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.

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.

The Kumaraswamy Gumbel distribution

The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. We propose a generalization-referred to as the Kumaraswamy Gumbel distribution-and provide a comprehensive treatment of its structural properties. We obtain the analytical shapes of the density and hazard rate functions. We calculate explicit expressions for the moments and generating function. The variation of the skewness and kurtosis measures is examined and the asymptotic distribution of the extreme values is investigated. Explicit expressions are also derived for the moments of order statistics. The methods of maximum likelihood and parametric bootstrap and a Bayesian procedure are proposed for estimating the model parameters. We obtain the expected information matrix. An application of the new model to a real dataset illustrates the potentiality of the proposed model. Two bivariate generalizations of the model are proposed.

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.

Irreversible spherical model and its stationary entropy production rate

The nonequilibrium stationary state of an irreversible spherical model is investigated on hypercubic lattices. The model is defined by Langevin equations similar to the reversible case, but with asymmetric transition rates. In spite of being irreversible, we have succeeded in finding an explicit form for the stationary probability distribution, which turns out to be of the Boltzmann-Gibbs type. This enables one to evaluate the exact form of the entropy production rate at the stationary state, which is non-zero if the dynamical rules of the transition rates are asymmetric.

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.

Effect of the thermostat in the molecular dynamics simulation on the folding of the model protein chignolin

Molecular dynamics simulations of the model protein chignolin with explicit solvent were carried out, in order to analyze the influence of the Berendsen thermostat on the evolution and folding of the peptide. The dependence of the peptide behavior on temperature was tested with the commonly employed thermostat scheme consisting of one thermostat for the protein and another for the solvent. The thermostat coupling time of the protein was increased to infinity, when the protein is not in direct contact with the thermal bath, a situation known as minimally invasive thermostat. In agreement with other works, it was observed that only in the last situation the instantaneous temperature of the model protein obeys a canonical distribution. As for the folding studies, it was shown that, in the applications of the commonly utilized thermostat schemes, the systems are trapped in local minima regions from which it has difficulty escaping. With the minimally invasive thermostat the time that the protein needs to fold was reduced by two to three times. These results show that the obstacles to the evolution of the extended peptide to the folded structure can be overcome when the temperature of the peptide is not directly controlled.

Independent predictors and a prognostic model for surgical outcome in refractory frontal lobe epilepsy

Purpose: Refractory frontal lobe epilepsy (FLE) remains one of the most challenging surgically remediable epilepsy syndromes. Nevertheless, definition of independent predictors and predictive models of postsurgical seizure outcome remains poorly explored in FLE. Methods: We retrospectively analyzed data from 70 consecutive patients with refractory FLE submitted to surgical treatment at our center from July 1994 to December 2006. Univariate results were submitted to logistic regression models and Cox proportional hazards regression to identify isolated risk factors for poor surgical results and to construct predictive models for surgical outcome in FLE. Results: From 70 patients submitted to surgery, 45 patients (64%) had favorable outcome and 37 (47%) became seizure free. Isolated risk factors for poor surgical outcome are expressed in hazard ratio (H.R.) and were time of epilepsy (H.R.=4.2; 95% C.I.=.1.5-11.7; p=0.006), ictal EEG recruiting rhythm (H.R. = 2.9; 95% C.I. = 1.1-7.7; p=0.033); normal MRI (H.R. = 4.8; 95% C.I. = 1.4-16.6; p = 0.012), and MRI with lesion involving eloquent cortex (H.R. = 3.8; 95% C.I. = 1.2-12.0; p = 0.021). Based on these variables and using a logistic regression model we constructed a model that correctly predicted long-term surgical outcome in up to 80% of patients. Conclusion: Among independent risk factors for postsurgical seizure outcome, epilepsy duration is a potentially modifiable factor that could impact surgical outcome in FLE. Early diagnosis, presence of an MRI lesion not involving eloquent cortex, and ictal EEG without recruited rhythm independently predicted favorable outcome in this series. (C) 2011 Elsevier B.V. All rights reserved.

Solvable model for template coexistence in protocells

Compartmentalization of self-replicating molecules (templates) in protocells is a necessary step towards the evolution of modern cells. However, coexistence between distinct template types inside a protocell can be achieved only if there is a selective pressure favoring protocells with a mixed template composition. Here we study analytically a group selection model for the coexistence between two template types using the diffusion approximation of population genetics. The model combines competition at the template and protocell levels as well as genetic drift inside protocells. At the steady state, we find a continuous phase transition separating the coexistence and segregation regimes, with the order parameter vanishing linearly with the distance to the critical point. In addition, we derive explicit analytical expressions for the critical steadystate probability density of protocell compositions.