Does Non-Gaussian Error Distribution Demand a New Approach? A Comparative Cancer Study for Multi-Site Analysis of Setup Margins in Radiotherapy

Authors: Kalyan Mondal, Muskaan NA, Abhijit Mandal, Anuj Vijay, Suresh Yadav, Samrat Dutta, Ganeshkumar Patel

Keywords: NEOPLASM, IMAGE-GUIDED RADIOTHERAPY, UNCERTAINTY ANALYSIS, RADIOTHERAPY SETUP MARGIN, VAN HERK’S FORMALISM

Abstract: Accurate setup margin (SM) estimation is essential in radiotherapy to ensure optimal target coverage and minimize radiation exposure to surrounding healthy tissues. Conventional approaches such as van Herk’s method rely on the assumption of normally distributed setup errors, which may not hold true in clinical scenarios involving small or skewed datasets. This study investigated an alternative, histogram-based method for estimating SMs that does not require Gaussian assumptions. Setup error data from 80 patients across four treatment sites (brain, head and neck, thorax, pelvis) were analyzed retrospectively using electronic portal imaging devices (EPIDs). SMs were calculated using both van Herk’s formula and a non-Gaussian method based on the 90% range of setup errors. Normality of data was assessed through the Shapiro–Wilk test, skewness and kurtosis, and Q–Q plots. The results revealed frequent non-normal distributions, particularly in thorax and pelvic sites, with the histogram-based method consistently producing larger, more conservative SMs. Median SM differences reached up to 3.63 mm, with significant effect sizes in most axes (Cohen’s d > 1.0). These findings indicate that the conventional Gaussian assumption may underestimate margins in certain clinical scenarios. The proposed method may offer improved accuracy for clinics with non-normal uncertainties or limited datasets. Further validation using advanced imaging tools like cone-beam CT is recommended.