Estimating Sojourn Time and Transition between Clinical States of HIV Patients under ART Follow up in Namibia
Simon Pombili Kashihalwa *
Department of Mathematics, Statistics and Actuarial Science, Namibia University of Science and Technology, Namibia.
Lilian Pazvakawambwa
Department of Statistics and Population Studies, University of Namibia, Namibia.
Josua Mwanyekange
Department of Mathematics, Statistics and Actuarial Science, Namibia University of Science and Technology, Namibia.
*Author to whom correspondence should be addressed.
Abstract
Background: Sojourn time refers to the amount of time a HIV patient spends in each clinical state in a single stay before he/she makes a transition to another state. HIV can be broken down into a number of intermediate states, based on CD4 counts. The four states of the Markov process of HIV 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/microliter of blood.
Aims: The aim of the study was to estimate sojourn and transition between clinical states of patients under ART in Namibia using homogenous semi-Markov processes, on data obtained from MoHSS.
Methods: A retrospective study design was used to obtain data on 2422 patients who were observed 11028 times, during 2008 to 2017 follow up period. The four staged semi-Markov model was employed to estimate sojourn times and transition between clinical states.
Results: Results indicates that 1637 (67.6%) were female and 785 (32.41%) were male .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, at treatment commencement (t = 0). As expected, the probabilities of transiting from good to worse states increased with time. After 6 months, the probabilities of transiting from state 1 to 3, and from state 1 to 4 are 0.023 and 0.004 respectively. Whereas after 12 months, the probabilities of transiting from state 1 to 3, and from state 1 to 4 are 0.059 and 0.010 respectively. As time increased the probabilities to remain 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). Sojourn times for states 1, 2, 3 and 4 were 22, 8, 10 and 15 months respectively.
Conclusions: Sojourn time is of interest in HIV modeling, as it gives a signal of how HIV is progressing. Longer sojourn times indicates slow HIV progression and shorter sojourn times indicates rapid HIV progression. As time increases, transition probabilities from good states to worse states increases.
Keywords: Stochastic, semi-Markov processes, multi-state model, CD4, progression