A stochastic model for prostate-specific antigen levels
prostate-specific antigen (PSA), prostate cancer, ontinuous stochastic model, deterministic model, stochastic differential equation, Chapman–Kolmogorov partial differential equation, exponential decay, method of images, radiotherapy, sensitivity analysis
We introduce a continuous stochastic model for the prostate-specific antigen (PSA) levels following radiotherapy and derive solutions for the associated partial differential (Kolmogorov–Chapman) equation. The solutions describe the evolution of the time-dependent density for PSA levels which take into account an absorbing condition along the boundary and various initial conditions. We include implications for single-dose and multi-dose radiation treatment regimens and discuss parameter estimation and sensitivity issues.