Simultaneous estimation of hunting pressure, harvest and hunter success rates using WinBUGS

The use of hierarchical Bayesian spatial models in the analysis of ecological data is increasingly prevalent. The implementation of these models has been heretofore limited to specifically written software that required extensive programming knowledge to create. The advent of WinBUGS provides access to Bayesian hierarchical models for those without the programming expertise to create their own models and allows for the more rapid implementation of new models and data analysis. This facility is demonstrated here using data collected by the Missouri Department of Conservation for the Missouri Turkey Hunting Survey of 1996. Three models are considered, the first uses the collected data to estimate the success rate for individual hunters at the county level and incorporates a conditional autoregressive (CAR) spatial effect. The second model builds upon the first by simultaneously estimating the success rate and harvest at the county level, while the third estimates the success rate and hunting pressure at the county level. These models are discussed in detail as well as their implementation in WinBUGS and the issues arising therein. Future areas of application for WinBUGS and the latest developments in WinBUGS are discussed as well.

WinBUGS code to run a network meta-analysis

WinBUGS code and data to reproduce our network meta-analysis from "Control strategies to prevent total hip replacement-related infections: a systematic review and mixed treatment comparison" published in BMJ Open.

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.

Incorporating parameter uncertainty into quantitative microbial risk assessment (QMRA)

Modern statistical models and computational methods can now incorporate uncertainty of the parameters used in Quantitative Microbial Risk Assessments (QMRA). Many QMRAs use Monte Carlo methods, but work from fixed estimates for means, variances and other parameters. We illustrate the ease of estimating all parameters contemporaneously with the risk assessment, incorporating all the parameter uncertainty arising from the experiments from which these parameters are estimated. A Bayesian approach is adopted, using Markov Chain Monte Carlo Gibbs sampling (MCMC) via the freely available software, WinBUGS. The method and its ease of implementation are illustrated by a case study that involves incorporating three disparate datasets into an MCMC framework. The probabilities of infection when the uncertainty associated with parameter estimation is incorporated into a QMRA are shown to be considerably more variable over various dose ranges than the analogous probabilities obtained when constants from the literature are simply ‘plugged’ in as is done in most QMRAs. Neglecting these sources of uncertainty may lead to erroneous decisions for public health and risk management.

Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.

A Bayesian analysis of an agricultural field trial with three spatial dimensions

Modern technology now has the ability to generate large datasets over space and time. Such data typically exhibit high autocorrelations over all dimensions. The field trial data motivating the methods of this paper were collected to examine the behaviour of traditional cropping and to determine a cropping system which could maximise water use for grain production while minimising leakage below the crop root zone. They consist of moisture measurements made at 15 depths across 3 rows and 18 columns, in the lattice framework of an agricultural field. Bayesian conditional autoregressive (CAR) models are used to account for local site correlations. Conditional autoregressive models have not been widely used in analyses of agricultural data. This paper serves to illustrate the usefulness of these models in this field, along with the ease of implementation in WinBUGS, a freely available software package. The innovation is the fitting of separate conditional autoregressive models for each depth layer, the ‘layered CAR model’, while simultaneously estimating depth profile functions for each site treatment. Modelling interest also lay in how best to model the treatment effect depth profiles, and in the choice of neighbourhood structure for the spatial autocorrelation model. The favoured model fitted the treatment effects as splines over depth, and treated depth, the basis for the regression model, as measured with error, while fitting CAR neighbourhood models by depth layer. It is hierarchical, with separate onditional autoregressive spatial variance components at each depth, and the fixed terms which involve an errors-in-measurement model treat depth errors as interval-censored measurement error. The Bayesian framework permits transparent specification and easy comparison of the various complex models compared.

Methods to improve gene signal: Application to cDNA microarrays

Microarrays are high throughput biological assays that allow the screening of thousands of genes for their expression. The main idea behind microarrays is to compute for each gene a unique signal that is directly proportional to the quantity of mRNA that was hybridized on the chip. A large number of steps and errors associated with each step make the generated expression signal noisy. As a result, microarray data need to be carefully pre-processed before their analysis can be assumed to lead to reliable and biologically relevant conclusions. This thesis focuses on developing methods for improving gene signal and further utilizing this improved signal for higher level analysis. To achieve this, first, approaches for designing microarray experiments using various optimality criteria, considering both biological and technical replicates, are described. A carefully designed experiment leads to signal with low noise, as the effect of unwanted variations is minimized and the precision of the estimates of the parameters of interest are maximized. Second, a system for improving the gene signal by using three scans at varying scanner sensitivities is developed. A novel Bayesian latent intensity model is then applied on these three sets of expression values, corresponding to the three scans, to estimate the suitably calibrated true signal of genes. Third, a novel image segmentation approach that segregates the fluorescent signal from the undesired noise is developed using an additional dye, SYBR green RNA II. This technique helped in identifying signal only with respect to the hybridized DNA, and signal corresponding to dust, scratch, spilling of dye, and other noises, are avoided. Fourth, an integrated statistical model is developed, where signal correction, systematic array effects, dye effects, and differential expression, are modelled jointly as opposed to a sequential application of several methods of analysis. The methods described in here have been tested only for cDNA microarrays, but can also, with some modifications, be applied to other high-throughput technologies. Keywords: High-throughput technology, microarray, cDNA, multiple scans, Bayesian hierarchical models, image analysis, experimental design, MCMC, WinBUGS.

Self perceived health status of schizophrenic patients in Spain: an analysis of geog raphical differences using bayesian approach

Objectives. This paper explores the use of regression models for estimating health status of schizophrenic patients, from a Bayesian perspective. Our aims are: 1- To obtain a set of values of health states of the EQ-5D based on self-assessed health from a sample of schizophrenic patients. 2- To analyse the differences in the health status and in patients’ perceptions of their health status between four mental-health districts in Spain. Methods. We develop two linear models with dummy variables. The first model seeks to obtain an index of the health status of the patients using a VAS as a dependent variable and the different dimensions of EQ-5D as regressors. The second model allows to analyse the differences between the self-assessed health status in the different geographic areas and also the differences between the patients’ self-assessed health states, irrespective of their actual health state, in the different geographic areas. The analysis is done using Bayesian approach with Gibbs sampling (computer program WinBUGS 1.4). Data concerning self-assessed EQ-5D with VAS from four geographic areas of schizophrenic patients were obtained for the purposes of this analysis. Results. We obtained the health status index for this sample and analysed the differences for this index between the four geographic areas. Our study reveals variables that explain the differences in patients’ health status and differences in their health states assessment. We consider four possible scenarios.

Métodos probabilísticos e estatísticos na gestão de fogos florestais

Tese de doutoramento, Estatística e Investigação Operacional (Probabilidades e Estatística), Universidade de Lisboa, Faculdade de Ciências, 2014

Determinação da prevalência de fibrilhação auricular na população portuguesa ao nível da NUTS III usando modelos hierárquicos bayesianos

A Fibrilhação Auricular é uma alteração do ritmo cardíaco designada por arritmia. Esta patologia é considerada a forma de arritmia mais frequentemente observada na prática clínica e que constitui uma importante causa de morbilidade pelo risco inerente de desenvolvimento de AVC. Em 2010 foi realizado um estudo epidemiológico na população Portuguesa com o objectivo determinar a prevalência de Fibrilhação Auricular na população portuguesa com idade igual ou superior a 40 anos, sob o acrónimo de FAMA. Os dados publicados indicaram uma estimativa de prevalência de 2,5%, com um aumento da prevalência em função da classe etária. A nível regional não foram observadas diferenças na taxa de prevalência. Estudos de mapeamento de doenças mostraram que a determinação de taxas de prevalência por região, quando o número de casos observados é relativamente baixo, apresentam sobredispersão e, consequentemente, uma falta de precisão nas estimativas obtidas através um método frequencista clássico. A utilização de modelos Bayesianos hierárquicos no mapeamento de doenças tem apresentado vantagem na estimação de valores de risco da doença comparativamente à abordagem clássica. Assim, é objectivo deste trabalho determinar a prevalência de Fibrilhação Auricular na população Portuguesa por região, ao nível da NUTS III, usando modelos hierárquicos Bayesianos. Os dados utilizados neste estudo são os dados referentes ao estudo FAMA, pós-estratificados para correcção dos ponderadores. O modelo Bayesiano proposto por Besag, York e Mollié (1991) foi usado para modelar os dados, covariando para a idade e índice de massa corporal. A revisão do desenho do estudo e o recálculo dos ponderadores foi realizado com recurso ao software R, survey, e a análise Bayesiana efectuada através do WinBugs. iii Os resultados deste estudo demonstram que o uso de modelos Bayesianos são uma melhor opção para a estimação de valores risco relativo e prevalência da doença. Contudo, a utilização de covariáveis não resultou numa melhoria considerável ao contrário do que seria esperado. Conclui-se que a Fibrilhação Auricular apresenta variações regionais significativas, a nível de NUTS III, que não devem ser desvalorizadas na determinação de políticas de saúde pública para controle da doença.

Longitudinal Poisson modeling: an application for CD4 counting in HIV-infected patients

In this paper, we present different ofrailtyo models to analyze longitudinal data in the presence of covariates. These models incorporate the extra-Poisson variability and the possible correlation among the repeated counting data for each individual. Assuming a CD4 counting data set in HIV-infected patients, we develop a hierarchical Bayesian analysis considering the different proposed models and using Markov Chain Monte Carlo methods. We also discuss some Bayesian discrimination aspects for the choice of the best model.

Estimação clássica e Bayesiana em modelos de sobrevida com fração de cura

In Survival Analysis, long duration models allow for the estimation of the healing fraction, which represents a portion of the population immune to the event of interest. Here we address classical and Bayesian estimation based on mixture models and promotion time models, using different distributions (exponential, Weibull and Pareto) to model failure time. The database used to illustrate the implementations is described in Kersey et al. (1987) and it consists of a group of leukemia patients who underwent a certain type of transplant. The specific implementations used were numeric optimization by BFGS as implemented in R (base::optim), Laplace approximation (own implementation) and Gibbs sampling as implemented in Winbugs. We describe the main features of the models used, the estimation methods and the computational aspects. We also discuss how different prior information can affect the Bayesian estimates

Clinical judgment to estimate pretest probability in the diagnosis of Cushing's syndrome under a Bayesian perspective

OBJECTIVE: To estimate the pretest probability of Cushing's syndrome (CS) diagnosis by a Bayesian approach using intuitive clinical judgment. MATERIALS AND METHODS: Physicians were requested, in seven endocrinology meetings, to answer three questions: "Based on your personal expertise, after obtaining clinical history and physical examination, without using laboratorial tests, what is your probability of diagnosing Cushing's Syndrome?"; "For how long have you been practicing Endocrinology?"; and "Where do you work?". A Bayesian beta regression, using the WinBugs software was employed. RESULTS: We obtained 294 questionnaires. The mean pretest probability of CS diagnosis was 51.6% (95%CI: 48.7-54.3). The probability was directly related to experience in endocrinology, but not with the place of work. CONCLUSION: Pretest probability of CS diagnosis was estimated using a Bayesian methodology. Although pretest likelihood can be context-dependent, experience based on years of practice may help the practitioner to diagnosis CS. Arq Bras Endocrinol Metab. 2012;56(9):633-7

Validation of candidate smear microscopy quality indicators, extracted from tuberculosis laboratory registers

SETTING: Kinshasa Province, Democratic Republic of Congo. OBJECTIVE: To identify and validate register-based indicators of acid-fast bacilli (AFB) microscopy quality. DESIGN: Selection of laboratories based on reliability and variation in routine smear rechecking results. Calculation of relative sensitivity (RS) compared to recheckers and its correlation coefficient (R) with candidate indicators based on a fully probabilistic analysis incorporating vague prior information using WinBUGS. RESULTS: The proportion of positive follow-up smears correlated well (median R 0.81, 95% credibility interval [CI] 0.58-0.93), and the proportion of first smear-positive cases fairly (median R 0.70, 95% CI 0.38-0.89) with RS. The proportions of both positive suspect and low positive case smears showed poor correlations (median R 0.27 and -0.22, respectively, with ranges including zero). CONCLUSIONS: The proportion of positives in follow-up smears is the most promising indicator of AFB smear sensitivity, while the proportion of positive suspects may be more indicative of accessibility and suspect selection. Both can be obtained from simple reports, and should be used for internal and external monitoring and as guidance for supervision. As proportion of low positive suspect smears and consistency within case series are more difficult to interpret, they should be used only on-site by laboratory professionals. All indicators require more research to define their optimal range in various settings.