Treatment plan quality control using multivariate control charts

Arkajyoti Roy*, Reisa Widjaja, Min Wang, Dan Cutright, Mahesh Gopalakrishnan, Bharat B. Mittal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Purpose: Statistical process control tools such as control charts were recommended by the American Association of Physicists in Medicine (AAPM) Task Group 218 for radiotherapy quality assurance. However, the tools needed to analyze multivariate, correlated data that are often encountered in treatment plan quality measures, are lacking. In this study, we develop quality control tools that can model multivariate plan quality measures with correlations and account for patient-specific risk factors, without adding a significant burden to clinical workflow. Methods and Materials: A multivariate, quality control chart is developed that includes a risk-adjustment model, Hotelling’s T2 statistic, and principal component analysis (PCA). Principal component analysis accounts for correlations among a set of organ-at-risk (OAR) dose-volume histogram (DVH) points that serves as proxies for plan quality. Risk-adjustment models estimate the principal components from PCA using a set of patient- and treatment-specific risk factors. The resulting residuals from the risk-adjustment models are used to compute the Hotelling’s T2 statistic; the corresponding multivariate control chart is then plotted based on the beta distribution followed by the statistic. Further, the box-cox transformation is used to account for non-normality in DVH points. We investigate the application of the proposed methodology via three multivariate control charts — a conventional chart that ignores risk-adjustment and PCA, a risk-adjusted chart ignoring PCA, and a PCA-based, risk-adjusted chart. These control charts are evaluated on 69 head-and-neck cases. Results: The conventional multivariate control chart fails to account for important patient-specific risk factors, including volumes and cross-sectional areas of the tumor and OARs and distances in-between. This failure leads to a larger number of false alarms. While the multivariate risk-adjusted control chart is able to reduce false alarms, it fails to account for correlations in DVH points. The multivariate PCA-based, risk-adjusted control chart can detect unusual plans after accounting for the correlations. By replanning, improvements are shown on an unusual plan identified by both risk-adjusted methods. Conclusions: The multivariate risk-adjusted control chart developed here enables quality control of plans prior to delivery. This methodology is generic and can be readily applied for other radiotherapy quality assurance protocols, such as gamma analysis pass rates.

Original languageEnglish (US)
Pages (from-to)2118-2126
Number of pages9
JournalMedical Physics
Issue number5
StatePublished - May 2021


  • control chart
  • multivariate
  • quality assurance
  • statistical process control

ASJC Scopus subject areas

  • Biophysics
  • Radiology Nuclear Medicine and imaging


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