Purpose: To investigate the application of power transformations on skewed plan quality measures used by multivariate quality control charts in radiotherapy.
Methods: We compute multivariate risk-adjusted control charts for treatment plan quality control, which employ the resulting residuals of a risk-adjustment model that uses a set of organ-at-risk (OAR) dose-volume histogram (DVH) points as proxies for plan quality. The risk-adjustment model adjusts the DVH points for a set of patient- and treatment-specific risk factors. Given an ordinary least squares (OLS) regression-based risk-adjustment model, an assumption is that the data is normally distributed, which is typically not the case for DVH data. Thus, we employ the Box-Cox transformation that is a power transformation to reduce the impact of skewness in the DVH points. The control charts are evaluated on 69 head-and-neck cases with the brainstem serving as the primary OAR.
Results: In the multivariate control chart with Box-Cox transformation, two patients (43 and 49) are signaled as out-of-control (OC), while the chart without Box-Cox transformation signals three patients (24, 43, and 49) as OC. The DVHs show that patient 49 is a high-quality plan, while patients 24 and 43 are poor quality plans with high brainstem dose. Replanning led to a sizable improvement in patient 43’s brainstem dose while patient 24 could not be improved without sacrificing tumor dose criteria. The risk-adjustment model and the control chart fails to account for the skewed DVH data without the Box-Cox transformation, leading to a false signal for patient 24.
Conclusion: A power transformation is necessary for non-normal DVH data for statistical modeling and quality control. The proposed Box-Cox transformation can scale and adjust the skewness of DVH data, leading to an improved performance of control charts for quality control in radiotherapy.