cran.r-project.org/).