Functional data analysis in NTCP modeling: A new method to explore the radiation dose-volume effects

Purpose: /Objective(s): To describe a novel method to explore radiation dose-volume effects. Functional data analysis is used to investigate the information contained in differential dose-volume histograms. The method is applied to the normal tissue complication probability modeling of rectal bleeding (RB) for patients irradiated in the prostatic bed by 3-dimensional conformal radiation therapy.

Methods and Materials: Kernel density estimation was used to estimate the individual probability density functions from each of the 141 rectum differential dosevolume histograms. Functional principal component analysis was performed on the estimated probability density functions to explore the variation modes in the dose distribution. The functional principal components were then tested for association with RB using logistic regression adapted to functional covariates (FLR). For comparison, 3 other normal tissue complication probability models were considered: The Lyman-Kutcher-Burman model, logistic model based on standard dosimetric parameters (LM), and logistic model based on multivariate principal component analysis (PCA).

Results: The incidence rate of grade ≥ 2 RB was 14%. V_65Gy was the most predictive factor for the LM (P =.058). The best fit for the Lyman-Kutcher-Burman model was obtained with n = 0.12, m = 0.17, and TD50 = 72.6 Gy. In PCA and FLR, the components that describe the interdependence between the relative volumes exposed at intermediate and high doses were the most correlated to the complication. The FLR parameter function leads to a better understanding of the volume effect by including the treatment specificity in the delivered mechanistic information. For RB grade ≥ 2, patients with advanced age are significantly at risk (odds ratio, 1.123; 95% confidence interval, 1.03-1.22), and the fits of the LM, PCA, and functional principal component analysis models are significantly improved by including this clinical factor.

Conclusion: Functional data analysis provides an attractive method for flexibly estimating the dose-volume effect for normal tissues in external radiation therapy.