Research Article
A Stochastic Framework for Evaluation of Prostate Cancer Progression and Treatment Dynamics
Philip de Melo*
,
Marie St. Rose
Issue:
Volume 14, Issue 2, June 2026
Pages:
17-29
Received:
24 March 2026
Accepted:
7 April 2026
Published:
24 April 2026
Abstract: Prostate cancer progression is inherently heterogeneous, driven by complex interactions among tumor biology, patient-specific factors, and treatment response. Existing deterministic models inadequately capture this variability, limiting their ability to represent the stochastic nature of disease evolution and to support reliable prediction in clinical settings. This study introduces a probabilistic framework for modeling prostate cancer progression based on the Fokker–Planck equation, which governs the temporal evolution of the probability density of a latent disease state. The latent state, associated with tumor burden and prostate-specific antigen (PSA) dynamics, evolves under the combined influence of deterministic and stochastic processes. The drift term characterizes tumor growth and therapeutic effects, while the diffusion term captures intrinsic biological variability arising from genetic mutations, microenvironmental conditions, and inter-patient heterogeneity. Numerical simulations demonstrate the evolution of disease-state distributions under varying treatment scenarios, highlighting the ability of the proposed framework to capture a spectrum of plausible trajectories rather than a single deterministic outcome. This enables a more realistic representation of disease progression and treatment response at both individual and population levels. The proposed approach provides a principled foundation for integrating stochastic tumor dynamics with clinical biomarkers and therapeutic interventions. By moving beyond deterministic assumptions, it supports the development of predictive, patient-specific models and advances the application of probabilistic reasoning in oncology and health informatics.
Abstract: Prostate cancer progression is inherently heterogeneous, driven by complex interactions among tumor biology, patient-specific factors, and treatment response. Existing deterministic models inadequately capture this variability, limiting their ability to represent the stochastic nature of disease evolution and to support reliable prediction in clini...
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Research Article
An AI-driven Framework for Evaluating Prostate Cancer Progression
Philip de Melo*
Issue:
Volume 14, Issue 2, June 2026
Pages:
30-41
Received:
7 April 2026
Accepted:
24 April 2026
Published:
12 May 2026
DOI:
10.11648/j.crj.20261402.12
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Views:
Abstract: Prostate cancer progression is a complex and heterogeneous process that cannot be fully captured by deterministic models or by reliance on a single biomarker such as prostate-specific antigen (PSA). While PSA is widely used in clinical practice, it provides an incomplete and sometimes misleading representation of the underlying tumor dynamics, particularly in cases of low PSA but significant disease burden or during treatment response. In this study, we utilize anonymous clinical data from prostate cancer patients and propose a stochastic modeling framework to characterize the temporal evolution of prostate cancer as a complex process, incorporating both deterministic biological mechanisms and stochastic variability across patients. The proposed model introduces a latent disease state representing tumor burden, which evolves according to drift and diffusion components reflecting tumor growth, treatment effects, and intrinsic biological uncertainty. In addition to PSA, key clinical variables such as Gleason grade group, disease stage, and treatment exposure are integrated into the model to enhance its clinical interpretability and predictive capability. Numerical simulations demonstrate that the stochastic framework captures clinically meaningful behaviors, including heterogeneous progression trajectories, treatment-induced declines in PSA, and divergence between observed PSA levels and true disease burden. Unlike traditional survival or regression-based approaches, the model provides a full probability distribution of disease states over time, allowing for uncertainty quantification and personalized risk assessment. The results suggest that incorporating latent-state stochastic dynamics can significantly improve the understanding and prediction of prostate cancer progression, offering a foundation for next-generation decision-support systems in precision oncology.
Abstract: Prostate cancer progression is a complex and heterogeneous process that cannot be fully captured by deterministic models or by reliance on a single biomarker such as prostate-specific antigen (PSA). While PSA is widely used in clinical practice, it provides an incomplete and sometimes misleading representation of the underlying tumor dynamics, part...
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