Josemar Rodrigues

Destructive weighted Poisson cure rate models.

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow a compound weighted Poisson distribution. This model is more flexible in terms of dispersion than the promotion time cure model. Moreover, it gives an interesting and realistic interpretation of the biological mechanism of the occurrence of event of interest as it includes a destructive process of the initial risk factors in a competitive scenario. In other words, what is recorded is only from the undamaged portion of the original number of risk factors.

Weighted balanced loss function and estimation of the mean time to failure

The purpose of this paper is to consider estimation of the mean time to failure using loss functions that reflect both of fit and precision of estimation. We show how this can be done using balanced loss functions (BLF) of the type introduced in Zellner (1994) and weighted balanced loss function (WBLF) introduced in this paper. Optimal point estimates relative to BLF and WBLF are shown to be a compromise between usual Bayesian and non-Bayesian estimates. Using diffuse and informative priors, posterior expected losses associated with alternative estimates are evaluated and compared.

A simple test for new better than used in expectation

We present a statistical procedure to test that a life distribution is exponential against the al ternative that it is continuous new better than used in expectation. The test is shown to be consistent and asymptotic relative efficiency resul ts are obtained against the competitor developed earlier by Hollander and Proschan [2], for certain families of alternatives.

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 of Zero-Inflated Distributions

Abstract In this paper zero-inflated distributions (ZID) are studied from the Bayesian point of view using the data augmentation algorithm. This type of discrete model arises in count data with excess of zeros. The zero-inflated Poisson distribution (ZIP) and an illustrative example via MCMC algorithm are considered.

A General Theory of Prediction in Finite Populations

Summary In this paper, we adopt the superpopulation approach to a finite population to develop a general theory of prediction for linear and quadratic functions of the population units. Most of the efforts are devoted to the problem of predicting quadratic forms, the population variance in particular, since much more attention has lately been devoted to the problem of the prediction of linear functions. As Godambe (1966), the problems considered are those for which the Gauss-Markov set-up of estimation is inapplicable. Several new predictors based on classical and Bayesian approaches to the population variance are formulated. The classical approach is based on the idea of totally sufficient statistics (Lauritzen, 1974). Some properties like unbiasedness, mean squared error and sensitivity to model misspecification of the derived predictors are studied. An attempt to characterize robustness conditions for protecting against model misspecification is formulated. An empirical investigation, based on a simulated population, is made to compare the performance of the suggested predictors.

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 data set.

A hands-on approach for fitting long-term survival models under the GAMLSS framework

In many data sets from clinical studies there are patients insusceptible to the occurrence of the event of interest. Survival models which ignore this fact are generally inadequate. The main goal of this paper is to describe an application of the generalized additive models for location, scale, and shape (GAMLSS) framework to the fitting of long-term survival models. In this work the number of competing causes of the event of interest follows the negative binomial distribution. In this way, some well known models found in the literature are characterized as particular cases of our proposal. The model is conveniently parameterized in terms of the cured fraction, which is then linked to covariates. We explore the use of the gamlss package in R as a powerful tool for inference in long-term survival models. The procedure is illustrated with a numerical example.

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 São Carlos, São 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 São Carlos, São Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.

A Bayesian analysis for estimating the number of species in a population using nonhomogeneous Poisson process

We propose a Bayesian approach using nonhomogeneous Poisson process to estimate the number of species of a population. The proposed methodology uses a [pi]-mixture to eliminate the unknown total mean of each species. One contribution of the article is to apply the Metropolis-within-Gibbs algorithm to obtain the marginal posterior distribution of the number of species and the capture mean time.