Continuous - Time Markov Modeling of Durvalumab Dynamics after Chemoradiotherapy in Stage III NSCLC (PACIFIC Era): Development, Validation, and Extrapolation

Abstract

Background: Immunotherapy in un-resectable stage III NSCLC shows delayed treatment effects and time-varying hazards that challenge proportional-hazards assumptions. We developed a Continuous-Time Markov Chain (CTMC) model - with piecewise hazards - to capture the temporal dynamics of durvalumab after chemoradiotherapy (PACIFIC era), enabling transparent extrapolation beyond early trial landmarks.

Methods: We specified a multi-state CTMC with absorbing death, and clinically interpretable transient states (pre-progression disease control and post-progression). Piecewise transition rates were calibrated to early PACIFIC landmarks (e.g., 0-12-24-36 months) for Overall Survival (OS) and Progression-Free Survival (PFS), using constrained optimization. External validity was assessed by comparing model-implied OS/PFS trajectories against published PACIFIC follow-ups and large real-world evidence. Uncertainty was quantified via parametric resampling of transition intensities and sensitivity to piecewise knots.

Results: The CTMC reproduced the hallmark delayed separation of survival curves and the long tail behavior typical of immune checkpoint inhibition. When calibrated only to early landmarks, the model generated plausible OS and PFS beyond 36 months, approaching 5-year targets reported in PACIFIC follow-ups (e.g., ~43% OS and ~33% PFS with durvalumab), while acknowledging mild underestimation of late PFS in sensitivity scenarios. Goodness-of-fit remained stable across alternative knot placements; uncertainty widened beyond 60 months, as expected from non individual data calibration.

Conclusions: A piecewise-hazard CTMC provides a transparent and reproducible framework to model non-proportional, time-dependent immunotherapy effects in stage III NSCLC, reconciling early trial information with clinically coherent long-term projections. This approach can support methodological rigor in survival analysis, scenario planning, and health-economic extrapolation in the PACIFIC setting and similar contexts.

Keywords: Continuous-Time Markov Chain; Non-Proportional Hazards; Immunotherapy; Durvalumab; Pacific; Stage III NSCLC; Survival Extrapolation

Citation

Zurita AJW, Ruíz MAG, Carmona DM, Ibáñez JP, Rivera GC, Sánchez CM. Continuous - Time Markov Modeling of Durvalumab Dynamics after Chemoradiotherapy in Stage III NSCLC (PACIFIC Era): Development, Validation, and Extrapolation. WebLog J Cancer Clin Res. wjcacr.2026.d2301. https://doi.org/10.5281/zenodo.19763230