Correcting TG 119 confidence limits

Abstract

Purpose: Task Group 119 (TG-119) has been adopted for evaluating the adequacy of intensity-modulated radiation therapy (IMRT) commissioning and for establishing patient-specific IMRT quality assurance (QA) passing criteria in clinical practice. TG-119 establishes 95% confidence limits (CLs), which help clinics identify systematic IMRT QA errors and identify outliers. In TG-119, the 95% CLs are established by fitting the Gamma Γ analysis passing rate results to an assumed distribution, then calculating the limit in which 95% of the data fall. CLs for a given dataset will depend greatly on the type of distribution used, and those determined by following the TG-119 guidelines are only valid if the underlying data follows a Gaussian distribution. Gaussian distributions assume symmetry about the mean, which would imply the possibility of negative Γ analysis failing rates. This study demonstrates that the gamma distribution is a more reasonable assumption for establishing CLs than the Gaussian distribution used in TG-119. Thus, the gamma distribution is suggested as a replacement to the conventional Gaussian statistical model used in TG-119.

Materials and methods: The moments estimator (ME) for the gamma family is used to obtain the CLs of the failing rates for all Γ analysis criteria. To demonstrate the congruence of the gamma distribution, the root mean squared error and the CL values for the MEs of the gamma and the Gaussian families were compared.

Results: In this study, the empirical 95% CLs generated using 302 plans represent the ground truth, which resulted in a 91.83% passing rate using 3%/3 mm error local criteria. The gamma distribution underestimates the 95% CL by 0.09%, while the Gaussian distribution overestimates the 95% CL by 4.12%.

Conclusions: Although IMRT QA equipment may vary between clinics, the mathematical formalism presented in this study applies to any combination of planning and delivery systems. This study has demonstrated that a gamma distribution should be favored over a Gaussian distribution when establishing CLs for IMRT QA.

Keywords: IMRTQA confidence limits; IMRTQA passing rates; TG 119; TG 119 confidence limits; TG 119 passing rates.