A Bayesian Long-term Survival Model Parametrized in the Cured Fraction

The main goal of this paper is to investigate a cure rate model that comprehends some well-known proposals found in the literature. In our work the number of competing causes of the event of interest follows the negative binomial distribution. The model is conveniently reparametrized through the cured fraction, which is then linked to covariates by means of the logistic link. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis in the proposed model. The procedure is illustrated with a numerical example.

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in -variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178].

Bayesian Estimation of the Logistic Positive Exponent IRT Model

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric ICC treats both correct and incorrect answers symmetrically, which results in a logical contradiction in ordering examinees on the ability scale. A data set corresponding to a mathematical test applied in Peruvian public schools is analyzed, where comparisons with other parametric IRT models also are conducted. Several model comparison criteria are discussed and implemented. The main conclusion is that the LPE and RLPE IRT models are easy to implement and seem to provide the best fit to the data set considered.

Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew-t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.

Evaluation of an average numerator relationship matrix model and a Bayesian hierarchical model for growth traits in Nellore cattle with uncertain paternity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estimação paramétrica e não-paramétrica em modelos de markov ocultos

In this work we study the Hidden Markov Models with finite as well as general state space. In the finite case, the forward and backward algorithms are considered and the probability of a given observed sequence is computed. Next, we use the EM algorithm to estimate the model parameters. In the general case, the kernel estimators are used and to built a sequence of estimators that converge in L1-norm to the density function of the observable process

A Markovian model market-Akerlof's lemons and the asymmetry of information

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bayesian binary regression model: an application to in-hospital death after AMI prediction

Um modelo bayesiano de regressão binária é desenvolvido para predizer óbito hospitalar em pacientes acometidos por infarto agudo do miocárdio. Métodos de Monte Carlo via Cadeias de Markov (MCMC) são usados para fazer inferência e validação. Uma estratégia para construção de modelos, baseada no uso do fator de Bayes, é proposta e aspectos de validação são extensivamente discutidos neste artigo, incluindo a distribuição a posteriori para o índice de concordância e análise de resíduos. A determinação de fatores de risco, baseados em variáveis disponíveis na chegada do paciente ao hospital, é muito importante para a tomada de decisão sobre o curso do tratamento. O modelo identificado se revela fortemente confiável e acurado, com uma taxa de classificação correta de 88% e um índice de concordância de 83%.

Planning accelerated life tests under Exponentiated-Weibull-Arrhenius model

Purpose - The purpose of this paper is to present designs for an accelerated life test (ALT). Design/methodology/approach - Bayesian methods and simulation Monte Carlo Markov Chain (MCMC) methods were used. Findings - In the paper a Bayesian method based on MCMC for ALT under EW distribution (for life time) and Arrhenius models (relating the stress variable and parameters) was proposed. The paper can conclude that it is a reasonable alternative to the classical statistical methods since the implementation of the proposed method is simple, not requiring advanced computational understanding and inferences on the parameters can be made easily. By the predictive density of a future observation, a procedure was developed to plan ALT and also to verify if the conformance fraction of the manufactured process reaches some desired level of quality. This procedure is useful for statistical process control in many industrial applications. Research limitations/implications - The results may be applied in a semiconductor manufacturer. Originality/value - The Exponentiated-Weibull-Arrhenius model has never before been used to plan an ALT. © Emerald Group Publishing Limited.

A non-homogeneous poisson model with spatial anisotropy applied to ozone data from Mexico City

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The FGM bivariate lifetime copula model: a bayesian approach

In this paper, we propose a bivariate distribution for the bivariate survival times based on Farlie-Gumbel-Morgenstern copula to model the dependence on a bivariate survival data. The proposed model allows for the presence of censored data and covariates. For inferential purpose a Bayesian approach via Markov Chain Monte Carlo (MCMC) is considered. Further, some discussions on the model selection criteria are given. In order to examine outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated via a simulation study and a real dataset.

A general threshold stress hybrid hazard model for lifetime data

In this paper we propose a hybrid hazard regression model with threshold stress which includes the proportional hazards and the accelerated failure time models as particular cases. To express the behavior of lifetimes the generalized-gamma distribution is assumed and an inverse power law model with a threshold stress is considered. For parameter estimation we develop a sampling-based posterior inference procedure based on Markov Chain Monte Carlo techniques. We assume proper but vague priors for the parameters of interest. A simulation study investigates the frequentist properties of the proposed estimators obtained under the assumption of vague priors. Further, some discussions on model selection criteria are given. The methodology is illustrated on simulated and real lifetime data set.

A Bayesian analysis of the Conway-Maxwell-Poisson cure rate model

The purpose of this paper is to develop a Bayesian analysis for the right-censored survival data when immune or cured individuals may be present in the population from which the data is taken. In our approach the number of competing causes of the event of interest follows the Conway-Maxwell-Poisson distribution which generalizes the Poisson distribution. Markov chain Monte Carlo (MCMC) methods are used to develop a Bayesian procedure for the proposed model. Also, some discussions on the model selection and an illustration with a real data set are considered.

Study of using marker assisted selection on a beef cattle breeding program by model comparison

A data set of a commercial Nellore beef cattle selection program was used to compare breeding models that assumed or not markers effects to estimate the breeding values, when a reduced number of animals have phenotypic, genotypic and pedigree information available. This herd complete data set was composed of 83,404 animals measured for weaning weight (WW), post-weaning gain (PWG), scrotal circumference (SC) and muscle score (MS), corresponding to 116,652 animals in the relationship matrix. Single trait analyses were performed by MTDFREML software to estimate fixed and random effects solutions using this complete data. The additive effects estimated were assumed as the reference breeding values for those animals. The individual observed phenotype of each trait was adjusted for fixed and random effects solutions, except for direct additive effects. The adjusted phenotype composed of the additive and residual parts of observed phenotype was used as dependent variable for models' comparison. Among all measured animals of this herd, only 3160 animals were genotyped for 106 SNP markers. Three models were compared in terms of changes on animals' rank, global fit and predictive ability. Model 1 included only polygenic effects, model 2 included only markers effects and model 3 included both polygenic and markers effects. Bayesian inference via Markov chain Monte Carlo methods performed by TM software was used to analyze the data for model comparison. Two different priors were adopted for markers effects in models 2 and 3, the first prior assumed was a uniform distribution (U) and, as a second prior, was assumed that markers effects were distributed as normal (N). Higher rank correlation coefficients were observed for models 3_U and 3_N, indicating a greater similarity of these models animals' rank and the rank based on the reference breeding values. Model 3_N presented a better global fit, as demonstrated by its low DIC. The best models in terms of predictive ability were models 1 and 3_N. Differences due prior assumed to markers effects in models 2 and 3 could be attributed to the better ability of normal prior in handle with collinear effects. The models 2_U and 2_N presented the worst performance, indicating that this small set of markers should not be used to genetically evaluate animals with no data, since its predictive ability is restricted. In conclusion, model 3_N presented a slight superiority when a reduce number of animals have phenotypic, genotypic and pedigree information. It could be attributed to the variation retained by markers and polygenic effects assumed together and the normal prior assumed to markers effects, that deals better with the collinearity between markers. (C) 2012 Elsevier B.V. All rights reserved.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.