Modelling Progression Of HIV/AIDS Disease Using Homogenous Semimarkov Processes: Cohort Study, Namibia

Abstract

The progression of HIV infection to AIDS and then to death can be considered as a Markovan stochastic process. Disease progression can be broken down into a finite number of intermediate states, based on CD4 counts. The four states of the Markov process of HIV/AIDS progression are commonly defined as: S1: CD4 count > 500 cells/microlitre of blood; S2: 350 < CD4 count ≤ 500 cells/microlitre of blood; S3: 200 < CD4 count ≤ 350 cells/microlitre of blood; S4: CD4 count ≤ 200 cells/microlitre of blood. The objective of this study was to model the progression of HIV/AIDS disease of patients under ART follow-up in Namibia using homogenous semi-Markov processes, using the data obtained from MoHSS. A retrospective study design was used to obtain data on 2422 patients who were observed 11028 times. The semi-Markov model was employed to estimate the transition probabilities, transition intensity rate and sojourn time. Time homogeneous model was fitted to assess effectiveness of ART by comparing the forward transition and reverse transitions. At treatment commencement (t = 0), 657(27.13%) patients started ART in state 1, 683(28.19%) patients started ART in state 2, 677(27.95%) patients started ART in state 3 and 405(16.72%) patients started ART in state 4. As expected the probabilities of transiting from good states to worse states increased with time (from state 1 to state 3 and 4 after 6 months is 0.023 and 0.004, after 12 months is 0.059 and 0.010 respectively). As time increase the probabilities of remaining in the same state is decreasing (probabilities of remaining in state 1 after 6, 12 and 18 months is 0.804, 0.698 and 0.633).