On estimation and influence diagnostics for log-Birnbaum-Saunders Student-t regression models: Full Bayesian analysis

The purpose of this paper is to develop a Bayesian approach for log-Birnbaum-Saunders Student-t regression models under right-censored survival data. Markov chain Monte Carlo (MCMC) methods are used to develop a Bayesian procedure for the considered model. In order to attenuate the influence of the outlying observations on the parameter estimates, we present in this paper Birnbaum-Saunders models in which a Student-t distribution is assumed to explain the cumulative damage. Also, some discussions on the model selection to compare the fitted models are given and case deletion influence diagnostics are developed for the joint posterior distribution based on the Kullback-Leibler divergence. The developed procedures are illustrated with a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective

Linear mixed models were developed to handle clustered data and have been a topic of increasing interest in statistics for the past 50 years. Generally. the normality (or symmetry) of the random effects is a common assumption in linear mixed models but it may, sometimes, be unrealistic, obscuring important features of among-subjects variation. In this article, we utilize skew-normal/independent distributions as a tool for robust modeling of linear mixed models under a Bayesian paradigm. The skew-normal/independent distributions is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal distribution, skew-t, skew-slash and the skew-contaminated normal distributions as special cases, providing an appealing robust alternative to the routine use of symmetric distributions in this type of models. The methods developed are illustrated using a real data set from Framingham cholesterol study. (C) 2009 Elsevier B.V. All rights reserved.

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 inference for a skew-normal IRT model under the centred parameterization

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is interest in studying latent variables. These latent variables are directly considered in the Item Response Models (IRM) and they are usually called latent traits. A usual assumption for parameter estimation of the IRM, considering one group of examinees, is to assume that the latent traits are random variables which follow a standard normal distribution. However, many works suggest that this assumption does not apply in many cases. Furthermore, when this assumption does not hold, the parameter estimates tend to be biased and misleading inference can be obtained. Therefore, it is important to model the distribution of the latent traits properly. In this paper we present an alternative latent traits modeling based on the so-called skew-normal distribution; see Genton (2004). We used the centred parameterization, which was proposed by Azzalini (1985). This approach ensures the model identifiability as pointed out by Azevedo et al. (2009b). Also, a Metropolis Hastings within Gibbs sampling (MHWGS) algorithm was built for parameter estimation by using an augmented data approach. A simulation study was performed in order to assess the parameter recovery in the proposed model and the estimation method, and the effect of the asymmetry level of the latent traits distribution on the parameter estimation. Also, a comparison of our approach with other estimation methods (which consider the assumption of symmetric normality for the latent traits distribution) was considered. The results indicated that our proposed algorithm recovers properly all parameters. Specifically, the greater the asymmetry level, the better the performance of our approach compared with other approaches, mainly in the presence of small sample sizes (number of examinees). Furthermore, we analyzed a real data set which presents indication of asymmetry concerning the latent traits distribution. The results obtained by using our approach confirmed the presence of strong negative asymmetry of the latent traits distribution. (C) 2010 Elsevier B.V. All rights reserved.

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.

Semiparametric Bayesian measurement error modeling

This work presents a Bayesian semiparametric approach for dealing with regression models where the covariate is measured with error. Given that (1) the error normality assumption is very restrictive, and (2) assuming a specific elliptical distribution for errors (Student-t for example), may be somewhat presumptuous; there is need for more flexible methods, in terms of assuming only symmetry of errors (admitting unknown kurtosis). In this sense, the main advantage of this extended Bayesian approach is the possibility of considering generalizations of the elliptical family of models by using Dirichlet process priors in dependent and independent situations. Conditional posterior distributions are implemented, allowing the use of Markov Chain Monte Carlo (MCMC), to generate the posterior distributions. An interesting result shown is that the Dirichlet process prior is not updated in the case of the dependent elliptical model. Furthermore, an analysis of a real data set is reported to illustrate the usefulness of our approach, in dealing with outliers. Finally, semiparametric proposed models and parametric normal model are compared, graphically with the posterior distribution density of the coefficients. (C) 2009 Elsevier Inc. All rights reserved.

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.

A robust Bayesian approach to null intercept measurement error model with application to dental data

Measurement error models often arise in epidemiological and clinical research. Usually, in this set up it is assumed that the latent variable has a normal distribution. However, the normality assumption may not be always correct. Skew-normal/independent distribution is a class of asymmetric thick-tailed distributions which includes the Skew-normal distribution as a special case. In this paper, we explore the use of skew-normal/independent distribution as a robust alternative to null intercept measurement error model under a Bayesian paradigm. We assume that the random errors and the unobserved value of the covariate (latent variable) follows jointly a skew-normal/independent distribution, providing an appealing robust alternative to the routine use of symmetric normal distribution in this type of model. Specific distributions examined include univariate and multivariate versions of the skew-normal distribution, the skew-t distributions, the skew-slash distributions and the skew contaminated normal distributions. The methods developed is illustrated using a real data set from a dental clinical trial. (C) 2008 Elsevier B.V. All rights reserved.

Comparasion of two minimally invasive methods on the longevity of glass ionomer cement restorations: short-term results of a pilot study

The purpose of this study was to evaluate the clinical performance of glass ionomer cement (GIC) restorations comparing two minimally invasive methods in permanent teeth after 12 months. Fifty pregnant women (second trimester of pregnancy), mean age 22 ± 5.30 years, were treated by two previously trained operators. The treatment approaches tested were: chemomechanical method (CarisolvTM; MediTeam) and atraumatic restorative treatment (ART). A split-mouth study design was used in which the two treatments were randomly placed in 50 matched pairs of permanent teeth. The chemomechanical method (CM) was the test group and the ART was the control group. The treatments were performed in Public Health Centers. The tested restorative material was a high-strength GIC (Ketac Molar; 3M/ESPE). The restorations were placed according to the ART guidelines. Two calibrated independent examiners evaluated the restorations in accordance with ART criteria. The inter-examiner kappa was 0.97. Data were analyzed using 95% confidence interval on the binomial distribution and Fisher's exact test at 5% significance level. In a 12-month follow-up, 86% of the restorations were evaluated. In the test group (CM), 100% (CI=93.3-100%) of the restorations were considered successful. In the control group (ART) 97.6% (CI=87.4-99.9%) of the restorations were considered successful and 2.4% unsuccessful (marginal defect >0.5 mm). There was no statistically significant difference between the 12-mounth success rate for both groups (Fisher's exact test: P=0.49) and between the two operators (Fisher's exact test: P=1.00). Both minimally invasive methods, chemomechanical method and ART, showed a similar clinical performance after 12 months of follow up.

Histopathological evaluation of different methods of experimental induction of periapical periodontitis

This study evaluated histopathologically different methods of experimental induction of periapical periodontitis. The radiographic and microbiological evaluations have been performed in a previous investigation. Fifty-seven root canals from dogs' teeth were assigned to 4 groups. In GI (n=14) and GII (n=14), the root canals were exposed to oral environment for 180 days; in GIII (n=14) and GIV (n=15) the root canals were exposed for 7 days and then the access cavities were restored and remained sealed for 53 days. The root apices of GI and GIII were perforated, whilst those of GII and GIV remained intact. After induction of periapical periodontitis, the dogs were euthanized. Serial sections were obtained and stained with hematoxylin and eosin. Data of the histopathological evaluation were submitted to Kruskal-Wallis and Dunn's tests at 5% significance level. The inflammatory periapical reaction and resorption of mineralized tissues were less intense in GII than in the other groups (p<0.05). There was no histopathological difference among the experimentally induced periapical lesions in the teeth with coronal sealing. On the other hand, when coronal sealing was not performed, greater intensity of induced periapical periodontitis was observed in the teeth with apical perforation.

Microbial distribution in the root canal system after periapical lesion induction using different methods

The aim of this study was to evaluate the microbial distribution in the root canal system after periapical lesion induction in dogs' teeth using different methods. Fifty-two root canals were assigned to 4 groups (n=13). Groups I and II: root canals were exposed to the oral cavity for 180 days; groups III and IV: root canals were exposed for 7 days and then the coronal openings were sealed for 53 days. The root apices of groups I and III were perforated, while those of groups II and IV remained intact. After the experimental periods, the animals were euthanized and the anatomic pieces containing the roots were processed and stained with the Brown & Brenn method to assess the presence and distribution of microorganisms. The incidence of microorganisms at different sites of the roots and periapical lesions was analyzed statistically by the chi-square test at 5% significance level. All groups presented microorganisms in the entire root canal system. A larger number of microorganisms was observed on the root canal walls, apical delta and dentinal tubules (p<0.05), followed by cementum and cemental resorption areas. In spite of the different periods of exposure to the oral environment, the methods used for induction of periapical periodontitis yielded similar distribution of microorganisms in the root canal system.

Comparative study of two commercially pure titanium casting methods

The interest in using titanium to fabricate removable partial denture (RPD) frameworks has increased, but there are few studies evaluating the effects of casting methods on clasp behavior. OBJECTIVE: This study compared the occurrence of porosities and the retentive force of commercially pure titanium (CP Ti) and cobalt-chromium (Co-Cr) removable partial denture circumferential clasps cast by induction/centrifugation and plasma/vacuum-pressure. MATERIAL AND METHODS: 72 frameworks were cast from CP Ti (n=36) and Co-Cr alloy (n=36; control group). For each material, 18 frameworks were casted by electromagnetic induction and injected by centrifugation, whereas the other 18 were casted by plasma and injected by vacuum-pressure. For each casting method, three subgroups (n=6) were formed: 0.25 mm, 0.50 mm, and 0.75 mm undercuts. The specimens were radiographed and subjected to an insertion/removal test simulating 5 years of framework use. Data were analyzed by ANOVA and Tukey's to compare materials and cast methods (α=0.05). RESULTS: Three of 18 specimens of the induction/centrifugation group and 9 of 18 specimens of plasma/vacuum-pressure cast presented porosities, but only 1 and 7 specimens, respectively, were rejected for simulation test. For Co-Cr alloy, no defects were found. Comparing the casting methods, statistically significant differences (p<0.05) were observed only for the Co-Cr alloy with 0.25 mm and 0.50 mm undercuts. Significant differences were found for the 0.25 mm and 0.75 mm undercuts dependent on the material used. For the 0.50 mm undercut, significant differences were found when the materials were induction casted. CONCLUSION: Although both casting methods produced satisfactory CP Ti RPD frameworks, the occurrence of porosities was greater in the plasma/vacuum-pressure than in the induction/centrifugation method, the latter resulting in higher clasp rigidity, generating higher retention force values.

Comparative study of intermaxillary relationships of manual and swallowing methods

This study compared the mandibular displacement from three methods of centric relation record using an anterior jig associated with (A) chin point guidance, (B) swallowing (control group) and (C) bimanual manipulation. Ten patients aged 25-39 years were selected if they met the following inclusion criteria: complete dentition (up to the second molars), Angle class I and absence of signs and symptoms of temporomandibular disorders and diagnostic casts showing stability in the maximum intercuspation (MI) position. Impressions of maxillary and mandibular arches were made with an irreversible hydrocolloid impression material. Master casts of each patient were obtained, mounted on a microscope table in MI as a reference position and 5 records of each method were made per patient. The mandibular casts were then repositioned with records interposed and new measurements were obtained. The difference between the two readings allowed measuring the displacement of the mandible in the anteroposterior and lateral axes. Data were analyzed statistically by ANOVA and Tukey's test at 5% significance level. There was no statistically significant differences (p>0.05) among the three methods for measuring lateral displacement (A=0.38 ± 0.26, B=0.32 ± 0.25 and C=0.32 ± 0.23). For the anteroposterior displacement (A=2.76 ± 1.43, B=2.46 ± 1.48 and C=2.97 ± 1.51), the swallowing method (B) differed significantly from the others (p<0.05), but no significant difference (p>0.05) was found between chin point guidance (A) and bimanual manipulation (C). In conclusion, the swallowing method produced smaller mandibular posterior displacement than the other methods.

Validity and reliability of methods for the detection of secondary caries around amalgam restorations in primary teeth

Secondary caries has been reported as the main reason for restoration replacement. The aim of this in vitro study was to evaluate the performance of different methods - visual inspection, laser fluorescence (DIAGNOdent), radiography and tactile examination - for secondary caries detection in primary molars restored with amalgam. Fifty-four primary molars were photographed and 73 suspect sites adjacent to amalgam restorations were selected. Two examiners evaluated independently these sites using all methods. Agreement between examiners was assessed by the Kappa test. To validate the methods, a caries-detector dye was used after restoration removal. The best cut-off points for the sample were found by a Receiver Operator Characteristic (ROC) analysis, and the area under the ROC curve (Az), and the sensitivity, specificity and accuracy of the methods were calculated for enamel (D2) and dentine (D3) thresholds. These parameters were found for each method and then compared by the McNemar test. The tactile examination and visual inspection presented the highest inter-examiner agreement for the D2 and D3 thresholds, respectively. The visual inspection also showed better performance than the other methods for both thresholds (Az = 0.861 and Az = 0.841, respectively). In conclusion, the visual inspection presented the best performance for detecting enamel and dentin secondary caries in primary teeth restored with amalgam.