Using Weibull Mixture Distributions to Model Heterogeneous Survival Data

Marín, J. Miguel; Rodríguez-Bernal, María Teresa; Wiper, Michael P.

doi:10.1081/sac-200068372

Cited by 38 publications

(31 citation statements)

References 18 publications

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“…We now assume that we observe possibly right-censored data for n subjects; y = ( y 1 ,…, y n ) where y i = ( t i , δ i ) and δ i is an indicator function such that (Marin et al 2005a): …”

Section: Modelsmentioning

confidence: 99%

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Modelling survival data to account for model uncertainty: a single model or model averaging?

2013

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This study considered the problem of predicting survival, based on three alternative models: a single Weibull, a mixture of Weibulls and a cure model. Instead of the common procedure of choosing a single “best” model, where “best” is defined in terms of goodness of fit to the data, a Bayesian model averaging (BMA) approach was adopted to account for model uncertainty. This was illustrated using a case study in which the aim was the description of lymphoma cancer survival with covariates given by phenotypes and gene expression. The results of this study indicate that if the sample size is sufficiently large, one of the three models emerge as having highest probability given the data, as indicated by the goodness of fit measure; the Bayesian information criterion (BIC). However, when the sample size was reduced, no single model was revealed as “best”, suggesting that a BMA approach would be appropriate. Although a BMA approach can compromise on goodness of fit to the data (when compared to the true model), it can provide robust predictions and facilitate more detailed investigation of the relationships between gene expression and patient survival.

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Section: Modelsmentioning

confidence: 99%

“…We chose small positive values for u α , v α , u γ , v γ to express vague prior knowledge about these parameters and we set ϕ = 1 (Marin et al 2005a). For a model with covariates, we employ a multivariate normal prior on β m , so that …”

Section: Modelsmentioning

confidence: 99%

Modelling survival data to account for model uncertainty: a single model or model averaging?

2013

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“…Touw (2009) studied the Bayesian estimation of Weibull mixture distribution with two components. Marín et al (2005) studied the case where the number of components in the Weibull mixture model is unknown and developed a Bayesian method using birth-death Markov Chain Monte Carlo (MCMC) simulation. In this study, we also assume that the number of components in the mixture is unknown and apply the Gibbs sampling technique together with the Bayes factor to estimate the model parameters and to determine the number of components.…”

Section: Corresponding Authormentioning

confidence: 99%

Reliability study of ultra-thin dielectric films with variable thickness levels

Yuan

Zhu

2012

IIE Transactions

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The time-dependent dielectric breakdown of ultra-thin gate oxides is one of the major reliability issues facing scaled metal-oxide semiconductor technologies. As the thickness of the gate dielectric film approaches its scaling limit, process issues such as poor wafer uniformity and oxide growth control become critical for ultra-thin gate dielectric reliability. This article investigates both the physics and statistical aspects of the reliability of the ultra-thin gate dielectric when film thickness variations are present. A physics-based Spatio-Temporal Monte Carlo Simulation (STMCS) model is developed to study the effects of thickness and thickness non-uniformity on dielectric reliability. Its use allows the root cause for the non-linear characteristic of the Weibull time-to-breakdown distribution observed in experimental studies to be revealed. In addition, a Bayesian Weibull Mixture (BWM) model is proposed to analyze the time-to-breakdown data considering the existence of thickness non-uniformity. Numerical results are presented that show that the proposed BWM model is significantly superior to the basic Weibull model for use in reliability projection. Both the STMCS and BWM models can successfully reproduce the experimentally observed non-linear characteristic of the Weibull time-to-breakdown distribution and thus can be used to predict device reliability when the dielectric films in a gate are of unequal thicknesses.

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“…Angelis et al [10] proposed an application of a mixture model to relative survival rates of colon cancer patients from the Finnish population-based cancer registry, and including major survival determinants as explicative covariates. Marin et al [11] have illustrated how bayesian methods can be used to fit a mixture of Weibull models with an unknown number of components to heterogeneous, possibly right-censored survival data using a birth death MCMC algorithm. AbuTaleb et al [12] presented the Bayesian estimation of lifetime parameters of Exponential distributions when survival time and censoring time are both exponentially distributed.…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis of 3-component mixture of distributions

2017

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Abstract. This article focuses on studying 3-component mixtures of Exponential, Rayleigh, Pareto and Burr Type-XII distributions in relation to reliability analysis. The main purpose of this study is to derive algebraic expressions for different functions of survival time. For these 3-component mixture distributions, the cumulative distribution function, hazard rate function, cumulative hazard rate function, reversed hazard rate function, mean residual life function and mean waiting time function are discussed. To study the behavior of different reliability functions, numerical results are presented for fixed values of parameters.

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Using Weibull Mixture Distributions to Model Heterogeneous Survival Data

Cited by 38 publications

References 18 publications

Modelling survival data to account for model uncertainty: a single model or model averaging?

Modelling survival data to account for model uncertainty: a single model or model averaging?

Reliability study of ultra-thin dielectric films with variable thickness levels

Reliability analysis of 3-component mixture of distributions

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