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Correcting TG 119 Confidence Interval Formalism Using Bayesian Statistics

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V Kearney

v kearney*, T Solberg , G Valdes , UCSF Comprehensive Cancer Center, San Francisco, CA


SU-E-FS2-3 (Sunday, July 30, 2017) 1:00 PM - 1:55 PM Room: Four Seasons 2

Purpose: TG-119 establishes 95% confidence intervals (CI)s, which help clinics identify systematic IMRT QA errors and identify outliers. The 95% CIs are established by fitting the Gamma analysis diode passing rate results to a parametric distribution, then calculating the interval for which 95% of the data falls within. CIs for a given data set will depend greatly on the type of distribution used. CIs calculated using the TG-119 guidelines, are only valid if the underlying data follows a Gaussian distribution. However, Gaussian distributions assume symmetry about the mean, which would imply negative Gamma analysis diode failing rates. This study, demonstrates theoretically and experimentally, that the gamma Γ function distribution is a reasonable assumption for establishing CIs, and that the Gaussian distribution used in TG-119 is not. The Γ distribution is suggested as replacements to the conventional Gaussian statistical model used in TG-119.

Methods: In discrete counting statistics, a negative binomial or a Poisson distribution is often assumed. Following conventional counting statistics, it is then reasonable to model the number of diodes that fail in each plan using the Poisson formalism. If a Poisson distribution is assumed for the number of diodes that fail, then it can be proven mathematically that the diode failing rate follows a Γ distribution, which is conjugate to the Poisson distribution.

Results: In this study, the empirical 95% CIs generated using 302 plans represented the ground truth, which resulted in a 91.83% passing rate for the 3mm-3% error criteria. The Γ distributions underestimated the 95% CI by 0.09%, and the Gaussian distribution overestimated the 95% CI by 4.12%.

Conclusion: Although IMRTQA equipment may vary between clinics, the mathematical formalism presented in this study applies to any combination of TPSs and delivery systems and should be adopted by every clinic to determine which plans are outliers.

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