A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis - latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.

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.

The exponential COM-Poisson distribution

The Conway-Maxwell Poisson (COMP) distribution as an extension of the Poisson distribution is a popular model for analyzing counting data. For the first time, we introduce a new three parameter distribution, so-called the exponential-Conway-Maxwell Poisson (ECOMP) distribution, that contains as sub-models the exponential-geometric and exponential-Poisson distributions proposed by Adamidis and Loukas (Stat Probab Lett 39:35-42, 1998) and KuAY (Comput Stat Data Anal 51:4497-4509, 2007), respectively. The new density function can be expressed as a mixture of exponential density functions. Expansions for moments, moment generating function and some statistical measures are provided. The density function of the order statistics can also be expressed as a mixture of exponential densities. We derive two formulae for the moments of order statistics. The elements of the observed information matrix are provided. Two applications illustrate the usefulness of the new distribution to analyze positive data.

Laboratorial training of examiners for using a visual caries detection system in epidemiological surveys

Background: In epidemiological surveys, a good reliability among the examiners regarding the caries detection method is essential. However, training and calibrating those examiners is an arduous task because it involves several patients who are examined many times. To facilitate this step, we aimed to propose a laboratory methodology to simulate the examinations performed to detect caries lesions using the International Caries Detection and Assessment System (ICDAS) in epidemiological surveys. Methods: A benchmark examiner conducted all training sessions. A total of 67 exfoliated primary teeth, varying from sound to extensive cavitated, were set in seven arch models to simulate complete mouths in primary dentition. Sixteen examiners (graduate students) evaluated all surfaces of the teeth under illumination using buccal mirrors and ball-ended probe in two occasions, using only coronal primary caries scores of the ICDAS. As reference standard, two different examiners assessed the proximal surfaces by direct visual inspection, classifying them in sound, with non-cavitated or with cavitated lesions. After, teeth were sectioned in the bucco-lingual direction, and the examiners assessed the sections in stereomicroscope, classifying the occlusal and smooth surfaces according to lesion depth. Inter-examiner reproducibility was evaluated using weighted kappa. Sensitivities and specificities were calculated at two thresholds: all lesions and advanced lesions (cavitated lesions in proximal surfaces and lesions reaching the dentine in occlusal and smooth surfaces). Conclusion: The methodology purposed for training and calibration of several examiners designated for epidemiological surveys of dental caries in preschool children using the ICDAS is feasible, permitting the assessment of reliability and accuracy of the examiners previously to the survey´s development.

Structure-function Relationships Using the Cirrus Spectral Domain Optical Coherence Tomograph and Standard Automated Perimetry

Purpose: To evaluate the relationship between glaucomatous structural damage assessed by the Cirrus Spectral Domain OCT (SDOCT) and functional loss as measured by standard automated perimetry (SAP). Methods: Four hundred twenty-two eyes (78 healthy, 210 suspects, 134 glaucomatous) of 250 patients were recruited from the longitudinal Diagnostic Innovations in Glaucoma Study and from the African Descent and Glaucoma Evaluation Study. All eyes underwent testing with the Cirrus SDOCT and SAP within a 6-month period. The relationship between parapapillary retinal nerve fiber layer thickness (RNFL) sectors and corresponding topographic SAP locations was evaluated using locally weighted scatterplot smoothing and regression analysis. SAP sensitivity values were evaluated using both linear as well as logarithmic scales. We also tested the fit of a model (Hood) for structure-function relationship in glaucoma. Results: Structure was significantly related to function for all but the nasal thickness sector. The relationship was strongest for superotemporal RNFL thickness and inferonasal sensitivity (R(2) = 0.314, P < 0.001). The Hood model fitted the data relatively well with 88% of the eyes inside the 95% confidence interval predicted by the model. Conclusions: RNFL thinning measured by the Cirrus SDOCT was associated with correspondent visual field loss in glaucoma.

Disproportionate single-species contribution to canopy-soil nutrient flux in an Amazonian rainforest

Rainfall, throughfall and stemflow were monitored on an event basis in an undisturbed open tropical rainforest with a large number of palm trees located in the southwestern Amazon basin of Brazil. Stemflow samples were collected from 24 trees with a diameter at breast height (DBH) > 5 cm, as well as eight young and four full-grown babassu palms (Attalea speciosa Mart.) for 5 weeks during the peak of the wet season. We calculated rainfall, throughfall and stemflow concentrations and fluxes of Na+, K+, Ca2+, Mg2+,, Cl-, SO42-, NO3- and H+ and stemflow volume-weighted mean concentrations and fluxes for three size classes of broadleaf trees and three size classes of palms. The concentrations of most solutes were higher in stemflow than in rainfall and increased with increasing tree and palm size. Concentration enrichments from rainfall to stemflow and throughfall were particularly high (81-fold) for NO3-. Stemflow fluxes of NO3- and H+ exceeded throughfall fluxes but stemflow fluxes of other solutes were less than throughfall fluxes. Stemflow solute fluxes to the forest soil were dominated by fluxes on babassu palms, which represented only 4% of total stem number and 10% of total basal area. For NO3-, stemflow contributed 51% of the total mass of nitrogen delivered to the forest floor (stemflow + throughfall) and represented more than a 2000-fold increase in NO3- flux compared what would have been delivered by rainfall alone on the equivalent area. Because these highly localized fluxes of both water and NO3- persist in time and space, they have the potential to affect patterns of soil moisture, microbial populations and other features of soil biogeochemistry conducive to the creation of hotspots for nitrogen leaching and denitrification, which could amount to an important fraction of total ecosystem fluxes. Because these hotspots occur over very small areas, they have likely gone undetected in previous studies and need to be considered as an important feature of the biogeochemistry of palm-rich tropical forest. (C) 2011 Elsevier B.V. All rights reserved.

A Poisson mixed model with nonnormal random effect distribution

In this paper, we propose a random intercept Poisson model in which the random effect is assumed to follow a generalized log-gamma (GLG) distribution. This random effect accommodates (or captures) the overdispersion in the counts and induces within-cluster correlation. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are, in general, required for deriving the marginal models, we obtain the multivariate negative binomial model from a particular parameter setting of the hierarchical model. An iterative process is derived for obtaining the maximum likelihood estimates for the parameters in the multivariate negative binomial model. Residual analysis is proposed and two applications with real data are given for illustration. (C) 2011 Elsevier B.V. All rights reserved.

The Poisson-exponential regression model under different latent activation schemes

In this paper, a new family of survival distributions is presented. It is derived by considering that the latent number of failure causes follows a Poisson distribution and the time for these causes to be activated follows an exponential distribution. Three different activation schemes are also considered. Moreover, we propose the inclusion of covariates in the model formulation in order to study their effect on the expected value of the number of causes and on the failure rate function. Inferential procedure based on the maximum likelihood method is discussed and evaluated via simulation. The developed methodology is illustrated on a real data set on ovarian cancer.

The Truncated Inflated Beta Distribution

The study of proportions is a common topic in many fields of study. The standard beta distribution or the inflated beta distribution may be a reasonable choice to fit a proportion in most situations. However, they do not fit well variables that do not assume values in the open interval (0, c), 0 < c < 1. For these variables, the authors introduce the truncated inflated beta distribution (TBEINF). This proposed distribution is a mixture of the beta distribution bounded in the open interval (c, 1) and the trinomial distribution. The authors present the moments of the distribution, its scoring vector, and Fisher information matrix, and discuss estimation of its parameters. The properties of the suggested estimators are studied using Monte Carlo simulation. In addition, the authors present an application of the TBEINF distribution for unemployment insurance data.