A Bayesian Markov Framework for Modeling Breast Cancer Progression

This study develops a three-state Markov framework to estimate the transition rates between normal, preclinical screen-detectable phase (PCDP), and clinical breast cancer using simulated data. Two exponential models are explored: a five-mode transition model and a six-mode transition model, the latter incorporating exact cancer case timings. Each model is analyzed both with and without covariates to evaluate their influence on breast cancer progression. Parameters are estimated utilizing maximum likelihood estimation and Bayesian models with Gibbs sampling to ensure robustness and methodological rigor. Additionally, a nonhomogeneous model based on the Weibull distribution is introduced to account for time-varying transition rates, providing a more dynamic perspective on disease progression. While the analysis is conducted with simulated data, the framework is adaptable to real-world datasets, offering valuable insights for refining screening policies and optimizing inter-screening intervals.