Statistical approach to the selection of the tolerances for distance to agreement improves the quality control of the dose delivery in radiotherapy

Abstract

In the study, a local approach to setting reference tolerance values for the distance-to-agreement (DTA) component of the gamma index is proposed. The reference tolerance values are calculated in simulations, following a dose delivery model presented in a previous work. An analytical model for determining the quantiles of DTA distribution is also proposed and verified. It is shown that the distributions of DTA values normalized with either quantiles or standard deviation of DTA distributions are universal over analyzed plans and points within a single plan. This enables statistically sound inference about the quality of dose delivery. In particular, based on the normalized distributions the comparison of planned and delivered doses can be formulated within the framework of statistical inference as a problem of multiple statistical testing. For every evaluated point P of a plan, one may formulate and test a null hypothesis that there is no delivery error against an alternative hypothesis that there is a delivery error in P. It is also shown that the proposed approach is more sensitive than the current standard approach to shift errors in high dose gradient regions.