An application of Bayesian statistical methods to adaptive radiotherapy

In adaptive radiotherapy, measured patient-specific setup variations are used to modify the patient setup and treatment plan, potentially many times during the treatment course. To estimate the setup adjustments and re-plan the treatment, the measured data are usually processed using Kalman filtering or by computing running averages. We propose, as an alternative, the use of Bayesian statistical methods, which combine a population (prior) distribution of systematic and random setup errors with the measurements to determine a patient-specific (posterior) probability distribution. The posterior distribution can either be used directly in the re-planning of the treatment or in the generation of statistics needed for adjustments. Based on the assumption that day-to-day setup variations are independent and identically distributed Normal distributions, we can efficiently compute parameters of the posterior distribution from parameters of the prior distribution and statistics of the measurements. We illustrate a simple procedure to apply the method in practice to adaptive radiotherapy, allowing for multiple adjustments of treatment parameters during the course of treatment.