The bootstrap method to improve statistical analysis of dosimetric data for radiotherapy outcomes

Abstract

Purpose: The purpose of this study is to validate a new technique in radiotherapy, the medical physicist needs to evaluate the dosimetric benefit and the risk of toxicity before integrating it in the clinical use. Methods: We validate a sound decision tool based on bootstrap method to help the radio oncologist and the medical physicist to usefully analyze the dosimetric data obtained from small-sized samples, with few patients. Statistical investigation principles are presented in the framework of a clinical example based on 36 patients with 6 different cancer sites treated with radiotherapy. For each patient, two treatment plans were generated. In plan 1, the dose was calculated using Modified Batho's (MB) density correction method integrated with pencil beam convolution (PBC) as type (a) algorithm. In plan 2, the dose was calculated using Anisotropic Analytical Algorithm (AAA) as type (b) algorithm. The delivered doses in monitor units (MUs) were compared using the two plans. Then, the bootstrap method was applied to the original data set to assess the dose differences and evaluate the impact of sample size on the 95% confidence interval (95%.CI). Shapiro-Wilks and Wilcoxon signed-rank tests were used to assess the normality of the data and determine the p-value. In addition, Spearman’s rank test was used to calculate the correlation coefficient between the doses calculated with both algorithms. Results: A significant difference was observed between AAA and MB for all tested radiation sites. Spearman’s test indicated a good correlation between the doses calculated with both methods. The bootstrap simulation with 1000 random samplings can be used for small populations with n = 10 and provides a true estimation. Conclusion: one must be cautious when implementing this method for radiotherapy: the data should be representative of the real variations of the cases and the cases should be as homogeneous as possible to avoid bias of over/under estimation of the results.