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A Bayesian Markov Framework for Modeling Breast Cancer Progression

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  • Tong Wu

    (Department of Management Science and Information Systems, College of Management, University of Massachusetts Boston, Boston, MA 02125, USA)

Abstract

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.

Suggested Citation

  • Tong Wu, 2024. "A Bayesian Markov Framework for Modeling Breast Cancer Progression," Mathematics, MDPI, vol. 13(1), pages 1-31, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:65-:d:1554872
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    References listed on IDEAS

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    1. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    2. Grace Hui-Min Wu & Shu-Hui Chang & Tony Hsiu-Hsi Chen, 2008. "A Bayesian Random-Effects Markov Model for Tumor Progression in Women with a Family History of Breast Cancer," Biometrics, The International Biometric Society, vol. 64(4), pages 1231-1237, December.
    3. Tony H. H. Chen & H. S. Kuo & M. F. Yen & M. S. Lai & L. Tabar & S. W. Duffy, 2000. "Estimation of Sojourn Time in Chronic Disease Screening Without Data on Interval Cases," Biometrics, The International Biometric Society, vol. 56(1), pages 167-172, March.
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