Modelling progression of HIV/AIDS disease using homogenous semi-markov processes: Cohort study, Namibia

A thesis submitted in partial fulfillment of the requirements for the Degree of Master of science in biostatistics

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). Estimated sojourn times for states 1, 2, 3 and 4 were 22 (40%), 8 (15%), 10 (18%) and 15 (27%) months respectively. As anticipated the conditional probability of staying in same state given number of month decreases with increasing time (conditional probabilities of remaining in state 2 after 6, 12 and 18 months is 0.547, 0.387 and 0.328). As expected the intensity indicates that the rate of transiting from good states to worst states is decreasing (the intensity of transiting from state 1 to 3 and 4 is p<0.001 and the intensity of transiting from state 2 to 3 and 4 is 0.04 and p<0.001). The strongest predictor of transition from state 1 to 2 is TDF/3TC/EFV, which has a hazard ratio of 1.338 (with p value of 0.002). Patients who were prescribed TDF/3TC/EFV, are over 1.338 times more likely to transit from state 1 to state 2 than patients who did not receive TDF/3TC/EFV. A hazard ratio of 0.678 for the predictor variable female shows that female were less likely to transit from state 2 to 3 than their male counterparts. The hazard ratios of females from a bad state to a better state are more than 1, which is an indication that females are less likely to respond to treatment compared to males. HIV can progress to AIDS without delay if there is no intervention. Early ART initiation is crucial at slowing prognosis of progressing from good states to worse states.