Correcting TG 119 confidence limits

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 ( CL s), which help clinics identify systematic IMRT QA errors and identify outliers. In TG ‐119, the 95% CL s 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. CL s 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 CL s 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 CL s 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 ME s of the gamma and the Gaussian families were compared. Results In this study, the empirical 95% CL s 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 CL s for IMRT QA .