Municipal distribution of bladder cancer mortality in Spain: Possible role of mining and industry

BACKGROUND Spain shows the highest bladder cancer incidence rates in men among European countries. The most important risk factors are tobacco smoking and occupational exposure to a range of different chemical substances, such as aromatic amines. METHODS This paper describes the municipal distribution of bladder cancer mortality and attempts to "adjust" this spatial pattern for the prevalence of smokers, using the autoregressive spatial model proposed by Besag, York and Molliè, with relative risk of lung cancer mortality as a surrogate. RESULTS It has been possible to compile and ascertain the posterior distribution of relative risk for bladder cancer adjusted for lung cancer mortality, on the basis of a single Bayesian spatial model covering all of Spain's 8077 towns. Maps were plotted depicting smoothed relative risk (RR) estimates, and the distribution of the posterior probability of RR>1 by sex. Towns that registered the highest relative risks for both sexes were mostly located in the Provinces of Cadiz, Seville, Huelva, Barcelona and Almería. The highest-risk area in Barcelona Province corresponded to very specific municipal areas in the Bages district, e.g., Suría, Sallent, Balsareny, Manresa and Cardona. CONCLUSION Mining/industrial pollution and the risk entailed in certain occupational exposures could in part be dictating the pattern of municipal bladder cancer mortality in Spain. Population exposure to arsenic is a matter that calls for attention. It would be of great interest if the relationship between the chemical quality of drinking water and the frequency of bladder cancer could be studied.

Disentangling the formation of contrasting tree line physiognomies combining model selection and Bayesian parameterization for simulation models.

Alpine tree-line ecotones are characterized by marked changes at small spatial scales that may result in a variety of physiognomies. A set of alternative individual-based models was tested with data from four contrasting Pinus uncinata ecotones in the central Spanish Pyrenees to reveal the minimal subset of processes required for tree-line formation. A Bayesian approach combined with Markov chain Monte Carlo methods was employed to obtain the posterior distribution of model parameters, allowing the use of model selection procedures. The main features of real tree lines emerged only in models considering nonlinear responses in individual rates of growth or mortality with respect to the altitudinal gradient. Variation in tree-line physiognomy reflected mainly changes in the relative importance of these nonlinear responses, while other processes, such as dispersal limitation and facilitation, played a secondary role. Different nonlinear responses also determined the presence or absence of krummholz, in agreement with recent findings highlighting a different response of diffuse and abrupt or krummholz tree lines to climate change. The method presented here can be widely applied in individual-based simulation models and will turn model selection and evaluation in this type of models into a more transparent, effective, and efficient exercise.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Geographic distribution of plant pathogens in response to climate change

Geographic distributions of pathogens are the outcome of dynamic processes involving host availability, susceptibility and abundance, suitability of climate conditions, and historical contingency including evolutionary change. Distributions have changed fast and are changing fast in response to many factors, including climatic change. The response time of arable agriculture is intrinsically fast, but perennial crops and especially forests are unlikely to adapt easily. Predictions of many of the variables needed to predict changes in pathogen range are still rather uncertain, and their effects will be profoundly modified by changes elsewhere in the agricultural system, including both economic changes affecting growing systems and hosts and evolutionary changes in pathogens and hosts. Tools to predict changes based on environmental correlations depend on good primary data, which is often absent, and need to be checked against the historical record, which remains very poor for almost all pathogens. We argue that at present the uncertainty in predictions of change is so great that the important adaptive response is to monitor changes and to retain the capacity to innovate, both by access to economic capital with reasonably long-term rates of return and by retaining wide scientific expertise, including currently less fashionable specialisms.

Inferences about the coefficient of correlation in the standard bivariate normal distribution

The study of the association between two random variables that have a joint normal distribution is of interest in applied statistics; for example, in statistical genetics. This article, targeted to applied statisticians, addresses inferences about the coefficient of correlation (ρ) in the bivariate normal and standard bivariate normal distributions using likelihood, frequentist, and Baycsian perspectives. Some results are surprising. For instance, the maximum likelihood estimator and the posterior distribution of ρ in the standard bivariate normal distribution do not follow directly from results for a general bivariate normal distribution. An example employing bootstrap and rejection sampling procedures is used to illustrate some of the peculiarities.

A bayesian model for mixed responses and skew laten variable to measure HRQoL in children

The aim of the thesi is to formulate a suitable Item Response Theory (IRT) based model to measure HRQoL (as latent variable) using a mixed responses questionnaire and relaxing the hypothesis of normal distributed latent variable. The new model is a combination of two models already presented in literature, that is, a latent trait model for mixed responses and an IRT model for Skew Normal latent variable. It is developed in a Bayesian framework, a Markov chain Monte Carlo procedure is used to generate samples of the posterior distribution of the parameters of interest. The proposed model is test on a questionnaire composed by 5 discrete items and one continuous to measure HRQoL in children, the EQ-5D-Y questionnaire. A large sample of children collected in the schools was used. In comparison with a model for only discrete responses and a model for mixed responses and normal latent variable, the new model has better performances, in term of deviance information criterion (DIC), chain convergences times and precision of the estimates.

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.

A Bayesian approach to estimating the regression coefficients of a multinomial logit model

A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches. ^

Bayesian population pharmacokinetic analysis of sirolimus

Objective: It is usual that data collected from routine clinical care is sparse and unable to support the more complex pharmacokinetic (PK) models that may have been reported in previous rich data studies. Informative priors may be a pre-requisite for model development. The aim of this study was to estimate the population PK parameters of sirolimus using a fully Bayesian approach with informative priors. Methods: Informative priors including prior mean and precision of the prior mean were elicited from previous published studies using a meta-analytic technique. Precision of between-subject variability was determined by simulations from a Wishart distribution using MATLAB (version 6.5). Concentration-time data of sirolimus retrospectively collected from kidney transplant patients were analysed using WinBUGS (version 1.3). The candidate models were either one- or two-compartment with first order absorption and first order elimination. Model discrimination was based on computation of the posterior odds supporting the model. Results: A total of 315 concentration-time points were obtained from 25 patients. Most data were clustered at trough concentrations with range of 1.6 to 77 hours post-dose. Using informative priors, either a one- or two-compartment model could be used to describe the data. When a one-compartment model was applied, information was gained from the data for the value of apparent clearance (CL/F = 18.5 L/h), and apparent volume of distribution (V/F = 1406 L) but no information was gained about the absorption rate constant (ka). When a two-compartment model was fitted to the data, the data were informative about CL/F, apparent inter-compartmental clearance, and apparent volume of distribution of the peripheral compartment (13.2 L/h, 20.8 L/h, and 579 L, respectively). The posterior distribution of the volume distribution of central compartment and ka were the same as priors. The posterior odds for the two-compartment model was 8.1, indicating the data supported the two-compartment model. Conclusion: The use of informative priors supported the choice of a more complex and informative model that would otherwise have not been supported by the sparse data.

A Bayesian approach to on-line learning

Online learning is discussed from the viewpoint of Bayesian statistical inference. By replacing the true posterior distribution with a simpler parametric distribution, one can define an online algorithm by a repetition of two steps: An update of the approximate posterior, when a new example arrives, and an optimal projection into the parametric family. Choosing this family to be Gaussian, we show that the algorithm achieves asymptotic efficiency. An application to learning in single layer neural networks is given.

Bayesian error bars for regression

Regression problems are concerned with predicting the values of one or more continuous quantities, given the values of a number of input variables. For virtually every application of regression, however, it is also important to have an indication of the uncertainty in the predictions. Such uncertainties are expressed in terms of the error bars, which specify the standard deviation of the distribution of predictions about the mean. Accurate estimate of error bars is of practical importance especially when safety and reliability is an issue. The Bayesian view of regression leads naturally to two contributions to the error bars. The first arises from the intrinsic noise on the target data, while the second comes from the uncertainty in the values of the model parameters which manifests itself in the finite width of the posterior distribution over the space of these parameters. The Hessian matrix which involves the second derivatives of the error function with respect to the weights is needed for implementing the Bayesian formalism in general and estimating the error bars in particular. A study of different methods for evaluating this matrix is given with special emphasis on the outer product approximation method. The contribution of the uncertainty in model parameters to the error bars is a finite data size effect, which becomes negligible as the number of data points in the training set increases. A study of this contribution is given in relation to the distribution of data in input space. It is shown that the addition of data points to the training set can only reduce the local magnitude of the error bars or leave it unchanged. Using the asymptotic limit of an infinite data set, it is shown that the error bars have an approximate relation to the density of data in input space.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Pricing farm-level agricultural insurance: a Bayesian approach

This paper applies Hierarchical Bayesian Models to price farm-level yield insurance contracts. This methodology considers the temporal effect, the spatial dependence and spatio-temporal models. One of the major advantages of this framework is that an estimate of the premium rate is obtained directly from the posterior distribution. These methods were applied to a farm-level data set of soybean in the State of the Parana (Brazil), for the period between 1994 and 2003. The model selection was based on a posterior predictive criterion. This study improves considerably the estimation of the fair premium rates considering the small number of observations.

Bayesian Model Averaging in the Instrumental Variable Regression Model

This paper considers the instrumental variable regression model when there is uncertainty about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainty can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very exible and can be easily adapted to analyze any of the di¤erent priors that have been proposed in the Bayesian instrumental variables literature. We show how to calculate the probability of any relevant restriction (e.g. the posterior probability that over-identifying restrictions hold) and discuss diagnostic checking using the posterior distribution of discrepancy vectors. We illustrate our methods in a returns-to-schooling application.

Probability of achieving optimal molecular response to imatinib in chronic myeloid leukemia (CML) patients: Pharmacokinetic/Pharmacodynamic (PK/PD) relationships observed under field-conditions

Objectives: Imatinib has been increasingly proposed for therapeutic drug monitoring (TDM), as trough concentrations (Cmin) correlate with response rates in CML patients. This analysis aimed to evaluate the impact of imatinib exposure on optimal molecular response rates in a large European cohort of patients followed by centralized TDM.¦Methods: Sequential PK/PD analysis was performed in NONMEM 7 on 2230 plasma (PK) samples obtained along with molecular response (PD) data from 1299 CML patients. Model-based individual Bayesian estimates of exposure, parameterized as to initial dose adjusted and log-normalized Cmin (log-Cmin) or clearance (CL), were investigated as potential predictors of optimal molecular response, while accounting for time under treatment (stratified at 3 years), gender, CML phase, age, potentially interacting comedication, and TDM frequency. PK/PD analysis used mixed-effect logistic regression (iterative two-stage method) to account for intra-patient correlation.¦Results: In univariate analyses, CL, log-Cmin, time under treatment, TDM frequency, gender (all p<0.01) and CML phase (p=0.02) were significant predictors of the outcome. In multivariate analyses, all but log-Cmin remained significant (p<0.05). Our model estimates a 54.1% probability of optimal molecular response in a female patient with a median CL of 14.4 L/h, increasing by 4.7% with a 35% decrease in CL (percentile 10 of CL distribution), and decreasing by 6% with a 45% increased CL (percentile 90), respectively. Male patients were less likely than female to be in optimal response (odds ratio: 0.62, p<0.001), with an estimated probability of 42.3%.¦Conclusions: Beyond CML phase and time on treatment, expectedly correlated to the outcome, an effect of initial imatinib exposure on the probability of achieving optimal molecular response was confirmed in field-conditions by this multivariate analysis. Interestingly, male patients had a higher risk of suboptimal response, which might not exclusively derive from their 18.5% higher CL, but also from reported lower adherence to the treatment. A prospective longitudinal study would be desirable to confirm the clinical importance of identified covariates and to exclude biases possibly affecting this observational survey.