Analysis of population pharmacokinetic data using NONMEM and WinBUGS

The aim of this report is to describe the use of WinBUGS for two datasets that arise from typical population pharmacokinetic studies. The first dataset relates to gentamicin concentration-time data that arose as part of routine clinical care of 55 neonates. The second dataset incorporated data from 96 patients receiving enoxaparin. Both datasets were originally analyzed by using NONMEM. In the first instance, although NONMEM provided reasonable estimates of the fixed effects parameters it was unable to provide satisfactory estimates of the between-subject variance. In the second instance, the use of NONMEM resulted in the development of a successful model, albeit with limited available information on the between-subject variability of the pharmacokinetic parameters. WinBUGS was used to develop a model for both of these datasets. Model comparison for the enoxaparin dataset was performed by using the posterior distribution of the log-likelihood and a posterior predictive check. The use of WinBUGS supported the same structural models tried in NONMEM. For the gentamicin dataset a one-compartment model with intravenous infusion was developed, and the population parameters including the full between-subject variance-covariance matrix were available. Analysis of the enoxaparin dataset supported a two compartment model as superior to the one-compartment model, based on the posterior predictive check. Again, the full between-subject variance-covariance matrix parameters were available. Fully Bayesian approaches using MCMC methods, via WinBUGS, can offer added value for analysis of population pharmacokinetic data.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Bayesian statistics for the calibration of the LISA Pathfinder experiment

The main goal of LISA Path finder (LPF) mission is to estimate the acceleration noise models of the overall LISA Technology Package (LTP) experiment on-board. This will be of crucial importance for the future space-based Gravitational-Wave (GW) detectors, like eLISA. Here, we present the Bayesian analysis framework to process the planned system identification experiments designed for that purpose. In particular, we focus on the analysis strategies to predict the accuracy of the parameters that describe the system in all degrees of freedom. The data sets were generated during the latest operational simulations organised by the data analysis team and this work is part of the LTPDA Matlab toolbox.

Analysis of Sampling Data

A Similar Exposure Group (SEG) can be created through the evaluation of workers performing the same or similar task, hazards they are exposed to, frequency and duration of their exposures, engineering controls available during their operations, personal protective equipment used, and exposure data. For this report, the samples of one facility that has collected nearly 40,000 various types of samples will be evaluated to determine if the creation of a SEG can be supported. The data will be reviewed for consistency with collection methods and laboratory detection limits. A subset of the samples may be selected based on the review. Data will also be statistically evaluated in order to determine whether the data is sufficient to terminate the sampling. IHDataAnalyst V1.27 will be used to assess the data. This program uses Bayesian Analysis to assist in making determinations. The 95 percent confidence interval will be calculated and evaluated in making decisions. This evaluation will be used to determine if a SEG can be created for any of the workers and determine the need for future sample collection. The data and evaluation presented in this report have been selected and evaluated specifically for the purposes of this project.

Modelos de volatilidade estocástica em séries financeiras: uma aplicação para o IBOVESPA

Neste artigo apresentamos uma análise Bayesiana para o modelo de volatilidade estocástica (SV) e uma forma generalizada deste, cujo objetivo é estimar a volatilidade de séries temporais financeiras. Considerando alguns casos especiais dos modelos SV usamos algoritmos de Monte Carlo em Cadeias de Markov e o software WinBugs para obter sumários a posteriori para as diferentes formas de modelos SV. Introduzimos algumas técnicas Bayesianas de discriminação para a escolha do melhor modelo a ser usado para estimar as volatilidades e fazer previsões de séries financeiras. Um exemplo empírico de aplicação da metodologia é introduzido com a série financeira do IBOVESPA.

Assessing influence in survival data with a cure fraction and covariates

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Some influence methods, such as the local influence, total local influence of an individual, local influence on predictions and generalized leverage were derived, analyzed and discussed in survival data with a cure fraction and covariates. The relevance of the approach was illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data is changed.

Detection of Hepatitis B virus subgenotype A1 in a Quilombo community from Maranhao, Brazil

Background: The Brazilian population is mainly descendant from European colonizers, Africans and Native Americans. Some Afro-descendants lived in small isolated communities since the slavery period. The epidemiological status of HBV infection in Quilombos communities from northeast of Brazil remains unknown. The aim of this study was to characterize the HBV genotypes circulating inside a Quilombo isolated community from Maranhao State, Brazil. Methods: Seventy-two samples from Frechal Quilombo community at Maranhao were collected. All serum samples were screened by enzyme-linked immunosorbent assays for the presence of hepatitis B surface antigen ( HBsAg). HBsAg positive samples were submitted to DNA extraction and a fragment of 1306 bp partially comprising HBsAg and polymerase coding regions (S/POL) was amplified by nested PCR and its nucleotide sequence was determined. Viral isolates were genotyped by phylogenetic analysis using reference sequences from each genotype obtained from GenBank (n = 320). Sequences were aligned using Muscle software and edited in the SE-AL software. Bayesian phylogenetic analyses were conducted using Markov Chain Monte Carlo (MCMC) method to obtain the MCC tree using BEAST v.1.5.3. Results: Of the 72 individuals, 9 (12.5%) were HBsAg-positive and 4 of them were successfully sequenced for the 1306 bp fragment. All these samples were genotype A1 and grouped together with other sequences reported from Brazil. Conclusions: The present study represents the first report on the HBV genotypes characterization of this community in the Maranhao state in Brazil where a high HBsAg frequency was found. In this study, we reported a high frequency of HBV infection and the exclusive presence of subgenotype A1 in an Afro-descendent community in the Maranhao State, Brazil.

New constraints on the chemical evolution of the solar neighbourhood and Galactic disc(s) Improved astrophysical parameters for the Geneva-Copenhagen Survey

We present a re-analysis of the Geneva-Copenhagen survey, which benefits from the infrared flux method to improve the accuracy of the derived stellar effective temperatures and uses the latter to build a consistent and improved metallicity scale. Metallicities are calibrated on high-resolution spectroscopy and checked against four open clusters and a moving group, showing excellent consistency. The new temperature and metallicity scales provide a better match to theoretical isochrones, which are used for a Bayesian analysis of stellar ages. With respect to previous analyses, our stars are on average 100 K hotter and 0.1 dex more metal rich, which shift the peak of the metallicity distribution function around the solar value. From Stromgren photometry we are able to derive for the first time a proxy for [alpha/Fe] abundances, which enables us to perform a tentative dissection of the chemical thin and thick disc. We find evidence for the latter being composed of an old, mildly but systematically alpha-enhanced population that extends to super solar metallicities, in agreement with spectroscopic studies. Our revision offers the largest existing kinematically unbiased sample of the solar neighbourhood that contains full information on kinematics, metallicities, and ages and thus provides better constraints on the physical processes relevant in the build-up of the Milky Way disc, enabling a better understanding of the Sun in a Galactic context.

A frailty modeling approach for parental effects in animal breeding

Survival models involving frailties are commonly applied in studies where correlated event time data arise due to natural or artificial clustering. In this paper we present an application of such models in the animal breeding field. Specifically, a mixed survival model with a multivariate correlated frailty term is proposed for the analysis of data from over 3611 Brazilian Nellore cattle. The primary aim is to evaluate parental genetic effects on the trait length in days that their progeny need to gain a commercially specified standard weight gain. This trait is not measured directly but can be estimated from growth data. Results point to the importance of genetic effects and suggest that these models constitute a valuable data analysis tool for beef cattle breeding.

Influence diagnostics for polyhazard models in the presence of covariates

In this paper, we present various diagnostic methods for polyhazard models. Polyhazard models are a flexible family for fitting lifetime data. Their main advantage over the single hazard models, such as the Weibull and the log-logistic models, is to include a large amount of nonmonotone hazard shapes, as bathtub and multimodal curves. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. A discussion of the computation of the likelihood displacement as well as the normal curvature in the local influence method are presented. Finally, an example with real data is given for illustration.

Molecular phylogenetics of Chaetodon and the Chaetodontidae (Teleostei : Perciformes) with reference to morphology

Butterflyfish are colourful, pan-tropical coastal fish that are important and distinctive members of coral reef communities. A successful systematic scheme and a robust phylogeny is considered essential in understanding further their biogeography and ecology, although recent cladistic treatments of butterflyfish phylogeny, based on soft tissue and bone morphology and coded at the generic and subgeneric levels, differ in character coding and subsequently tree topology. This study provides an independent test of the morphologically based hypotheses, using molecular systematic data from two partial mitochondrial gene fragments, cytochrome b (cytb) and small subunit rRNA (rrnS), for 52 ingroup chaetodontids and seven pomacanthids used to root the molecular trees. Individual gene trees were largely compatible and a combined molecular phylogeny, inferred from Bayesian analysis, was used to test alternative hypotheses suggested by morphological analyses. The tree was also used to map the latest morphological matrix in order to evaluate potential synapomorphies for various nodes defining butterflyfish interrelationships. A clade comprised of Chelmon and Coradion was sister group to other chaetodontids. Heniochus and Hemitaurichthys were each resolved as monophyletic groups, and as sister taxa Of the taxa sampled, Prognothodes was resolved as the sister genus to Chaeotodon. Of the ten Chaetodon subgenera sampled, all were monophyletic but their interrelationships differed significantly from that inferred from morphological characters. Lepidochaetodon was the most basal subgenus followed by Exornator and the remaining subgenera. Molecular data support the sister group relationship between Corallochaetodon and Citharoedus suggested by morphology, but major differences occur among the remaining more derived taxa. Chaetodon trifascialis and C. oligacanthus were resolved as sister taxa adding weight to the inclusion of the latter in C. Megaprotodon. Of those pairs of taxa known to hybridize and sampled with molecular data, all were closely related phylogenetically, except those hybrids known to occur in the Rabdophorus subgenus. Two base changes separated C. pelewensis from C. paucifasciatus which have been regarded previously as a single species. Cytb provided greater resolution than rrnS and will likely provide additional resolution with greater taxon sampling.

The phylogeography of African Brazilians

Background/Aims: Approximately four million Africans were taken as slaves to Brazil, where they interbred extensively with Amerindians and Europeans. We have previously shown that while most White Brazilians carry Y chromosomes of European origin, they display high proportions of African and Amerindian mtDNA lineages, because of sex-biased genetic admixture. Methods: We studied the Y chromosome and mtDNA haplogroup structure of 120 Black males from Sao Paulo, Brazil. Results: Only 48% of the Y chromosomes, but 85% of the mtDNA haplogroups were characteristic of sub-Saharan Africa, confirming our previous observation of sexually biased mating. We mined literature data for mtDNA and Y chromosome haplogroup frequencies for African native populations from regions involved in Atlantic Slave Trade. Principal Components Analysis and Bayesian analysis of population structure revealed no genetic differentiation of Y chromosome marker frequencies between the African regions. However, mtDNA examination unraveled considerable genetic structure, with three clusters at Central-West Africa, West Africa and Southeast Africa. A hypothesis is proposed to explain this structure. Conclusion: Using these mtDNA data we could obtain for the first time an estimate of the relative ancestral contribution of Central-West (0.445), West (0.431) and Southeast Africa (0.123) to African Brazilians from Sao Paulo. These estimates are consistent with historical information. Copyright (c) 2008 S. Karger AG, Basel.

Molecular Characterization, Distribution, and Dynamics of Hepatitis C Virus Genotypes in Blood Donors in Colombia

Hepatitis C virus (HCV) is a frequent cause of acute and chronic hepatitis and a leading cause for cirrhosis of the liver and hepatocellular carcinoma. HCV is classified in six major genotypes and more than 70 subtypes. In Colombian blood banks, serum samples were tested for anti-HCV antibodies using a third-generation ELISA. The aim of this study was to characterize the viral sequences in plasma of 184 volunteer blood donors who attended the ""Banco Nacional de Sangre de la Cruz Roja Colombiana,`` Bogota, Colombia. Three different HCV genomic regions were amplified by nested PCR. The first of these was a segment of 180 bp of the 5`UTR region to confirm the previous diagnosis by ELISA. From those that were positive to the 5`UTR region, two further segments were amplified for genotyping and subtyping by phylogenetic analysis: a segment of 380 bp from the NS5B region; and a segment of 391 bp from the E1 region. The distribution of HCV subtypes was: 1b (82.8%), 1a (5.7%), 2a (5.7%), 2b (2.8%), and 3a (2.8%). By applying Bayesian Markov chain Monte Carlo simulation, it was estimated that HCV-1b was introduced into Bogota around 1950. Also, this subtype spread at an exponential rate between about 1970 to about 1990, after which transmission of HCV was reduced by anti-HCV testing of this population. Among Colombian blood donors, HCV genotype 1b is the most frequent genotype, especially in large urban conglomerates such as Bogota, as is the case in other South American countries. J. Med. Virol. 82: 1889-1898, 2010. (C) 2010 Wiley-Liss, Inc.

Bronchoscopic lung-volume reduction with Exhale airway stents for emphysema (EASE trial): randomised, sham-controlled, multicentre trial

Background Airway bypass is a bronchoscopic lung-volume reduction procedure for emphysema whereby transbronchial passages into the lung are created to release trapped air, supported with paclitaxel-coated stents to ease the mechanics of breathing. The aim of the EASE (Exhale airway stents for emphysema) trial was to evaluate safety and efficacy of airway bypass in people with severe homogeneous emphysema. Methods We undertook a randomised, double-blind, sham-controlled study in 38 specialist respiratory centres worldwide. We recruited 315 patients who had severe hyperinflation (ratio of residual volume [RV] to total lung capacity of >= 0.65). By computer using a random number generator, we randomly allocated participants (in a 2:1 ratio) to either airway bypass (n=208) or sham control (107). We divided investigators into team A (masked), who completed pre-procedure and post-procedure assessments, and team B (unmasked), who only did bronchoscopies without further interaction with patients. Participants were followed up for 12 months. The 6-month co-primary efficacy endpoint required 12% or greater improvement in forced vital capacity (FVC) and 1 point or greater decrease in the modified Medical Research Council dyspnoea score from baseline. The composite primary safety endpoint incorporated five severe adverse events. We did Bayesian analysis to show the posterior probability that airway bypass was superior to sham control (success threshold, 0.965). Analysis was by intention to treat. This study is registered with ClinicalTrials.gov, number NCT00391612. Findings All recruited patients were included in the analysis. At 6 months, no difference between treatment arms was noted with respect to the co-primary efficacy endpoint (30 of 208 for airway bypass vs 12 of 107 for sham control; posterior probability 0.749, below the Bayesian success threshold of 0.965). The 6-month composite primary safety endpoint was 14.4% (30 of 208) for airway bypass versus 11.2% (12 of 107) for sham control (judged non-inferior, with a posterior probability of 1.00 [Bayesian success threshold >0.95]). Interpretation Although our findings showed safety and transient improvements, no sustainable benefit was recorded with airway bypass in patients with severe homogeneous emphysema.

Hepatitis Delta virus genotype 8 infection in Northeast Brazil: Inheritance from African slaves?

Hepatitis Delta virus (HDV) is endemic worldwide, but its prevalence varies in different geographical areas. While in the Brazilian Amazon, HDV is known to be endemic and to represent a significant public health problem, few studies have assessed its prevalence in other regions in the country. This study evaluated the seroprevalence of HDV among HBsAg chronic carriers from Maranhao state, a region located in the Northeast of Brazil. Among 133 patients, 5 had anti-HD, of whom 3 had HDV RNA. HDV genotypes were characterized by Bayesian phylogenetic analysis of nucleotide sequences from the HDAg coding region. HDV-3 was identified in one patient who lives in Maranhao, but was born in Amazonas state (Western Amazon basin). Phylogenetic analysis shows that this HDV-3 sequence grouped with other HDV-3 sequences isolated in this state, which suggests that the patient probably contracted HDV infection there. Surprisingly, the other two patients were infected with HDV-8, an African genotype. These patients were born and have always lived in Urbano Santos, a rural county of Maranhao state, moreover they had never been to Africa and denied any contact with people from that continent. This is the first description of the HDV-8 in non-native African populations. This genotype may have been introduced to Brazil through the slaves brought to the country from the West Africa regions during the 16-18th centuries. Our results indicate that the need of clinical and epidemiological studies to investigate the presence of this infection in other areas in Brazil. (C) 2011 Elsevier B.V. All rights reserved.