Bayesian Estimation of Parameters and Comparison of Shared Gamma Frailty Models

Hanagal, David D.; Dabade, Alok D.

doi:10.1080/03610918.2012.661909

Cited by 17 publications

(5 citation statements)

References 15 publications

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“…High prior variances ensure that the prior is flat in order to reflect uncertainties about treatment effects. While such priors have been used efficiently in literature (Sahu, Dey, Aslanidou, and Sinha 1997;Ibrahim, Chen, and Sinha 2001;Santos and Achcar 2011;Hanagal and Dabade 2013;Sidhu, Jain, and Sharma 2018) for the shape parameter λ such diffused prior distributions do not yield a proper posterior density. Earlier researchers (Azzalini 1985;Azzalini and Capitanio 1999;Loperfido 2004, 2006;Sartori 2006;Bayes and Branco 2007;Canale and Scarpa 2013) have also noted that estimation of λ poses some intrinsic problems.…”

Section: Prior Densitiesmentioning

confidence: 99%

Modeling Dependence in Survival Times using Log-Skew Normal Shared Frailties

Sidhu

Sharma²,

Jain³

2023

AJS

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In survival studies, event times under a common influence are often grouped together in clusters. The association between and within these clusters can be studied using frailty models where randomness in the data or heterogeneity arising due to unknown covariates is described using a frailty variable. In shared frailty models, frailty value is common or shared for all observations within a cluster while it is conditionally independent for different clusters. In this article, we consider a model whose baseline distribution is Weibull and shared frailties follow log skew-normal distribution. This distribution increases flexibility of the model as it allows the frailty term to be positively or negatively skewed and estimation of skewness parameter enables us to comment on dependence structure of the random component. A simulation study is performed and Bayesian estimates of treatment effects, variance and skewness of frailty term are obtained using Metropolis-Hastings algorithm. It is shown that while bias and expected loss for estimates of all parameters reduce as dataset size increases, frailty parameters are more efficiently estimated when the random component is considered to be skewed. The model is also applied to two real-life datasets where positive and negative skewness is observed in the frailty term.

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Section: Prior Densitiesmentioning

confidence: 99%

Modeling Dependence in Survival Times using Log-Skew Normal Shared Frailties

Sidhu

Sharma²,

Jain³

2023

AJS

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“…

λ (t) = \frac{β}{η} {((), \frac{t}{η})}^{β - 1}

R false(t false) = \exp [- {((), \frac{t}{η})}^{β}]

where, β and η are the shape parameter and the scale parameter of the Weibull distribution, respectively. These parameters can be obtained with estimation methods such as the support vector regression [29], the least square method [30], and the Bayesian parameter estimation [31].…”

Section: The Proposed Opportunistic Maintenance Strategymentioning

confidence: 99%

An opportunistic maintenance strategy for wind turbines

Wang

Teng

Zhang

et al. 2021

IET Renewable Power Gen

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Maintenance strategies aim at reduction of the operation and maintenance cost of wind turbines. An opportunistic maintenance strategy offers cost advantages over the traditional preventive replacement maintenance strategy by considering cost dependency among maintenance activities. A new opportunistic maintenance strategy of wind turbines is proposed here. First, the proposed strategy includes two sets of reliability thresholds to handle subassemblies those are in operational and failed wind turbines. Using the reliability thresholds, ten maintenance modes and their service conditions are presented. Second, the Weibull distribution with an age reduction factor is introduced to describe reliability variation of subassemblies under imperfect maintenance. Third, the maintenance cost in each maintenance mode is expressed by a reliability variation‐based function that is dependent on the stage of maintenance activities. Fourth, due to the randomness of failures, the expected total maintenance cost is determined with Monte Carlo simulation. The proposed approach has been validated with the data provided by a wind farm located in Northern China.

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“…Frailty model with gamma distribution has been studied in Vaupel et al (1979) , Oakes (1982), Clayton and Cuzick (1985), and Andersen et al (1993). The gamma distribution is the most commonly used frailty distribution, largely because of its mathematical convenience; see, for example, Hanagal (2006Hanagal ( , 2007Hanagal ( & 2013. Another choice is the inverse Gaussian distribution.…”

Section: Introductionmentioning

confidence: 99%

The Transmuted Generalized Gamma Distribution: Properties and Application

Lucena¹,

Silva²,

Cordeiro³

2021

Journal of Data Science

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The unknown or unobservable risk factors in the survival analysis cause heterogeneity between individuals. Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. The most common shared frailty model is a model in which frailty act multiplicatively on the hazard function. In this paper, we introduce the shared inverse Gaussian frailty model with the reversed hazard rate and the generalized inverted exponential distribution and the generalized exponential distribution as baseline distributions. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo(MCMC) technique to estimate the parameters involved in the models. We present a simulation study to compare the true values of the parameters with the estimated values. Also we apply the proposed models to the Australian twin data set and a better model is suggested.

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Bayesian Estimation of Parameters and Comparison of Shared Gamma Frailty Models

Cited by 17 publications

References 15 publications

Modeling Dependence in Survival Times using Log-Skew Normal Shared Frailties

Modeling Dependence in Survival Times using Log-Skew Normal Shared Frailties

An opportunistic maintenance strategy for wind turbines

The Transmuted Generalized Gamma Distribution: Properties and Application

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