On the hazard function of Birnbaum–Saunders distribution and associated inference

Kundu, Debasis; Kannan, Nandini; Balakrishnan, N.

doi:10.1016/j.csda.2007.09.021

Cited by 122 publications

(74 citation statements)

References 21 publications

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“…The application of the Cox model for analyzing rare and common diseases can also be extended to accommodate situations in which there are forces accelerating or decelerating the time to event of interest. The Birnbaum-Saunders [Birnbaum and Saunders, 1969;Kundu et al, 2008] parametric LTS models [Locatelli et al, 2007, Pitkäniemi et al, 2007 and also a nonparametric LTS model, for instance, might be appropriate alternatives for modeling each one of these situations. Since genetic and environmental factors might be involved in that acceleration or deceleration process, extending these models in genetic analysis would be useful.…”

Section: Discussionmentioning

confidence: 99%

Genetic Analysis of Age-at-Onset for Cardiovascular Risk Factors in a Brazilian Family Study

Giolo¹,

Pereira²,

Andrade

et al. 2009

Hum Hered

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Background/Aims: Statistical analysis of age-at-onset involving family data is particularly complicated because there is a correlation pattern that needs to be modeled and also because there are measurements that are censored. In this paper, our main purpose was to evaluate the effect of genetic and shared family environmental factors on age-at-onset of three cardiovascular risk factors: hypertension, diabetes and high cholesterol. Methods: The mixed-effects Cox model proposed by Pankratz et al. [2005] was used to analyze the data from 81 families, involving 1,675 individuals from the village of Baependi, in the state of Minas Gerais, Brazil. Results: The analyses performed showed that the polygenic effect plays a greater role than the shared family environmental effect in explaining the variability of the age-at-onset of hypertension, diabetes and high cholesterol. The model which simultaneously evaluated both effects indicated that there are individuals which may have risk of hypertension due to polygenic effects 130% higher than the overall average risk for the entire sample. For diabetes and high cholesterol the risks of some individuals were 115 and 45%, respectively, higher than the overall average risk for the entire population. Conclusions: Results showed evidence of significant polygenic effects indicating that age-at-onset is a useful trait for gene mapping of the common complex diseases analyzed. In addition, we found that the polygenic random component might absorb the effects of some covariates usually considered in the risk evaluation, such as gender, age and BMI.

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Section: Discussionmentioning

confidence: 99%

Genetic Analysis of Age-at-Onset for Cardiovascular Risk Factors in a Brazilian Family Study

Giolo¹,

Pereira²,

Andrade

et al. 2009

Hum Hered

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“…The third period (2011 to the present) is characterized by a new inventiveness, breaking the link with lifetime data analysis and hence extended application in new areas such as: biology, crop yield assessment, econometrics, energy production, forestry, industry, informatics, insurance, inventory management, medicine, psychology, neurology, pollution monitoring, quality control, sociology and seismology; see, for example, Bhatti (2010); Kotz et al (2010); Balakrishnan et al (2011); Leiva et al (2010Leiva et al ( , 2011Leiva et al ( , 2012; Vilca et al (2010); Villegas et al (2011); Azevedo et al (2012); Ferreira et al (2012); Paula et al (2012); Santos-Neto et al (2012; Marchant et al (2013; Saulo et al (2013Saulo et al ( , 2018; Barros et al (2014); Rojas et al (2015); Wanke and Leiva (2015); Bourguignon et al (2017); Garcia-Papani et al (2017); ; Lillo et al (2018) and the references therein. In addition, risk and hazard analysis applications, in engineering and medicine, using the BS distribution were performed by Bebbington et al (2008); Kundu et al (2008); Azevedo et al (2012); Athayde (2017); Leão et al (2017Leão et al ( , 2018aLeão et al ( , 2018b; Athayde et al (2018) and Desousa et al (2018). Furthermore, the issue of robust parameter estimation has been considered, for example, by Wang et al (2013Wang et al ( , 2015 and Lemonte (2016).…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Multivariate Birnbaum-Saunders Distributions: Modelling and Applications

Aykroyd

Leiva

Marchant

2018

Risks

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Abstract:Since its origins and numerous applications in material science, the Birnbaum-Saunders family of distributions has now found widespread uses in some areas of the applied sciences such as agriculture, environment and medicine, as well as in quality control, among others. It is able to model varied data behaviour and hence provides a flexible alternative to the most usual distributions. The family includes Birnbaum-Saunders and log-Birnbaum-Saunders distributions in univariate and multivariate versions. There are now well-developed methods for estimation and diagnostics that allow in-depth analyses. This paper gives a detailed review of existing methods and of relevant literature, introducing properties and theoretical results in a systematic way. To emphasise the range of suitable applications, full analyses are included of examples based on regression and diagnostics in material science, spatial data modelling in agricultural engineering and control charts for environmental monitoring. However, potential future uses in new areas such as business, economics, finance and insurance are also discussed. This work is presented to provide a full tool-kit of novel statistical models and methods to encourage other researchers to implement them in these new areas. It is expected that the methods will have the same positive impact in the new areas as they have had elsewhere.

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“…For any k > 0, kW ∼ BS(λ, kβ). Kundu et al (2008) discussed the shape of its hazard function. The probability density function (pdf) corresponding to (1.1) is g λ,β (w) = κ(λ, β)w where κ(λ, β) = exp(λ −2 )/(2λ √ 2πβ) and τ(u) = u + u −1 .…”

Section: Introductionmentioning

confidence: 99%

A new extended Birnbaum-Saunders model with cure fraction: classical and Bayesian approach

Ortega

Cordeiro

Suzuki

et al. 2017

CSAM

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A four-parameter extended fatigue lifetime model called the odd Birnbaum-Saunders geometric distribution is proposed. This model extends the odd Birnbaum-Saunders and Birnbaum-Saunders distributions. We derive some properties of the new distribution that include expressions for the ordinary moments and generating and quantile functions. The method of maximum likelihood and a Bayesian approach are adopted to estimate the model parameters; in addition, various simulations are performed for different parameter settings and sample sizes. We propose two new models with a cure rate called the odd Birnbaum-Saunders mixture and odd Birnbaum-Saunders geometric models by assuming that the number of competing causes for the event of interest has a geometric distribution. The applicability of the new models are illustrated by means of ethylene data and melanoma data with cure fraction.

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On the hazard function of Birnbaum–Saunders distribution and associated inference

Cited by 122 publications

References 21 publications

Genetic Analysis of Age-at-Onset for Cardiovascular Risk Factors in a Brazilian Family Study

Genetic Analysis of Age-at-Onset for Cardiovascular Risk Factors in a Brazilian Family Study

Multivariate Birnbaum-Saunders Distributions: Modelling and Applications

A new extended Birnbaum-Saunders model with cure fraction: classical and Bayesian approach

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