Survival probabilities for HIV infected patients through semi-Markov processes

In this paper we apply a parametric semi-Markov pro cess to model the dynamic evolution of HIV-1 infected patients. The seriousne ss of the infection is rendered by the CD4+ T-lymphocyte counts. For this purpose we introd uce the main features of non- homogeneous semi-Markov models. After determining t he 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 i nterval transition probabilities. These quantities appear to be of fundamental importance f or clinical predictions. We also estimate the survival probabilities for HIV infecte d 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 aforeme ntioned semi-Markov processes in order to estimate clinical costs. For this purpose we generate random trajectories from the semi-Markov processes through Monte Carlo simul ation. The proposed model is then applied to a large database provided by ISS (I stituto Superiore di Sanità, Rome, Italy), and all the quantities of interest are comp uted.