{"id":{"repo_id":"oxford-brookes","oai_identifier":"tle:e828e4da-de08-2f34-37b0-8cc3bbaf7150:d6bd9758-527a-46cd-bfe2-c433766e8fca:1"},"canonical_url":"https://search.dev.ndltd.org/etd/oxford-brookes/tle:e828e4da-de08-2f34-37b0-8cc3bbaf7150:d6bd9758-527a-46cd-bfe2-c433766e8fca:1","repository":{"repo_id":"oxford-brookes","name":"Oxford Brookes University","base_url":"https://radar.brookes.ac.uk/radar/oai"},"display":{"title":"Non-parametric competing risks with multivariate frailty models","abstract":"This research focuses on two theories: (i) competing risks and (ii) random eect (frailty) models. The theory of competing risks provides a structure for inference in problems where cases are subject to several types of failure. Random eects in competing risk models consist of two underlying distributions: the conditional distribution of the response variables, given the random eect, depending on the explanatory variables each with a failure type specic random eect; and the distribution of the random eect. In this situation, the distribution of interest is the unconditional distribution of the response variable, which may or may not have a tractable form. The parametric competing risk model, in which it is assumed that the failure times are coming from a known distribution, is widely used such as Weibull, Gamma and other distributions. The Gamma distribution has been widely used as a frailty distribution, perhaps due to its simplicity since it has a closed form expression of the unconditional hazard function. However, it is unrealistic to believe that a few parametric models are suitable for all types of failure time. This research focuses on a distribution free of the multivariate frailty models. Another approach used to overcome this problem is using nite mixture of parametric frailty especially those who have a closed form of unconditional survival function. In addition, the advantages and disadvantages of a parametric competing risk models with multivariate parametric and/or non-parametric frailty (correlated random eects) are investigated. In this research, four main models are proposed: rst, an application of a new computation and analysis of a multivariate frailty with competing risk model using Cholesky decomposition of the Lognormal frailty. Second, a correlated Inverse Gaussian frailty in the presence of competing risks model. Third, a non-parametric multivariate frailty with parametric competing risk model is proposed. Finally, a simulation study of nite mixture of Inverse Gaussian frailty showed the ability of this model to t dierent frailty distribution. One main issue in multivariate analysis is the time it needs to t the model. The proposed non-parametric model showed a signicant time decrease in estimating the model parameters (about 80% less time compared the Log-Normal frailty with nested loops). A real data of recurrence of breast cancer is used as the applications of these models.","abstract_html":"This research focuses on two theories: (i) competing risks and (ii) random eect (frailty) models. The theory of competing risks provides a structure for inference in problems where cases are subject to several types of failure. Random eects in competing risk models consist of two underlying distributions: the conditional distribution of the response variables, given the random eect, depending on the explanatory variables each with a failure type specic random eect; and the distribution of the random eect. In this situation, the distribution of interest is the unconditional distribution of the response variable, which may or may not have a tractable form. The parametric competing risk model, in which it is assumed that the failure times are coming from a known distribution, is widely used such as Weibull, Gamma and other distributions. The Gamma distribution has been widely used as a frailty distribution, perhaps due to its simplicity since it has a closed form expression of the unconditional hazard function. However, it is unrealistic to believe that a few parametric models are suitable for all types of failure time. This research focuses on a distribution free of the multivariate frailty models. Another approach used to overcome this problem is using nite mixture of parametric frailty especially those who have a closed form of unconditional survival function. In addition, the advantages and disadvantages of a parametric competing risk models with multivariate parametric and/or non-parametric frailty (correlated random eects) are investigated. In this research, four main models are proposed: rst, an application of a new computation and analysis of a multivariate frailty with competing risk model using Cholesky decomposition of the Lognormal frailty. Second, a correlated Inverse Gaussian frailty in the presence of competing risks model. Third, a non-parametric multivariate frailty with parametric competing risk model is proposed. Finally, a simulation study of nite mixture of Inverse Gaussian frailty showed the ability of this model to t dierent frailty distribution. One main issue in multivariate analysis is the time it needs to t the model. The proposed non-parametric model showed a signicant time decrease in estimating the model parameters (about 80% less time compared the Log-Normal frailty with nested loops). A real data of recurrence of breast cancer is used as the applications of these models.","abstract_has_math":false,"creators":["Masuadi, E"],"institution":"Oxford Brookes University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013","date_published":"2013","updated_at":"2026-07-24T03:44:18Z","subjects":[],"languages":["en"],"rights":["All rights reserved"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://radar.brookes.ac.uk/radar/items/e828e4da-de08-2f34-37b0-8cc3bbaf7150/1/","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Masuadi, E"]},{"key":"dc:creator","label":"Author","values":["Masuadi, E"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013"]},{"key":"dc:publisher","label":"Institution","values":["Oxford Brookes University"]},{"key":"dc:type","label":"Dc Type","values":["thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["All rights reserved"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://radar.brookes.ac.uk/radar/items/e828e4da-de08-2f34-37b0-8cc3bbaf7150/1/","https://radar.brookes.ac.uk/radar/file/e828e4da-de08-2f34-37b0-8cc3bbaf7150/1/masuadi2013non.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This research focuses on two theories: (i) competing risks and (ii) random eect (frailty) models. The theory of competing risks provides a structure for inference in problems where cases are subject to several types of failure. Random eects in competing risk models consist of two underlying distributions: the conditional distribution of the response variables, given the random eect, depending on the explanatory variables each with a failure type specic random eect; and the distribution of the random eect. In this situation, the distribution of interest is the unconditional distribution of the response variable, which may or may not have a tractable form. The parametric competing risk model, in which it is assumed that the failure times are coming from a known distribution, is widely used such as Weibull, Gamma and other distributions. The Gamma distribution has been widely used as a frailty distribution, perhaps due to its simplicity since it has a closed form expression of the unconditional hazard function. However, it is unrealistic to believe that a few parametric models are suitable for all types of failure time. This research focuses on a distribution free of the multivariate frailty models. Another approach used to overcome this problem is using nite mixture of parametric frailty especially those who have a closed form of unconditional survival function. In addition, the advantages and disadvantages of a parametric competing risk models with multivariate parametric and/or non-parametric frailty (correlated random eects) are investigated. In this research, four main models are proposed: rst, an application of a new computation and analysis of a multivariate frailty with competing risk model using Cholesky decomposition of the Lognormal frailty. Second, a correlated Inverse Gaussian frailty in the presence of competing risks model. Third, a non-parametric multivariate frailty with parametric competing risk model is proposed. Finally, a simulation study of nite mixture of Inverse Gaussian frailty showed the ability of this model to t dierent frailty distribution. One main issue in multivariate analysis is the time it needs to t the model. The proposed non-parametric model showed a signicant time decrease in estimating the model parameters (about 80% less time compared the Log-Normal frailty with nested loops). A real data of recurrence of breast cancer is used as the applications of these models."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Non-parametric competing risks with multivariate frailty models"]}]}],"canonical_facts":{"dc:contributor":["Masuadi, E"],"dc:creator":["Masuadi, E"],"dc:date":["2013"],"dc:description":["This research focuses on two theories: (i) competing risks and (ii) random eect (frailty) models. The theory of competing risks provides a structure for inference in problems where cases are subject to several types of failure. Random eects in competing risk models consist of two underlying distributions: the conditional distribution of the response variables, given the random eect, depending on the explanatory variables each with a failure type specic random eect; and the distribution of the random eect. In this situation, the distribution of interest is the unconditional distribution of the response variable, which may or may not have a tractable form. The parametric competing risk model, in which it is assumed that the failure times are coming from a known distribution, is widely used such as Weibull, Gamma and other distributions. The Gamma distribution has been widely used as a frailty distribution, perhaps due to its simplicity since it has a closed form expression of the unconditional hazard function. However, it is unrealistic to believe that a few parametric models are suitable for all types of failure time. This research focuses on a distribution free of the multivariate frailty models. Another approach used to overcome this problem is using nite mixture of parametric frailty especially those who have a closed form of unconditional survival function. In addition, the advantages and disadvantages of a parametric competing risk models with multivariate parametric and/or non-parametric frailty (correlated random eects) are investigated. In this research, four main models are proposed: rst, an application of a new computation and analysis of a multivariate frailty with competing risk model using Cholesky decomposition of the Lognormal frailty. Second, a correlated Inverse Gaussian frailty in the presence of competing risks model. Third, a non-parametric multivariate frailty with parametric competing risk model is proposed. Finally, a simulation study of nite mixture of Inverse Gaussian frailty showed the ability of this model to t dierent frailty distribution. One main issue in multivariate analysis is the time it needs to t the model. The proposed non-parametric model showed a signicant time decrease in estimating the model parameters (about 80% less time compared the Log-Normal frailty with nested loops). A real data of recurrence of breast cancer is used as the applications of these models."],"dc:format":["application/pdf"],"dc:identifier":["https://radar.brookes.ac.uk/radar/items/e828e4da-de08-2f34-37b0-8cc3bbaf7150/1/","https://radar.brookes.ac.uk/radar/file/e828e4da-de08-2f34-37b0-8cc3bbaf7150/1/masuadi2013non.pdf"],"dc:language":["en"],"dc:publisher":["Oxford Brookes University"],"dc:rights":["All rights reserved"],"dc:title":["Non-parametric competing risks with multivariate frailty models"],"dc:type":["thesis"]},"updated_at":"2026-07-24T03:44:18Z"}