A Multi-State Non-Homogeneous Semi-Markov Model with Application to HIV/AIDS Disease Progression

Source abstract

HIV disease progression is inherently a multistate stochastic process in which transition rates among immunological states vary over time and are influenced by therapeutic interventions. Because conventional homogeneous Markov models cannot adequately capture this temporal heterogeneity, this study developed and evaluated a multistate non-homogeneous semi-Markov model (MNHSMM) to characterize HIV progression across six clinically defined immunological states and estimate state-specific sojourn-time distributions and transition probabilities according to calendar time and treatment status. Longitudinal data from 500 adults living with HIV, followed for a median of 84 months, were analyzed. The MNHSMM incorporated Weibull-distributed sojourn times and time-varying transition kernels parameterized using B-spline functions, with parameters estimated through maximum likelihood. Model performance was compared with that of homogeneous Markov and homogeneous semi-Markov models using the Akaike information criterion (AIC), Bayesian information criterion (BIC), and likelihood-ratio tests. The MNHSMM achieved the lowest AIC (3281.4) and BIC (3402.6) and significantly outperformed the homogeneous semi-Markov model (χ² = 174.2, df = 16, p < .001). The mean sojourn time in the asymptomatic state was 28.4 months (95% CI [25.1, 31.7]). Patients receiving antiretroviral therapy exhibited significantly longer sojourn times across all nonabsorbing states and a 37% lower probability of transitioning to death within five years. These findings establish the MNHSMM as a statistically superior and clinically informative framework for modeling HIV progression. Its temporal flexibility can improve long-term survival prediction and inform the identification of optimal antiretroviral therapy intervention windows, with implications for healthcare planning in sub-Saharan Africa and beyond.