On the feasibility of extracting dose–response curves from clinical DVH data using correlation and regression analysis

Abstract

To quantify the ability of correlation and regression analysis to extract the normal lung doseresponse function from dose volume histogram (DVH) and radiation pneumonitis (RP) data. Methods: A local injury model is adopted, in which radiation-induced damage (functional loss) G is the integral of the DVH with function R(D). RP risk is H(G) where H() is the sigmoid cumulative distribution of functional reserve. RP incidence is a Bernoulli function of risk. A homogeneous patient cohort is assumed, allowing non-dose-related factors to be ignored. Clinically realistic DVHs are combined with the injury model to simulate RP data. Results: Correlation analysis is often used to identify a subset of predictor variables that are significantly correlated with outcome, for inclusion in a predictive model. In the local injury model, all DVH metrics VD contribute to damage through the integral with R(D). Correlation analysis therefore has limited value. The subset of VD that are most significantly correlated with incidence varies randomly from trial to trial as a result of random variations in the DVH set, and does not necessarily reveal anything useful about the patient cohort or the underlying biological dose-response relationship. Regression or matrix analysis has the potential to extract R(D) from damage or risk data, provided smoothness regularization is employed. Extraction of R(D) from incidence data was not successful, due to its higher level of statistical variability. Conclusions: To the authors' knowledge, smoothness regularization has not been applied to this problem, so represents a novel approach. Dose-response functions can be successfully extracted from measurements of integral (as opposed to regional) lung damage G, suggesting value in re-visiting available measurements of ventilation, perfusion and radiographic damage. The techniques developed here can potentially be used to extract the dose-response functions of different tissues from multiple types of quantitative volumetric imaging data.