Treatment plan quality control using multivariate control charts

Abstract

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 T 2 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 T 2 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 chartsa 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.

Phase I quality control framework for monitoring organ-at-risk dose

“…where R i is the vector containing the residual of patient i, ̅ R is the vector containing the mean of the residuals across all patients, and S is the covariance matrix [5,10]. The Hotelling's T 2 statistic is a measure of the distance between a residual and ̅ R [11].…”

“…Evaluating a plan by comparing DVH points to established dose tolerances has limitations. First, this evaluation method does not consider variations in patient anatomies and treatment histories, and without accounting for these variations, treatment plans cannot be compared with one another or to established dose tolerances [5]. Second, evaluating individual DVH points does not fully evaluate the structure, and reviewing many points individually is time-consuming and resource-intensive.…”

“…Second, evaluating individual DVH points does not fully evaluate the structure, and reviewing many points individually is time-consuming and resource-intensive. Considering these limitations, Roy et al [5]. developed a multivariate risk-adjusted Hotelling's T 2 control chart, which accounts for variations in patient anatomies and treatment histories when monitoring plan quality.…”

“…developed a multivariate risk-adjusted Hotelling's T 2 control chart, which accounts for variations in patient anatomies and treatment histories when monitoring plan quality. However, this control chart is limited in identifying all patients receiving extreme OAR doses due to the underlying distributional assumption of normality [5,6]. When the distribution of DVH points deviate from this assumption, this control chart may incorrectly signal poor quality plans to be acceptable.…”

How can we champion diversity, equity and inclusion within Lean Six Sigma? Practical suggestions for quality improvement

“…A move towards incorporating multivariate control charts (where multiple measures of performance reflect diversity, such as Hotelling’s T 2 chart) may be more appropriate than conventional control charts alone. Alternatively, other statistics like cumulative sum (CUSUM) and estimated weighted moving average may be more sensitive for detecting changes in smaller subpopulations 15. While the context, setting and scope will help determine the specific variables and select which multivariate chart is most appropriate, we can envision control charts that holistically combine means for different aspects of inclusivity (access to care, healthcare outcomes, patient satisfaction, etc).…”