Program Information
Bayesian Inference of Local Relapse Data Using a Poisson-Based Tumour Control Probability Model
D La Russa1*, (1) The Ottawa Hospital Cancer Centre, Ottawa, ON
Presentations
SU-E-T-144 (Sunday, July 12, 2015) 3:00 PM - 6:00 PM Room: Exhibit Hall
Purpose: The purpose of this project is to develop a robust method of parameter estimation for a Poisson-based TCP model using Bayesian inference.
Methods: Bayesian inference was performed using the PyMC3 probabilistic programming framework written in Python. A Poisson-based TCP regression model that accounts for clonogen proliferation was fit to observed rates of local relapse as a function of equivalent dose in 2 Gy fractions for a population of 623 stage-I non-small-cell lung cancer patients. The Slice Markov Chain Monte Carlo sampling algorithm was used to sample the posterior distributions, and was initiated using the maximum of the posterior distributions found by optimization. The calculation of TCP with each sample step required integration over the free parameter α, which was performed using an adaptive 24-point Gauss-Legendre quadrature. Convergence was verified via inspection of the trace plot and posterior distribution for each of the fit parameters, as well as with comparisons of the most probable parameter values with their respective maximum likelihood estimates.
Results: Posterior distributions for α, the standard deviation of α (σ), the average tumour cell-doubling time (Td), and the repopulation delay time (Tk), were generated assuming α/β = 10 Gy, and a fixed clonogen density of 10⁷ cm⁻³. Posterior predictive plots generated from samples from these posterior distributions are in excellent agreement with the observed rates of local relapse used in the Bayesian inference. The most probable values of the model parameters also agree well with maximum likelihood estimates.
Conclusion: A robust method of performing Bayesian inference of TCP data using a complex TCP model has been established.
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