Multi-state and Semi-Markov Modelling of Prostate Cancer Disease Trajectories and Mortality Dynamics

Abstract

Background: Previous prostate cancer research has often been conducted in clinical or laboratory settings and has relied on traditional survival models that focus on a single disease endpoint. Such approaches do not fully account for intermediate disease states, transition risks, or disease-state occupancy times. This study aimed to model the dynamic progression and survival of prostate cancer using continuous-time Multi-State Markov and Semi-Markov frameworks. Methods: A retrospective longitudinal study was conducted using clinical data from 300 patients with prostate cancer. The dataset included cancer stage, treatment exposure, tumour characteristics, survival outcomes and follow-up duration. Three disease states or stages were considered: Early-stage disease, Advanced-stage disease and Death. Transition intensities, transition probabilities, mean sojourn times and transition-specific hazard ratios were estimated using Continuous-Time Multi-State and Semi-Markov models. Results: The largest proportion of patients had Stage II disease (30.00%), followed by Stage III disease (27.67%). The transition intensity from Early-stage disease to Advanced-stage disease (0.1603) was higher than the direct transition from Early-stage disease to Death (0.0724), suggesting a sequential disease progression pattern. Mean sojourn time was shorter in Early-stage disease (4.297 months) than in Advanced-stage disease (93.924 months). At 60 months, 61.90% of patients initially in Early-stage disease had transitioned to Death. Increasing age was associated with mortality among patients with Advanced-stage disease (HR = 1.013), whereas radiation therapy was associated with a lower mortality hazard in this group (HR = 0.721). Conclusion: The multi-state modelling framework provided a structured representation of prostate cancer progression by accounting for intermediate disease states, transition-specific risks, state occupancy times and treatment-related effects.