Mixture Hazard Models for Lifetime Data

Louzada-Neto, Francisco; Mazucheli, Josmar; Achcar, Jorge Alberto

doi:10.1002/1521-4036(200201)44:1<3::aid-bimj3>3.0.co;2-d

Cited by 17 publications

(4 citation statements)

References 23 publications

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“…Instead, we observe only the maximum lifetime value among all risks. For more details on latent risk problem, interested readers can refer to Basu and Klein (Basu Klein, 1982) and Louzada-Neto (Louzada-Neto, 1999).…”

Section: The Ceg Modelmentioning

confidence: 99%

Objective Bayesian Snalysis for the Complementary Exponential Geometric Model Applied to Cancer Data

Granzotto¹,

Tomazella²,

Louzada³

2017

IJSP

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In this paper we provide a reference Bayesian framework to a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric (CEG). To this end, we presented some of the main properties of this model and its characteristics related to the reliability analysis. A simulation study is performed to analyse the frequentist properties of credible intervals from the reference posterior distribution among of the standard error and mean square error (MSE) of estimations. The presented methodology is illustrated by the use of a real data set which presents the study of time until the cure of cervix lesions, that are precursors cancer lesions in the cervix. According to to INCA (Cancer National Institute), cervical cancer stands as the fourth cause of death among women in Brazil. Together with breast cancer, it is one of the most common malignancy affecting women worldwide. For this reason, patients must be carefully evaluated for metastatic disease. These data were collected in the Woman Clinic which is sited in Maringá city (Paraná State, Brazil).

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Section: The Ceg Modelmentioning

confidence: 99%

Objective Bayesian Snalysis for the Complementary Exponential Geometric Model Applied to Cancer Data

Granzotto¹,

Tomazella²,

Louzada³

2017

IJSP

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“…Since 2000 alone, they have been adopted in mixture hazard models (Louzada-Neto et al 2002), spatio-temporal models (Stroud et al 2001), structural equation models (Zhu and Lee 2001), disease mapping (Green and Richardson 2002), analysis of proportions (Brooks 2001), correlated data and clustered models (Chib and Hamilton 2000, Dunson 2000, Chen and Dey 2000, classification and discrimination (Wruck et al 2001), experimental design and analysis (Nobile andGreen 2000, Sebastiani andWynn 2000), random effects generalised linear models (Lenk and DeSarbo 2000) and binary data (Basu and Mukhopadhyay 2000). Mixtures of Weibulls (Tsionas 2002) and Gammas (Wiper et al 2001) have been considered, along with computational issues associated with MCMC methods (Liang and Wong 2001), issues of convergence (Liang and Wong 2001), the display…”

Section: Extensions To the Mixture Frameworkmentioning

confidence: 99%

Bayesian Modelling and Inference on Mixtures of Distributions

Marin¹,

Mengersen²,

Robert³

2005

Handbook of Statistics

327

364

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'But, as you have already pointed out, we do not need any more disjointed clues,' said Bartholomew. 'That has been our problem all along: we have a mass of small facts and small scraps of information, but we are unable to make any sense out of them. The last thing we need is more.' Susanna Gregory, A Summer of Discontent IntroductionToday's data analysts and modellers are in the luxurious position of being able to more closely describe, estimate, predict and infer about complex systems of interest, thanks to ever more powerful computational methods but also wider ranges of modelling distributions. Mixture models constitute a fascinating illustration of these aspects: while within a parametric family, they offer malleable approximations in non-parametric settings; although based on standard distributions, they pose highly complex computational challenges; and they are both easy to constrain to meet identifiability requirements and fall within the class of ill-posed problems. They also provide an endless benchmark for assessing new techniques, from the EM algorithm to reversible jump methodology. In particular, they exemplify the

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“…The EG distribution is a compound of the geometric with the exponential distribution. The EG distribution is characterized in a latent competing risks scenarios (Louzada-Neto, 1999) where the competing causes are unknown and only the minimum failure lifetime is observed. It also accommodates decreasing failure rates.…”

Section: Introductionmentioning

confidence: 99%

The long-term exponentiated complementary exponential geometric distribution under a latent complementary causes framework

Louzada

Yamachi²,

Marchi³

et al. 2014

Tend. Mat. Apl. Comput.

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ABSTRACT. In this paper we proposed a new long-term distribution derived from the exponentiated complementary exponential geometric distribution (LECEG). The LECEG distribution is obtained straightforwardly from the exponentiated complementary exponential geometric (ECEG) and accommodates decreasing and unimodal hazard functions in a latent complementary causes scenario, where only the maximum lifetime among all causes is observed. We derive the density, quantile, survival and failure rate functions for the proposed distribution, as well as some proprieties such as the characteristic function, mean, variance and r-th order statistics. The estimation is based on maximum likelihood approach. A simulation study is performed in order to assess the performance of the maximum likelihood estimates. The practical importance of the new distribution was demonstrated in three real datasets.

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Mixture Hazard Models for Lifetime Data

Cited by 17 publications

References 23 publications

Objective Bayesian Snalysis for the Complementary Exponential Geometric Model Applied to Cancer Data

Objective Bayesian Snalysis for the Complementary Exponential Geometric Model Applied to Cancer Data

Bayesian Modelling and Inference on Mixtures of Distributions

The long-term exponentiated complementary exponential geometric distribution under a latent complementary causes framework

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