Posterior Simulation in the Generalized Linear Model with Semiparmetric Random Effects

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model, normal base measures and Gibbs sampling procedures based on the Pólya urn scheme are often used to simulate posterior draws. These algorithms are applicable in the conjugate case when (for a normal base measure) the likelihood is normal. In the non-conjugate case, the algorithms proposed by MacEachern and Müller (1998) and Neal (2000) are often applied to generate posterior samples. Some common problems associated with simulation algorithms for non-conjugate MDP models include convergence and mixing difficulties. This paper proposes an algorithm based on the Pólya urn scheme that extends the Gibbs sampling algorithms to non-conjugate models with normal base measures and exponential family likelihoods. The algorithm proceeds by making Laplace approximations to the likelihood function, thereby reducing the procedure to that of conjugate normal MDP models. To ensure the validity of the stationary distribution in the non-conjugate case, the proposals are accepted or rejected by a Metropolis-Hastings step. In the special case where the data are normally distributed, the algorithm is identical to the Gibbs sampler.

The Optimal Confidence Region for a Random Parameter

Under a two-level hierarchical model, suppose that the distribution of the random parameter is known or can be estimated well. Data are generated via a fixed, but unobservable realization of this parameter. In this paper, we derive the smallest confidence region of the random parameter under a joint Bayesian/frequentist paradigm. On average this optimal region can be much smaller than the corresponding Bayesian highest posterior density region. The new estimation procedure is appealing when one deals with data generated under a highly parallel structure, for example, data from a trial with a large number of clinical centers involved or genome-wide gene-expession data for estimating individual gene- or center-specific parameters simultaneously. The new proposal is illustrated with a typical microarray data set and its performance is examined via a small simulation study.

On the Accelerated Failure Time Model for Current Status and Interval Censored Data

This paper introduces a novel approach to making inference about the regression parameters in the accelerated failure time (AFT) model for current status and interval censored data. The estimator is constructed by inverting a Wald type test for testing a null proportional hazards model. A numerically efficient Markov chain Monte Carlo (MCMC) based resampling method is proposed to simultaneously obtain the point estimator and a consistent estimator of its variance-covariance matrix. We illustrate our approach with interval censored data sets from two clinical studies. Extensive numerical studies are conducted to evaluate the finite sample performance of the new estimators.

A Diagnostic Test for the Mixing Distribution in a Generalised Linear Mixed Model

We introduce a diagnostic test for the mixing distribution in a generalised linear mixed model. The test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimates of a subset of the fixed effects in the model. We derive the asymptotic variance of this difference, and propose a test statistic that has a limiting chi-square distribution under the null hypothesis that the mixing distribution is correctly specified. For the important special case of the logistic regression model with random intercepts, we evaluate via simulation the power of the test in finite samples under several alternative distributional forms for the mixing distribution. We illustrate the method by applying it to data from a clinical trial investigating the effects of hormonal contraceptives in women.

LIKELIHOOD ESTIMATION OF CONJUGACY RELATIONSHIPS IN LINEAR MODELS WITH APPLICATIONS TO HIGH-THROUGHPUT GENOMICS

In the simultaneous estimation of a large number of related quantities, multilevel models provide a formal mechanism for efficiently making use of the ensemble of information for deriving individual estimates. In this article we investigate the ability of the likelihood to identify the relationship between signal and noise in multilevel linear mixed models. Specifically, we consider the ability of the likelihood to diagnose conjugacy or independence between the signals and noises. Our work was motivated by the analysis of data from high-throughput experiments in genomics. The proposed model leads to a more flexible family. However, we further demonstrate that adequately capitalizing on the benefits of a well fitting fully-specified likelihood in the terms of gene ranking is difficult.

A SURVEY OF THE LIKELIHOOD APPROACH TO BIOEQUIVALENCE TRIALS

Bioequivalence trials are abbreviated clinical trials whereby a generic drug or new formulation is evaluated to determine if it is "equivalent" to a corresponding previously approved brand-name drug or formulation. In this manuscript, we survey the process of testing bioequivalence and advocate the likelihood paradigm for representing the resulting data as evidence. We emphasize the unique conflicts between hypothesis testing and confidence intervals in this area - which we believe are indicative of the existence of the systemic defects in the frequentist approach - that the likelihood paradigm avoids. We suggest the direct use of profile likelihoods for evaluating bioequivalence and examine the main properties of profile likelihoods and estimated likelihoods under simulation. This simulation study shows that profile likelihoods are a reasonable alternative to the (unknown) true likelihood for a range of parameters commensurate with bioequivalence research. Our study also shows that the standard methods in the current practice of bioequivalence trials offers only weak evidence from the evidential point of view.

A HIDDEN MARKOV MODEL FOR JOINT ESTIMATION OF GENOTYPE AND COPY NUMBER IN HIGH-THROUGHPUT SNP CHIPS

Amplifications and deletions of chromosomal DNA, as well as copy-neutral loss of heterozygosity have been associated with diseases processes. High-throughput single nucleotide polymorphism (SNP) arrays are useful for making genome-wide estimates of copy number and genotype calls. Because neighboring SNPs in high throughput SNP arrays are likely to have dependent copy number and genotype due to the underlying haplotype structure and linkage disequilibrium, hidden Markov models (HMM) may be useful for improving genotype calls and copy number estimates that do not incorporate information from nearby SNPs. We improve previous approaches that utilize a HMM framework for inference in high throughput SNP arrays by integrating copy number, genotype calls, and the corresponding confidence scores when available. Using simulated data, we demonstrate how confidence scores control smoothing in a probabilistic framework. Software for fitting HMMs to SNP array data is available in the R package ICE.

Automatic Labeling of Software Components and their Evolution using Log-Likelihood Ratio of Word Frequencies in Source Code

As more and more open-source software components become available on the internet we need automatic ways to label and compare them. For example, a developer who searches for reusable software must be able to quickly gain an understanding of retrieved components. This understanding cannot be gained at the level of source code due to the semantic gap between source code and the domain model. In this paper we present a lexical approach that uses the log-likelihood ratios of word frequencies to automatically provide labels for software components. We present a prototype implementation of our labeling/comparison algorithm and provide examples of its application. In particular, we apply the approach to detect trends in the evolution of a software system.

Affective attitudes to face images associated with intracerebral EEG source location before face viewing

We investigated whether different, personality-related affective attitudes are associated with different brain electric field (EEG) sources before any emotional challenge (stimulus exposure). A 27-channel EEG was recorded in 15 subjects during eyes-closed resting. After recording, subjects rated 32 images of human faces for affective appeal. The subjects in the first (i.e., most negative) and fourth (i.e., most positive) quartile of general affective attitude were further analyzed. The EEG data (mean=25±4.8 s/subject) were subjected to frequency-domain model dipole source analysis (FFT-Dipole-Approximation), resulting in 3-dimensional intracerebral source locations and strengths for the delta–theta, alpha, and beta EEG frequency band, and for the full range (1.5–30 Hz) band. Subjects with negative attitude (compared to those with positive attitude) showed the following source locations: more inferior for all frequency bands, more anterior for the delta–theta band, more posterior and more right for the alpha, beta and 1.5–30 Hz bands. One year later, the subjects were asked to rate the face images again. The rating scores for the same face images were highly correlated for all subjects, and original and retest affective mean attitude was highly correlated across subjects. The present results show that subjects with different affective attitudes to face images had different active, cerebral, neural populations in a task-free condition prior to viewing the images. We conclude that the brain functional state which implements affective attitude towards face images as a personality feature exists without elicitors, as a continuously present, dynamic feature of brain functioning.

Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features

We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investigate the performance of our results from both the theoretical and simulation based point of view. A major consequence of our work is that the detection of qualitative features of a density in a deconvolution problem is a doable task, although the minimax rates for pointwise estimation are very slow.

Development of an ex vivo protocol to model bone fracture in laying hens resulting from collisions.

Fractures of the keel bone, a bone extending ventrally from the sternum, are a serious health and welfare problem in free range laying hens. Recent findings suggest that a major cause of keel damage within extensive systems is collisions with internal housing structures, though investigative efforts have been hindered by difficulties in examining mechanisms and likely influencing factors at the moment of fracture. The objectives of this study were to develop an ex vivo impact protocol to model bone fracture in hens caused by collision, to assess impact and bird-related factors influencing fracture occurrence and severity, and to identify correlations of mechanical and structural properties between different skeletal sites. We induced keel bone fractures in euthanized hens using a drop-weight impact tester able to generate a range of impact energies, producing fractures that replicate those commonly found in commercial settings. The results demonstrated that impact energies of a similar order to those expected in normal housing were able to produce fractures, and that greater collision energies resulted in an increased likelihood of fractures and of greater severity. Relationships were also seen with keel's lateral surface bone mineral density, and the peak reactive force (strength) at the base of the manubrial spine. Correlations were also identified between the keel and long bones with respect to both strength and bone mineral density. This is the first study able to relate impact and bone characteristics with keel bone fracture at the moment of collision. Greater understanding of these relationships will provide means to reduce levels of breakage and severity in commercial systems.

An Innovative Approach to Impacting Student Academic Achievement and Attitudes: Pilot Study of the HEADS UP Virtual Molecular Biology Lab

Introduction: The Virtual Molecular Biology Lab is an innovative, computer-based educational program designed to teach advanced high school biology students how to create a transgenic mouse model in a simulated laboratory setting. It was created in an effort to combat the current decrease in adolescent enthusiasm for and academic achievement in science and science careers, especially in Hispanic students. Because studies have found that hands-on learning, particularly computer-based instruction, is effective in enhancing science achievement, the Virtual Lab is a potential tool for increasing the number of Hispanic students that choose to enter science fields. [See PDF for complete abstract]

Carbon dioxide and climate impulse response functions for the computation of greenhouse gas metrics: a multi-model analysis

The responses of carbon dioxide (CO2) and other climate variables to an emission pulse of CO2 into the atmosphere are often used to compute the Global Warming Potential (GWP) and Global Temperature change Potential (GTP), to characterize the response timescales of Earth System models, and to build reduced-form models. In this carbon cycle-climate model intercomparison project, which spans the full model hierarchy, we quantify responses to emission pulses of different magnitudes injected under different conditions. The CO2 response shows the known rapid decline in the first few decades followed by a millennium-scale tail. For a 100 Gt-C emission pulse added to a constant CO2 concentration of 389 ppm, 25 ± 9% is still found in the atmosphere after 1000 yr; the ocean has absorbed 59 ± 12% and the land the remainder (16 ± 14%). The response in global mean surface air temperature is an increase by 0.20 ± 0.12 °C within the first twenty years; thereafter and until year 1000, temperature decreases only slightly, whereas ocean heat content and sea level continue to rise. Our best estimate for the Absolute Global Warming Potential, given by the time-integrated response in CO2 at year 100 multiplied by its radiative efficiency, is 92.5 × 10−15 yr W m−2 per kg-CO2. This value very likely (5 to 95% confidence) lies within the range of (68 to 117) × 10−15 yr W m−2 per kg-CO2. Estimates for time-integrated response in CO2 published in the IPCC First, Second, and Fourth Assessment and our multi-model best estimate all agree within 15% during the first 100 yr. The integrated CO2 response, normalized by the pulse size, is lower for pre-industrial conditions, compared to present day, and lower for smaller pulses than larger pulses. In contrast, the response in temperature, sea level and ocean heat content is less sensitive to these choices. Although, choices in pulse size, background concentration, and model lead to uncertainties, the most important and subjective choice to determine AGWP of CO2 and GWP is the time horizon.

Present state of global wetland extent and wetland methane modelling: conclusions from a model inter-comparison project (WETCHIMP)

Global wetlands are believed to be climate sensitive, and are the largest natural emitters of methane (CH4). Increased wetland CH4 emissions could act as a positive feedback to future warming. The Wetland and Wetland CH4 Inter-comparison of Models Project (WETCHIMP) investigated our present ability to simulate large-scale wetland characteristics and corresponding CH4 emissions. To ensure inter-comparability, we used a common experimental protocol driving all models with the same climate and carbon dioxide (CO2) forcing datasets. The WETCHIMP experiments were conducted for model equilibrium states as well as transient simulations covering the last century. Sensitivity experiments investigated model response to changes in selected forcing inputs (precipitation, temperature, and atmospheric CO2 concentration). Ten models participated, covering the spectrum from simple to relatively complex, including models tailored either for regional or global simulations. The models also varied in methods to calculate wetland size and location, with some models simulating wetland area prognostically, while other models relied on remotely sensed inundation datasets, or an approach intermediate between the two. Four major conclusions emerged from the project. First, the suite of models demonstrate extensive disagreement in their simulations of wetland areal extent and CH4 emissions, in both space and time. Simple metrics of wetland area, such as the latitudinal gradient, show large variability, principally between models that use inundation dataset information and those that independently determine wetland area. Agreement between the models improves for zonally summed CH4 emissions, but large variation between the models remains. For annual global CH4 emissions, the models vary by ±40% of the all-model mean (190 Tg CH4 yr−1). Second, all models show a strong positive response to increased atmospheric CO2 concentrations (857 ppm) in both CH4 emissions and wetland area. In response to increasing global temperatures (+3.4 °C globally spatially uniform), on average, the models decreased wetland area and CH4 fluxes, primarily in the tropics, but the magnitude and sign of the response varied greatly. Models were least sensitive to increased global precipitation (+3.9 % globally spatially uniform) with a consistent small positive response in CH4 fluxes and wetland area. Results from the 20th century transient simulation show that interactions between climate forcings could have strong non-linear effects. Third, we presently do not have sufficient wetland methane observation datasets adequate to evaluate model fluxes at a spatial scale comparable to model grid cells (commonly 0.5°). This limitation severely restricts our ability to model global wetland CH4 emissions with confidence. Our simulated wetland extents are also difficult to evaluate due to extensive disagreements between wetland mapping and remotely sensed inundation datasets. Fourth, the large range in predicted CH4 emission rates leads to the conclusion that there is both substantial parameter and structural uncertainty in large-scale CH4 emission models, even after uncertainties in wetland areas are accounted for.

Cancer patients' attitudes toward cancer trials

Background. Accurate measurement of attitudes toward participation in cancer treatment trials (CTs) and cancer prevention trials (CPTs) across varied groups could assist health researchers and educators when addressing attitudinal barriers to participation in these trials. ^ Methods. The Attitudes toward Cancer Trials Scales (ACTS) instrument development was based on a conceptual model developed from research literature, clinical practice experience, and empirical testing of items with a sample of 312 respondents. The ACTS contains two scales, the Cancer Trials (CT) scale (4 components; 18 items) and the Cancer Prevention Trials (CPT) scale (3 components; 16 items). Cronbach's alpha values for the CT and CPT scales, respectively, were 0.86 and 0.89. These two scales along with sociodemographic and cancer trial history variables were distributed in a mail survey of former patients of a large cancer research center. The disproportionate stratified probability sampling procedure yielded 925 usable responses (54% response rate). ^ Results. Prevalence of favorable attitudes toward CTs and CPTs was 66% and 69%, respectively. There were no significant differences in mean scale scores by cancer site or gender, but African Americans had more favorable attitudes toward CTs than European Americans. Multiple regression analysis indicated that older age, lower education level, and prior CT participation history were associated with more favorable attitudes toward CTs. Prior CT participation and prior CPT participation were associated with more favorable attitudes toward CPTs. Results also provided evidence of reliability and construct validity for both scales. ^ Conclusions. Middle age, higher education, and European American ethnicity are associated with less positive attitudes about participating in cancer treatment trials. Availability of a psychometrically sound instrument to measure attitudes may facilitate a better understanding decision making regarding participation in CTs and CPTs. It is this author's intention that the ACTS' scales will be used by other investigators to measure attitudes toward CTs and CPTs in various groups of persons, and that the many issues regarding participation in trials might become more explicit. ^