Modelling Progression of HIV/AIDS Disease Stages Using Semi-Markov Processes

The aim of this study is to model the progression of HIV/AIDS disease of an individual patient under ART follow-up using semi-Markov processes. Recorded hospital data were obtained for a cohort of 710 patients at Felege-Hiwot referral hospital, Ethiopia, who have been under ART followup from June 2005 to August 2009. States of the Markov process are defined by the seriousness of the sickness based on the CD4 counts in cells/microliter. The five states considered are: state one (CD4 count > 500); state two (350 < CD4 count ≤ 500); state three (200 < CD4 count ≤ 350); state four (CD4 count ≤ 200); and state five (Death). The first four states are named as good or alive states. The findings obtained from the current study are as follows: within the good states, the transition probability from a given state to the next worse state increases with time, gets optimum at a time and then decreases with increasing time. This means that there is some period of time when such probability is highest for a patient to transit to a worse state of the disease. Moreover, the probability of dying decreases with increasing CD4 counts over time. For an HIV/AIDS patient in a specific state of the disease, the probability of being in same state decreases over time. Within the good states, the results show that probability of being in a better state is non-zero, but less than the probability of being in worse state. At any time of the process, there is more likely to be in worse state than to be in better one. The conditional probability of staying in same state until a given number of month decreases with increasing time. The reliability analysis also revealed that the survival probabilities are all declining over time. This implies that patient conditions should be improved with ART to improve the survival probability.