Robust frailty modelling using non-proportional hazards models

Ha, Il Do; MacKenzie, Gilbert

doi:10.1177/1471082x0801000304

Cited by 9 publications

(7 citation statements)

References 36 publications

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“…Prior to this solution, the GTDL model was used successfully with λ 0 = 1, when it was designated the TDL model. However, today, the Gamma frailty extension is preferred (Blagojevic et al 2003;MacKenzie and Ha 2007;Ha and MacKenzie 2010).…”

Section: Remarkmentioning

confidence: 99%

The XGTDL family of survival distributions

MacKenzie

Blagojevic‐Bucknall

Al-tawarah

et al. 2021

Jpn J Stat Data Sci

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Non-PH parametric survival modelling is developed within the framework of the multiple logistic function. The family considered comprises three basic models: (a) a PH model, (b) an accelerated life model and (c) a model which is non-proportional hazards and non-accelerated life. The last model, the generalised time-dependent logistic model was described first by the author in 1996 and this model gives its name to the entire family. The family is generalised by means of a Gamma frailty extension which is shown to accommodate crossing hazards data. A further generalisation is the inclusion of a dispersion model. These extensions lead naturally to the concept of a multi-parameter regression model described by Burke and MacKenzie in which the scale and shape parameters are modelled simultaneously as functions of covariates. Where possible, we include the MPR extension in the XGTDL family. Following a simulation study, the new models are used to analyse two sets survival data and the methods are discussed.

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Section: Remarkmentioning

confidence: 99%

The XGTDL family of survival distributions

MacKenzie

Blagojevic‐Bucknall

Al-tawarah

et al. 2021

Jpn J Stat Data Sci

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“…Due to the complexity of the GTDL-RWLF model, the regularity conditions are not easy to verify analytically. In this case, simulation studies are required; see, for example, Ha and MacKenzie (2010), Ortega et al (2015), and Barriga et al (2019). Following this idea, in the next section, we describe a simulation study performed to investigate whether the usual asymptotic properties of the ML estimators hold.…”

Section: A L G O R I T H M 1 Generator Of Random Times From the Gtdl-rwlf Modelmentioning

confidence: 99%

Nonproportional hazards model with a frailty term for modeling subgroups with evidence of long‐term survivors: Application to a lung cancer dataset

et al. 2021

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“…In order to make inferences on frailty models, we have some options. For instance, obtaining the marginal hazard and reliability functions and using the traditional likelihood function; or choosing other methods that obviate the need for marginalization, such as the h-likelihood approach proposed by Ha et al [48] and used in [49]. This paper considers the marginal hazard and reliability functions.…”

Section: B Gtdl Frailty Modelmentioning

confidence: 99%

Incorporation of Frailties Into a Non-Proportional Hazard Regression Model and Its Diagnostics for Reliability Modeling of Downhole Safety Valves

et al. 2020

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In this paper, our proposal consists of incorporating frailty into a statistical methodology for modeling time-to-event data, based on non-proportional hazards regression model. Specifically, we use the generalized time-dependent logistic (GTDL) model with a frailty term introduced in the hazard function to control for unobservable heterogeneity among the sampling units. We also add a regression in the parameter that measures the effect of time, since it can directly reflect the influence of covariates on the effect of time-to-failure. The practical relevance of the proposed model is illustrated in a real problem based on a data set for downhole safety valves (DHSVs) used in offshore oil and gas production wells. The reliability estimation of DHSVs can be used, among others, to predict the blowout occurrence, assess the workover demand and aid decision-making actions.INDEX TERMS Downhole safety valve, frailty model, generalized time-dependent logistic, hydrogen sulfide concentration, non-proportional hazard.

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Robust frailty modelling using non-proportional hazards models

Cited by 9 publications

References 36 publications

The XGTDL family of survival distributions

The XGTDL family of survival distributions

Nonproportional hazards model with a frailty term for modeling subgroups with evidence of long‐term survivors: Application to a lung cancer dataset

Incorporation of Frailties Into a Non-Proportional Hazard Regression Model and Its Diagnostics for Reliability Modeling of Downhole Safety Valves

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