  Purpose: To quantify the ability of correlation and regression analysis to
extract the normal lung dose-response function from dose volume histogram (DVH)
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 predictor variables that are
correlated with outcome, for inclusion in a predictive model. In the local
injury model, all DVH metrics VD contribute to damage. Correlation analysis
therefore has limited value. The subset of VD significantly correlated with
incidence varies randomly from trial to trial due to 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 can 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 author's 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.
