Application of Semi-Markov Process For Model Incremental Change in HIV Staging with Cost Effect

In the recent past, both non-parametric and parametric approaches have consistently been used to model cost effectiveness in a variety of health applications. This study applies the semi-Markov model while presenting the sojourn time with well-defined probability distributions. We employed the Weibull distribution to model the hazard function for each of the defined transition paths. We defined three distinct states of the semi-Markov process using the quantity of HIV virus in the blood of an HIV-infected person i.e., viral load (VL) copies in a milliliter (copies/mL). The three states were defined; VL < 200 copies/mL, 200 copies/mL < VL < 1,000 copies/mL, VL > 1,000 copies/mL and an absorbing state which is naturally death. We also developed a cumulative cost function, purposely to determine the average estimated cost per patient in each of the defined states. Incremental Cost Effectiveness Ratio (ICER) was utilized in the analysis of cost-effectiveness while comparing two program strategies i.e., Patients under the differentiated care model (DCM) and those who are not considered to be in any model of differentiated care during their respective ongoing clinical follow up. Results show the mean cost of the patients for each state 1, 2, and 3 was $765, $ 829, and $ 1,395 respectively. More so, the computed ICER ratio was $ 484/life-year-saved. In conclusion, the cost of keeping patients in state 1 (on DCM) was relatively cheaper and more efficient compared to the other states.