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Biometrical Letters

The Journal of Polish Biometric Society

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Survival probabilities for HIV infected patients through semi-Markov processes

Giovanni Masala / Giuseppina Cannas / Marco Micocci
Published Online: 2014-06-06 | DOI: https://doi.org/10.2478/bile-2014-0002


In this paper we apply a parametric semi-Markov process to model the dynamic evolution of HIV-1 infected patients. The seriousness of the infection is rendered by the CD4+ T-lymphocyte counts. For this purpose we introduce the main features of nonhomogeneous semi-Markov models. After determining the transition probabilities and the waiting time distributions in each state of the disease, we solve the evolution equations of the process in order to estimate the interval transition probabilities. These quantities appear to be of fundamental importance for clinical predictions. We also estimate the survival probabilities for HIV infected patients and compare them with respect to certain categories, such as gender, age group or type of antiretroviral therapy. Finally we attach a reward structure to the aforementioned semi-Markov processes in order to estimate clinical costs. For this purpose we generate random trajectories from the semi-Markov processes through Monte Carlo simulation. The proposed model is then applied to a large database provided by ISS (Istituto Superiore di Sanità, Rome, Italy), and all the quantities of interest are computed.

Keywords : semi-Markov process; HIV states; waiting time distribution; evolution equation; survival probabilities; Monte Carlo simulation


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About the article

Published Online: 2014-06-06

Published in Print: 2014-06-01

Citation Information: Biometrical Letters, Volume 51, Issue 1, Pages 13–36, ISSN (Online) 1896-3811, DOI: https://doi.org/10.2478/bile-2014-0002.

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© by Giovanni Masala. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. BY-NC-ND 3.0

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