Prostate cancer: progression of prostate-specific antigen after external beam irradiation

This paper is concerned with the development of a stochastic path of prostate-specific antigen (PSA) level after radiation treatment for prostate cancer. PSA is a biomarker for prostate cancer, higher levels of which indicate the seriousness of the cancer progression. Following the deterministic modeling of the data by the previous authors, Cox et al., this paper is concerned with the theoretical knowledge that could be gained by the stochastic modeling in discrete form of the PSA path over time. The expected value of the PSA level is computed and compared with the deterministic model and it is found that they are the same for about the first year after radiation therapy. The American Society for Therapeutic Radiology has set a consensus panel definition of biochemical failure following radiation therapy: the rise in three consecutive levels of PSA is considered to be a failure of the radiation therapy. Knowledge of the path of PSA presented in this paper would be useful in the management of the radiation treatment and in particular assessing quantitatively any clinically based policy for defining recurrence after radiation therapy. Application of the model is illustrated by fitting it to clinical data available in the University of Michigan cancer center.