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.

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827-842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.

A log-linear regression model for the beta-Birnbaum-Saunders distribution with censored data

The beta-Birnbaum-Saunders (Cordeiro and Lemonte, 2011) and Birnbaum-Saunders (Birnbaum and Saunders, 1969a) distributions have been used quite effectively to model failure times for materials subject to fatigue and lifetime data. We define the log-beta-Birnbaum-Saunders distribution by the logarithm of the beta-Birnbaum-Saunders distribution. Explicit expressions for its generating function and moments are derived. We propose a new log-beta-Birnbaum-Saunders regression model that can be applied to censored data and be used more effectively in survival analysis. We obtain the maximum likelihood estimates of the model parameters for censored data and investigate influence diagnostics. The new location-scale regression model is modified for the possibility that long-term survivors may be presented in the data. Its usefulness is illustrated by means of two real data sets. (C) 2011 Elsevier B.V. All rights reserved.

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.

An extended Lindley distribution

In this paper we introduce an extension of the Lindley distribution which offers a more flexible model for lifetime data. Several statistical properties of the distribution are explored, such as the density, (reversed) failure rate, (reversed) mean residual lifetime, moments, order statistics, Bonferroni and Lorenz curves. Estimation using the maximum likelihood and inference of a random sample from the distribution are investigated. A real data application illustrates the performance of the distribution. (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

The geometric Birnbaum-Saunders regression model with cure rate

In this paper, we propose a cure rate survival model by assuming the number of competing causes of the event of interest follows the Geometric distribution and the time to event follow a Birnbaum Saunders distribution. We consider a frequentist analysis for parameter estimation of a Geometric Birnbaum Saunders model with cure rate. Finally, to analyze a data set from the medical area. (C) 2011 Elsevier B.V. All rights reserved.

Bartlett corrections in Birnbaum-Saunders nonlinear regression models

Lemonte and Cordeiro [Birnbaum-Saunders nonlinear regression models, Comput. Stat. Data Anal. 53 (2009), pp. 4441-4452] introduced a class of Birnbaum-Saunders (BS) nonlinear regression models potentially useful in lifetime data analysis. We give a general matrix Bartlett correction formula to improve the likelihood ratio (LR) tests in these models. The formula is simple enough to be used analytically to obtain several closed-form expressions in special cases. Our results generalize those in Lemonte et al. [Improved likelihood inference in Birnbaum-Saunders regressions, Comput. Stat. DataAnal. 54 (2010), pp. 1307-1316], which hold only for the BS linear regression models. We consider Monte Carlo simulations to show that the corrected tests work better than the usual LR tests.

INFERENCES FOR THE CHANGE-POINT OF THE EXPONENTIATED WEIBULL HAZARD FUNCTION

In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.

The negative binomial-beta Weibull regression model to predict the cure of prostate cancer

In this article, for the first time, we propose the negative binomial-beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.

Petroleum contamination impact on macrobenthic communities under the influence of an oil refinery: Integrating chemical and biological multivariate data

Petroleum contamination impact on macrobenthic communities in the northeast portion of Todos os Santos Bay was assessed combining in multivariate analyses, chemical parameters such as aliphatic and polycyclic aromatic hydrocarbon indices and concentration ratios with benthic ecological parameters. Sediment samples were taken in August 2000 with a 0.05 m(2) van Veen grab at 28 sampling locations. The predominance of n-alkanes with more than 24 carbons, together with CPI values close to one, and the fact that most of the stations showed UCM/resolved aliphatic hydrocarbons ratios (UCM:R) higher than two, indicated a high degree of anthropogenic contribution, the presence of terrestrial plant detritus, petroleum products and evidence of chronic oil pollution. The indices used to determine the origin of PAH indicated the occurrence of a petrogenic contribution. A pyrolytic contribution constituted mainly by fossil fuel combustion derived PAH was also observed. The results of the stepwise multiple regression analysis performed with chemical data and benthic ecological descriptors demonstrated that not only total PAH concentrations but also specific concentration ratios or indices such as >= C24:< C24, An/178 and Fl/Fl + Py, are determining the structure of benthic communities within the study area. According to the BIO-ENV results petroleum related variables seemed to have a main influence on macrofauna community structure. The PCA ordination performed with the chemical data resulted in the formation of three groups of stations. The decrease in macrofauna density, number of species and diversity from groups III to I seemed to be related to the occurrence of high aliphatic hydrocarbon and PAH concentrations associated with fine sediments. Our results showed that macrobenthic communities in the northeast portion of Todos os Santos Bay are subjected to the impact of chronic oil pollution as was reflected by the reduction in the number of species and diversity. These results emphasise the importance to combine in multivariate approaches not only total hydrocarbon concentrations but also indices, isomer pair ratios and specific compound concentrations with biological data to improve the assessment of anthropogenic impact on marine ecosystems. (c) 2008 Elsevier Ltd. All rights reserved.

Detecting an abnormality in a recovery boiler using dynamic multivariate data analysis with parallel coordinate plots

Data visualization techniques are powerful in the handling and analysis of multivariate systems. One such technique known as parallel coordinates was used to support the diagnosis of an event, detected by a neural network-based monitoring system, in a boiler at a Brazilian Kraft pulp mill. Its attractiveness is the possibility of the visualization of several variables simultaneously. The diagnostic procedure was carried out step-by-step going through exploratory, explanatory, confirmatory, and communicative goals. This tool allowed the visualization of the boiler dynamics in an easier way, compared to commonly used univariate trend plots. In addition it facilitated analysis of other aspects, namely relationships among process variables, distinct modes of operation and discrepant data. The whole analysis revealed firstly that the period involving the detected event was associated with a transition between two distinct normal modes of operation, and secondly the presence of unusual changes in process variables at this time.

Multivariate analyses of UV-Vis absorption spectral data from cachaca wood extracts: a model to classify aged Brazilian cachacas according to the wood species used

Multivariate analyses of UV-Vis spectral data from cachaca wood extracts provide a simple and robust model to classify aged Brazilian cachacas according to the wood species used in the maturation barrels. The model is based on inspection of 93 extracts of oak and different Brazilian wood species by a non-aged cachaca used as an extraction solvent. Application of PCA (Principal Components Analysis) and HCA (Hierarchical Cluster Analysis) leads to identification of 6 clusters of cachaca wood extracts (amburana, amendoim, balsamo, castanheira, jatoba, and oak). LDA (Linear Discriminant Analysis) affords classification of 10 different wood species used in the cachaca extracts (amburana, amendoim, balsamo, cabreuva-parda, canela-sassafras, castanheira, jatoba, jequitiba-rosa, louro-canela, and oak) with an accuracy ranging from 80% (amendoim and castanheira) to 100% (balsamo and jequitiba-rosa). The methodology provides a low-cost alternative to methods based on liquid chromatography and mass spectrometry to classify cachacas aged in barrels that are composed of different wood species.

THE LOG-BURR XII REGRESSION MODEL FOR GROUPED SURVIVAL DATA

The log-Burr XII regression model for grouped survival data is evaluated in the presence of many ties. The methodology for grouped survival data is based on life tables, where the times are grouped in k intervals, and we fit discrete lifetime regression models to the data. The model parameters are estimated by maximum likelihood and jackknife methods. To detect influential observations in the proposed model, diagnostic measures based on case deletion, so-called global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to these measures, the total local influence and influential estimates are also used. We conduct Monte Carlo simulation studies to assess the finite sample behavior of the maximum likelihood estimators of the proposed model for grouped survival. A real data set is analyzed using a regression model for grouped data.

A new long-term lifetime distribution induced by a latent complementary risk framework

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.

Quantitative Chemical Profile and Multivariate Statistical Analysis of Alembic Distilled Sugarcane Spirit Fractions

Concentrations of 39 organic compounds were determined in three fractions (head, heart and tail) obtained from the pot still distillation of fermented sugarcane juice. The results were evaluated using analysis of variance (ANOVA), Tukey's test, principal component analysis (PCA), hierarchical cluster analysis (HCA) and linear discriminant analysis (LDA). According to PCA and HCA, the experimental data lead to the formation of three clusters. The head fractions give rise to a more defined group. The heart and tail fractions showed some overlap consistent with its acid composition. The predictive ability of calibration and validation of the model generated by LDA for the three fractions classification were 90.5 and 100%, respectively. This model recognized as the heart twelve of the thirteen commercial cachacas (92.3%) with good sensory characteristics, thus showing potential for guiding the process of cuts.