Numerical Treatment of Homogeneous Semi-Markov Processes in Transient Case–a Straightforward Approach

Corradi, Giulia; Janssen, Jacques; Manca, Raimondo

doi:10.1023/b:mcap.0000017715.28371.85

Cited by 64 publications

(46 citation statements)

References 10 publications

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“…Specifically, AIDS patient who is in the third state of the disease may have a highest waiting time until month t compared to the patients who is in the first and second stage of the disease with a given time. This result is similar to the result obtained in previous studies (Goshu and Dessie, 2013;Giuseppe et al, 2007;Corradi et al, 2004).…”

Section: Discussionsupporting

confidence: 93%

“…An approximate solution of (10) can be obtained using the general numerical integration formula given in Corradi et al (2004). In the same paper, they proved that the numerical solution of the process converges to the discrete time HSMP described as an infinite countable linear system Equation 11:…”

Section: Semi-markov For Predicting the Probability Of Waiting Timementioning

confidence: 96%

“…For solving the evolution Equation 13, Corradi et al (2004) proposed the following algorithm with suggested matrix form Equation 14: Given an epoch T is fixed, matrices G T and P, the algorithm solves the linear system (14) for the unknown matrix Φ…”

Section: Semi-markov For Predicting the Probability Of Waiting Timementioning

confidence: 99%

“…Among recent papers in biomedicine, Masala et al (2014;Goshu and Dessie, 2013;Giuseppe et al, 2007) analyzed HIV/AIDS dynamic evolution as defined by CD4 levels from a macroscopic point of view by means of homogeneous semi-Markov stochastic processes. Numerical analyses of the homogeneous semi-Markov process are dealt by Corradi et al (2004;Janssen and Manca, 2001). Other more readings include (Davidov and Zelen, 2000;Viladent and Van Ackere, 2007;Satten and Sternberg, 1999;Baryarama et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

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Multi-State Models of Hiv/Aids by Homogeneous Semi-Markov Process

Dessie¹

2014

American Journal of Biostatistics

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Multi-state stochastic models are useful tools for studying complex dynamics such as chronic diseases. The purpose of this study is to determine factors associated with the progression between different stages of the disease and to model the progression of HIV/AIDS disease of an individual patient under ART follow-up using semi-Markov processes. A sample of 1456 patients has been taken from a hospital record at Amhara Referral Hospitals, Amhara Region, Ethiopia, who have been under ART follow up from June 2006 to August 2013. The states of disease progression adopted in the multi-state model were defined based on of the following CD4 cell counts: ≥500(SI); 200 to 499(SII); <200(SIII); and Death (D). The first three states are named as good. Female patients were 1.6 times more likely to move from state 2 to state 1 than those of male patients (adjusted HR = 1.60, CI = 1.02-2.49). Patients, who is not drug addicted, were 2.49 times more likely to move from state 3 to state 2 than those of drug addicted(adjusted HR = 2.67, CI = 1.52-4.68). Patients with tuberculosis were 2.67 times more likely to move from state 3 to state 4 than those with no tuberculosis (adjusted HR = 2.67, CI = 1.52-4.68). On the other hand, the probability of staying in same state until a given number of month decreases with increasing time. Multi-state modeling is a powerful approach for studying chronic diseases and estimating factors associated with transitions between each stage of progression. The major predictors of the intensity of transitions between different states of HIV/AIDS patients were gender, age, drug addicted and TB status. The dynamic nature of the AIDS progression is confirmed with particular findings that there is more likely to be in worse state than better one unless interventions are made.

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Section: Discussionsupporting

confidence: 93%

Section: Semi-markov For Predicting the Probability Of Waiting Timementioning

confidence: 96%

Section: Semi-markov For Predicting the Probability Of Waiting Timementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi-State Models of Hiv/Aids by Homogeneous Semi-Markov Process

Dessie¹

2014

American Journal of Biostatistics

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“…where Ψ is R 2 -order matrix with Before solving equation (13), equation (9) At this point, an important advantage of the proposed numerical method takes place: whereas for other numerical methods as the proposed in Corradi et al (2004) and Monte Carlo simulations the number of discretization points should be increased to obtain improved accuracies, the proposed procedure with only 16 points is able to provide valuable results with less computational cost than these methods, as it will be showed through the example in section 6.…”

Section: Numerical Inversion Of Laplace Transformsmentioning

confidence: 99%

A continuous-time semi-markov bayesian belief network model for availability measure estimation of fault tolerant systems

Moura

Droguett

2008

Pesqui. Oper.

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In this work it is proposed a model for the assessment of availability measure of fault tolerant systems based on the integration of continuous time semi-Markov processes and Bayesian belief networks. This integration results in a hybrid stochastic model that is able to represent the dynamic characteristics of a system as well as to deal with cause-effect relationships among external factors such as environmental and operational conditions. The hybrid model also allows for uncertainty propagation on the system availability. It is also proposed a numerical procedure for the solution of the state probability equations of semi-Markov processes described in terms of transition rates. The numerical procedure is based on the application of Laplace transforms that are inverted by the Gauss quadrature method known as Gauss Legendre. The hybrid model and numerical procedure are illustrated by means of an example of application in the context of fault tolerant systems.Keywords: semi-Markov processes; Bayesian belief networks; Laplace transforms; availability measure; fault tolerant systems. ResumoNeste trabalho, é proposto um modelo baseado na integração entre processos semi-Markovianos e redes Bayesianas para avaliação da disponibilidade de sistemas tolerantes à falha. Esta integração resulta em um modelo estocástico híbrido o qual é capaz de representar as características dinâmicas de um sistema assim como tratar as relações de causa e efeito entre fatores externos tais como condições ambientais e operacionais. Além disso, o modelo híbrido permite avaliar a propagação de incerteza sobre a disponibilidade do sistema. É também proposto um procedimento numérico para a solução das equações de probabilidade de estado de processos semi-Markovianos descritos por taxas de transição. Tal procedimento numérico é baseado na aplicação de transformadas de Laplace que são invertidas pelo método de quadratura Gaussiana conhecido como Gauss Legendre. O modelo híbrido e procedimento numérico são ilustrados por meio de um exemplo de aplicação no contexto de sistemas tolerantes à falha.Palavras-chave: processos semi-Markovianos; redes Bayesianas; transformadas de Laplace; disponibilidade; sistemas tolerantes à falha.

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2012

Stochastic Methods for Pension Funds

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Numerical Treatment of Homogeneous Semi-Markov Processes in Transient Case–a Straightforward Approach

Cited by 64 publications

References 10 publications

Multi-State Models of Hiv/Aids by Homogeneous Semi-Markov Process

Multi-State Models of Hiv/Aids by Homogeneous Semi-Markov Process

A continuous-time semi-markov bayesian belief network model for availability measure estimation of fault tolerant systems

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