A robust approach to establish tolerance limits for the gamma passing rate‐based patient‐specific quality assurance using the heuristic control charts
Authors: Xiao Qing , Bai Long , Li Guangjun , Zhang Xiangbin , Li Zhibin , Duan Lian , Peng Ruilin , Zhong Renming , Wang Qiang , Wang Xuetao , Bai Sen 
Published: November 2021

Purpose

Establishing the tolerance limits of patient‐specific quality assurance (PSQA) processes based on the gamma passing rate (GPR) by using normal statistical process control (SPC) methods involves certain problems. The aim of this study was threefold: (a) to show that the heuristic SPC method can replace the quantile method for establishing tolerance limits in PSQA processes and is more robust, (b) to introduce an iterative procedure of “Identify‐Eliminate‐Recalculate” for establishing the tolerance limits in PSQA processes with unknown states based on retrospective GPRs, and (c) to recommend a workflow to define tolerance limits based on actual clinical retrospective GPRs.

Materials and Methods

A total of 1671 volumetric‐modulated arc therapy (VMAT) pretreatment plans were measured on four linear accelerators (linacs) and analyzed by treatment sites using the GPRs under the 2%/2 mm, 3%/2 mm, and 3%/3 mm criteria. Normality testing was performed using the Anderson‐Darling (AD) statistic and the optimal distributions of GPRs were determined using the Fitter Python package. The iterative “Identify‐Eliminate‐Recalculate” procedure was used to identify the PSQA outliers. The tolerance limits of the initial PSQAs, remaining PSQAs after elimination, and in‐control PSQAs after correction were calculated using the conventional Shewhart method, two transformation methods, three heuristic methods, and two quantile methods. The tolerance limits of PSQA processes with different states for the respective methods, linacs, and treatment sites were comprehensively compared and analyzed.

Results

It was found that 75% of the initial PSQA processes and 63% of the in‐control processes were non‐normal (AD test, p < 0.05). The optimal distributions of GPRs for the initial and in‐control PSQAs varied with different linacs and treatment sites. In the implementation of the “Identify‐Eliminate‐Recalculate” procedure, the quantile methods could not identify the out‐of‐control PSQAs effectively due to the influence of outliers. The tolerance limits of the in‐control PSQAs, calculated using the quantile of optimal fitting distributions, represented the ground truth. The tolerance limits of the in‐control PSQAs and remaining PSQAs after elimination calculated using the heuristic methods were considerably close to the ground truth (the maximum average absolute deviations were 0.50 and 1.03%, respectively). Some transformation failures occurred under both transformation methods. For the in‐control PSQAs at 3%/2 mm gamma criteria, the maximum differences in the tolerance limits for four linacs and different treatment sites were 3.10 and 5.02%, respectively.

Conclusions

The GPR distributions of PSQA processes vary with different linacs and treatment sites but most are skewed. In applying SPC methodologies to PSQA processes, heuristic methods are robust. For in‐control PSQA processes, the tolerance limits calculated by heuristic methods are in good agreement with the ground truth. For unknown PSQA processes, the tolerance limits calculated by the heuristic methods after the iterative “Identify‐Eliminate‐Recalculate” procedure are closest to the ground truth. Setting linac‐ and treatment site‐specific tolerance limits for PSQA processes is necessary for clinical applications.