TITLE:
Application of Exponential Distribution in Modeling of State Holding Time in HIV/AIDS Transition Dynamics
AUTHORS:
Nahashon Mwirigi
KEYWORDS:
Markov Chain, Markov Process, Semi Markov Process Markov Decision Tree, Stochastic Process, Survival Rate, CD4+ Levels, Absorption Rates, AFT Model, PH Model
JOURNAL NAME:
Open Journal of Modelling and Simulation,
Vol.12 No.4,
October
25,
2024
ABSTRACT: Markov modeling of HIV/AIDS progression was done under the assumption that the state holding time (waiting time) had a constant hazard. This paper discusses the properties of the hazard function of the Exponential distributions and its modifications namely; Parameter proportion hazard (PH) and Accelerated failure time models (AFT) and their effectiveness in modeling the state holding time in Markov modeling of HIV/AIDS progression with and without risk factors. Patients were categorized by gender and age with female gender being the baseline. Data simulated using R software was fitted to each model, and the model parameters were estimated. The estimated P and Z values were then used to test the null hypothesis that the state waiting time data followed an Exponential distribution. Model identification criteria; Akaike information criteria (AIC), Bayesian information criteria (BIC), log-likelihood (LL), and R2 were used to evaluate the performance of the models. For the Survival Regression model, P and Z values supported the non-rejection of the null hypothesis for mixed gender without interaction and supported the rejection of the same for mixed gender with interaction term and males aged 50 - 60 years. Both Parameters supported the non-rejection of the null hypothesis in the rest of the age groups. For Gender male with interaction both P and Z values supported rejection in all the age groups except the age group 20 - 30 years. For Cox Proportional hazard and AFT models, both P and Z values supported the non-rejection of the null hypothesis across all age groups. The P-values for the three models supported different decisions for and against the Null hypothesis with AFT and Cox values supporting similar decisions in most of the age groups. Among the models considered, the regression assumption provided a superior fit based on (AIC), (BIC), (LL), and R2 Model identification criteria. This was particularly evident in age and gender subgroups where the data exhibited non-proportional hazards and violated the assumptions required for the Cox Proportional Hazard model. Moreover, the simplicity of the regression model, along with its ability to capture essential state transitions without over fitting, made it a more appropriate choice.