ABSTRACT
Most item response theory (IRT) models for dichotomous responses are based on probit or logit link functions which assume a symmetric relationship between the probability of a correct response and the latent traits of individuals taking a test. This assumption restricts the use of those models to the case in which all items behave symmetrically. On the other hand, asymmetric models proposed in the literature impose that all the items in a test behave asymmetrically. This assumption is inappropriate for great majority of tests which are, in general, composed of both symmetric and asymmetric items. Furthermore, a straightforward extension of the existing models in the literature would require a prior selection of the items' symmetry/asymmetry status. This paper proposes a Bayesian IRT model that accounts for symmetric and asymmetric items in a flexible but parsimonious way. That is achieved by assigning a finite mixture prior to the skewness parameter, with one of the mixture components being a point mass at zero. This allows for analyses under both model selection and model averaging approaches. Asymmetric item curves are designed through the centred skew normal distribution, which has a particularly appealing parametrization in terms of parameter interpretation and computational efficiency. An efficient Markov chain Monte Carlo algorithm is proposed to perform Bayesian inference and its performance is investigated in some simulated examples. Finally, the proposed methodology is applied to a data set from a large-scale educational exam in Brazil.
Subject(s)
Algorithms , Humans , Bayes Theorem , Markov Chains , Monte Carlo MethodABSTRACT
Cure fraction models have been widely used to model time-to-event data when part of the individuals survives long-term after disease and are considered cured. Most cure fraction models neglect the measurement error that some covariates may experience which leads to poor estimates for the cure fraction. We introduce a Bayesian promotion time cure model that accounts for both mismeasured covariates and atypical measurement errors. This is attained by assuming a scale mixture of the normal distribution to describe the uncertainty about the measurement error. Extending previous works, we also assume that the measurement error variance is unknown and should be estimated. Three classes of prior distributions are assumed to model the uncertainty about the measurement error variance. Simulation studies are performed evaluating the proposed model in different scenarios and comparing it to the standard promotion time cure fraction model. Results show that the proposed models are competitive ones. The proposed model is fitted to analyze a dataset from a melanoma clinical trial assuming that the Breslow depth is mismeasured.
Subject(s)
Models, Statistical , Bayes Theorem , Computer Simulation , Humans , Normal DistributionABSTRACT
In this paper, we consider a piecewise exponential model (PEM) with random time grid to develop a full semiparametric Bayesian cure rate model. An elegant mechanism enjoying several attractive features for modeling the randomness of the time grid of the PEM is assumed. To model the prior behavior of the failure rates of the PEM we assume a hierarchical modeling approach that allows us to control the degree of parametricity in the right tail of the survival curve. Properties of the proposed model are discussed in detail. In particular, we investigate the impact of assuming a random time grid for the PEM on the estimation of the cure fraction. We further develop an efficient collapsed Gibbs sampler algorithm for carrying out posterior computation. A Bayesian diagnostic method for assessing goodness of fit and performing model comparisons is briefly discussed. Finally, we illustrate the usefulness of the new methodology with the analysis of a melanoma clinical trial that has been discussed in the literature.
Subject(s)
Biometry/methods , Models, Statistical , Algorithms , Bayes Theorem , Clinical Trials as Topic , Female , Humans , Male , Melanoma/therapy , Survival Analysis , Treatment OutcomeABSTRACT
In this paper we introduce a misclassification model for the meiosis I non-disjunction fraction in numerical chromosomal anomalies named trisomies. We obtain posteriors, and their moments, for the probability that a non-disjunction occurs in the first division of meiosis and for the misclassification errors. We also extend previous works by providing the exact posterior, and its moments, for the probability that a non-disjunction occurs in the first division of meiosis assuming the model proposed in the literature which does not consider that data are subject to misclassification. We perform Monte Carlo studies in order to compare Bayes estimates obtained by using both models. An application to Down Syndrome data is also presented.
Subject(s)
Meiosis/genetics , Models, Genetic , Models, Statistical , Trisomy/genetics , Bayes Theorem , Computer Simulation , Humans , Monte Carlo MethodABSTRACT
One of the greatest challenges related to the use of piecewise exponential models (PEMs) is to find an adequate grid of time-points needed in its construction. In general, the number of intervals in such a grid and the position of their endpoints are ad-hoc choices. We extend previous works by introducing a full Bayesian approach for the piecewise exponential model in which the grid of time-points (and, consequently, the endpoints and the number of intervals) is random. We estimate the failure rates using the proposed procedure and compare the results with the non-parametric piecewise exponential estimates. Estimates for the survival function using the most probable partition are compared with the Kaplan-Meier estimators (KMEs). A sensitivity analysis for the proposed model is provided considering different prior specifications for the failure rates and for the grid. We also evaluate the effect of different percentage of censoring observations in the estimates. An application to a real data set is also provided. We notice that the posteriors are strongly influenced by prior specifications, mainly for the failure rates parameters. Thus, the priors must be fairly built, say, really disclosing the expert prior opinion.
Subject(s)
Bayes Theorem , Kaplan-Meier Estimate , Models, Statistical , Computer Simulation , Markov Chains , Monte Carlo Method , TelecommunicationsABSTRACT
Esse estudo analisa dados do vestibular da Universidade Federal de Minas Gerais de 2004, mediante um modelo de regressão não paramétrico, o Classification and Regression Trees. Seu objetivo foi identificar os principais fatores de aprovação e, também, verificar se esses fatores eram os mesmos para os cursos diurnos e noturnos. A resposta a essas questões permitiria verificar se a expansão do turno noturno feita por essa universidade vinha promovendo maior inserção social. Observou-se que, em geral, a conclusão do ensino médio em escolas públicas federais ou particulares, o conhecimento de língua estrangeira e o pertencimento a um grupo socioeconômico alto são fatores fortemente associados à aprovação do candidato. Verificou-se, ainda, que nos cursos noturnos as variáveis socioeconômicas têm maior relevância, enquanto nos cursos diurnos a formação do candidato adquire maior peso. Finalmente, o fator socioeconômico médio tende a ser maior para os candidatos aprovados.(AU)
This study analyses data from 2004 Federal University of Minas Gerais' general entrance examination, making use of a non-parametrical regression model: the Classification and Regression Trees. Its aims were to identify the main factors of college approval and, also, to verify if these factors were the same for both daytime and nighttime courses, in order to be able to affirm that the expansion of nighttime courses was promoting, in this university, a higher social insertion. In general, it was observed that the attendance to a federal or private high school, the knowledge of foreign languages and a higher socioeconomic status were factors strongly associated with candidates' approval. In nighttime courses, it was found that socioeconomics variables had a higher importance, while variables related to the quality of previous schooling had more weight in daytime courses. The average socioeconomic factor tended to be higher in the group of the approved candidates.(AU)
ABSTRACT
Este trabalho visa a conhecer melhor o perfil dos candidatos oriundos de escolas das redes públicas e privadas de ensino que tentaram ingressar na UFMG em 2004. Busca-se identificar quais das características definidas no questionário socioeconômico e cultural aplicado no ato da inscrição do candidato podem estar mais associadas com a aprovação no vestibular. Conclui-se que o local de moradia e o conhecimento de língua estrangeira são as variáveis mais fortemente associadas com a aprovação do candidato de escolas particulares e escolas públicas, respectivamente. Verificou-se que, entre os candidatos que concluíram o ensino médio em escolas públicas, os que estudaram em escolas públicas federais tendem a se concentrar nos grupos com maiores chances de aprovação.
This paper aims to better understand the profile of the candidates for the UFMG entrance examination in 2004, coming from public and private schools. The objective is to identify which of the characteristics defined through a socioeconomic and cultural questionnaire answered by the candidates upon their application for the entrance examination may be associated with their approval at the University exams. It was found that the place where the candidates live and their knowledge of a foreign language are the variants more strongly related to the approval of the candidates of private schools and public schools, respectively. It was also found that, among the candidates who concluded high school at public schools that attained the highest chances of approval, there was a large percentage of candidates that attended high school in federal establishments.
ABSTRACT
In this paper we analyze the fraction of non-disjunction in Meiosis I assuming reference (non-informative) priors. We consider Jeffreys's approach to built a non-informative prior (Jeffreys's prior) for the fraction of non-disjunction in Meiosis I. We prove that Jeffreys's prior is a proper distribution. We perform Monte Carlo studies in order to compare Bayes estimates obtained assuming Jeffreys's and uniform priors. We consider full Bayesian significance test (FBST) and Bayes factor (BF) for testing precise hypothesis on the fraction of non-disjunction in Meiosis I. The ultimate goal of this paper is to compare these two test procedures through simulation studies using both prior specifications. An application to Down Syndrome data is also presented.
Subject(s)
Bayes Theorem , Down Syndrome/genetics , Meiosis/genetics , Models, Genetic , Humans , Monte Carlo Method , Nondisjunction, GeneticABSTRACT
The main causes of numerical chromosomal anomalies, including trisomies, arise from an error in the chromosomal segregation during the meiotic process, named a non-disjunction. One of the most used techniques to analyze chromosomal anomalies nowadays is the polymerase chain reaction (PCR), which counts the number of peaks or alleles in a polymorphic microsatellite locus. It was shown in previous works that the number of peaks has a multinomial distribution whose probabilities depend on the non-disjunction fraction F. In this work, we propose a Bayesian approach for estimating the meiosis I non-disjunction fraction F. in the absence of the parental information. Since samples of trisomic patients are, in general, small, the Bayesian approach can be a good alternative for solving this problem. We consider the sampling/importance resampling technique and the Simpson rule to extract information from the posterior distribution of F. Bayes and maximum likelihood estimators are compared through a Monte Carlo simulation, focusing on the influence of different sample sizes and prior specifications in the estimates. We apply the proposed method to estimate F. for patients with trisomy of chromosome 21 providing a sensitivity analysis for the method. The results obtained show that Bayes estimators are better in almost all situations.
