Multivariable modeling of radiotherapy outcomes, including dose–volume and clinical factors

Purpose: The probability of a specific radiotherapy outcome is typically a complex, unknown function of dosimetric and clinical factors. Current models are usually oversimplified. We describe alternative methods for building multivariable dose–response models.

Methods: Representative data sets of esophagitis and xerostomia are used. We use a logistic regression framework to approximate the treatment–response function. Bootstrap replications are performed to explore variable selection stability. To guard against under/overfitting, we compare several analytical and data-driven methods for model-order estimation. Spearman’s coefficient is used to evaluate performance robustness. Novel graphical displays of variable cross correlations and bootstrap selection are demonstrated.

Results: Bootstrap variable selection techniques improve model building by reducing sample size effects and unveiling variable cross correlations. Inference by resampling and Bayesian approaches produced generally consistent guidance for model order estimation. The optimal esophagitis model consisted of 5 dosimetric/clinical variables. Although the xerostomia model could be improved by combining clinical and dose–volume factors, the improvement would be small.

Conclusions: Prediction of treatment response can be improved by mixing clinical and dose–volume factors. Graphical tools can mitigate the inherent complexity of multivariable modeling. Bootstrap-based variable selection analysis increases the reliability of reported models. Statistical inference methods combined with Spearman’s coefficient provide an efficient approach to estimating optimal model order.

Keywords:  Treatment response modeling , Normal tissue complication probability , Logistic regression , Model selection , Information theory , Radiotherapy