Conditional Probabilities of AIDS Disease Transitions Using Semi-Markov Models

Analyzing progression of diseases is vital to monitor patient's traversal over time through a disease. Clinical study settings present modeling challenges, as patients' disease trajectories are only partially observed, and patients' disease statuses are only assessed at clinic visit times. HIV disease is a continuum of progressive damage to the immune system from the time of infection to the manifestation of severe immunologic damage. We proposed a semi-Markov model and collected data at Yirgalem General Hospital. Our study found that for an HIV/AIDS patient the transition probability from a given state to the next worse state increases within the good states as time gets optimum and then decreases with increasing time during a follow up. In a specific state of the disease a patient will stay in that state with a non- zero probability in good states and a patient will transit to the next state either to the worst or to the good state with a non-zero probability. The probability of being in same state decreases over time. With the good or alive states, the probability of being in a better state is non-zero, but less than the probability of being in worst states. The survival probabilities are decreasing with increasing time. Therefore, we recommend that increased clinical care for patients on ART services should be strengthen and patients need to regularly check their CD4 T cell count in the appropriate day based on physician order to timely know and monitor their disease status to improve the survival probability and to reduce mortality.