A flexible model for survival data with a cure rate: a Bayesian approach

In this paper we deal with a Bayesian analysis for right-censored survival data suitable for populations with a cure rate. We consider a cure rate model based on the negative binomial distribution, encompassing as a special case the promotion time cure model. Bayesian analysis is based on Markov chain Monte Carlo (MCMC) methods. We also present some discussion on model selection and an illustration with a real dataset.

A bivariate regression model for matched paired survival data: local influence and residual analysis

The use of bivariate distributions plays a fundamental role in survival and reliability studies. In this paper, we consider a location scale model for bivariate survival times based on the proposal of a copula to model the dependence of bivariate survival data. For the proposed model, we consider inferential procedures based on maximum likelihood. Gains in efficiency from bivariate models are also examined in the censored data setting. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the bivariate regression model for matched paired survival data. Sensitivity analysis methods such as local and total influence are presented and derived under three perturbation schemes. The martingale marginal and the deviance marginal residual measures are used to check the adequacy of the model. Furthermore, we propose a new measure which we call modified deviance component residual. The methodology in the paper is illustrated on a lifetime data set for kidney patients.

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.

Generalized log-gamma regression models with cure fraction

In this paper, the generalized log-gamma regression model is modified to allow the possibility that long-term survivors may be present in the data. This modification leads to a generalized log-gamma regression model with a cure rate, encompassing, as special cases, the log-exponential, log-Weibull and log-normal regression models with a cure rate typically used to model such data. The models attempt to simultaneously estimate the effects of explanatory variables on the timing acceleration/deceleration of a given event and the surviving fraction, that is, the proportion of the population for which the event never occurs. The normal curvatures of local influence are derived under some usual perturbation schemes and two martingale-type residuals are proposed to assess departures from the generalized log-gamma error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.

Hypotheses Testing on a Multivariate Null Intercept Errors-in-Variables Model

Considering the Wald, score, and likelihood ratio asymptotic test statistics, we analyze a multivariate null intercept errors-in-variables regression model, where the explanatory and the response variables are subject to measurement errors, and a possible structure of dependency between the measurements taken within the same individual are incorporated, representing a longitudinal structure. This model was proposed by Aoki et al. (2003b) and analyzed under the bayesian approach. In this article, considering the classical approach, we analyze asymptotic test statistics and present a simulation study to compare the behavior of the three test statistics for different sample sizes, parameter values and nominal levels of the test. Also, closed form expressions for the score function and the Fisher information matrix are presented. We consider two real numerical illustrations, the odontological data set from Hadgu and Koch (1999), and a quality control data set.

Sparse block-Jacobi matrices with arbitrarily accurate Hausdorff dimension

We show that the Hausdorff dimension of the spectral measure of a class of deterministic, i.e. nonrandom, block-Jacobi matrices may be determined with any degree of precision, improving a result of Zlatos [Andrej Zlatos,. Sparse potentials with fractional Hausdorff dimension, J. Funct. Anal. 207 (2004) 216-252]. (C) 2010 Elsevier Inc. All rights reserved.

Automatic camera control in virtual environments augmented using multiple sparse videos

Automated virtual camera control has been widely used in animation and interactive virtual environments. We have developed a multiple sparse camera based free view video system prototype that allows users to control the position and orientation of a virtual camera, enabling the observation of a real scene in three dimensions (3D) from any desired viewpoint. Automatic camera control can be activated to follow selected objects by the user. Our method combines a simple geometric model of the scene composed of planes (virtual environment), augmented with visual information from the cameras and pre-computed tracking information of moving targets to generate novel perspective corrected 3D views of the virtual camera and moving objects. To achieve real-time rendering performance, view-dependent textured mapped billboards are used to render the moving objects at their correct locations and foreground masks are used to remove the moving objects from the projected video streams. The current prototype runs on a PC with a common graphics card and can generate virtual 2D views from three cameras of resolution 768 x 576 with several moving objects at about 11 fps. (C)2011 Elsevier Ltd. All rights reserved.

Software maintenance project delays prediction using Bayesian Networks

Managing software maintenance is rarely a precise task due to uncertainties concerned with resources and services descriptions. Even when a well-established maintenance process is followed, the risk of delaying tasks remains if the new services are not precisely described or when resources change during process execution. Also, the delay of a task at an early process stage may represent a different delay at the end of the process, depending on complexity or services reliability requirements. This paper presents a knowledge-based representation (Bayesian Networks) for maintenance project delays based on specialists experience and a corresponding tool to help in managing software maintenance projects. (c) 2006 Elsevier Ltd. All rights reserved.

Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

Deviance residuals in generalised log-gamma regression models with censored observations

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.

Measuring time series predictability using support vector regression

Most studies involving statistical time series analysis rely on assumptions of linearity, which by its simplicity facilitates parameter interpretation and estimation. However, the linearity assumption may be too restrictive for many practical applications. The implementation of nonlinear models in time series analysis involves the estimation of a large set of parameters, frequently leading to overfitting problems. In this article, a predictability coefficient is estimated using a combination of nonlinear autoregressive models and the use of support vector regression in this model is explored. We illustrate the usefulness and interpretability of results by using electroencephalographic records of an epileptic patient.

On beta regression residuals

We propose two new residuals for the class of beta regression models, and numerically evaluate their behaviour relative to the residuals proposed by Ferrari and Cribari-Neto. Monte Carlo simulation results and empirical applications using real and simulated data are provided. The results favour one of the residuals we propose.

Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications. (C) 2010 Elsevier B.V. All rights reserved.