Use of statistical approaches to improve the quality control of the dose delivery in radiotherapy.

The gamma index is a measure used routinely for the quality control of dose delivery in radiotherapy, implemented in commercial systems for the verification of treatment plans. It involves comparison of the difference between planned and delivered doses to a single reference. The same reference value is selected for all points in the plan that can potentially hide dose delivery errors, especially in medium and low dose areas. In this study, a receiver operating characteristic analysis is used to demonstrate the limits of the performance of the global gamma index as a method for detecting dose delivery errors. The performance of a global gamma index is compared with two approaches based on statistical tests for outlier detection. Two statistical approaches are considered: according to the first, the distribution of the delivered doses is estimated based on an appropriate calibration procedure. According to the second, the distribution of the delivered doses is estimated based on the detection of relatively homogeneous regions of a plan and analyzing the distributions of planned doses within these regions. The performance of the three approaches is compared based on analytical considerations and in simulations in which errors are intentionally introduced to the plan delivery and noise related to dose delivery is modeled. We have shown that a statistics-based approach to gamma analysis generally leads to better detection of true delivery errors. The results of analytical consideration coincide with the simulations. In simulations, we observe that both statistical approaches are better detectors of true delivery errors than the global method for the gamma-index passing rate in the range from 0.9-1.0. It is shown that the global gamma index is a weak detector of dose delivery errors, which in some circumstances behaves only slightly better than a purely random classifier.