An examination of some dose-time relationships in therapeutic radiology

Abstract

We have compared three representations of dose-time (or fraction number) relations in radiation therapy on published data for cancer of the breast, Hodgkin's disease, squamous cell carcinoma of the aerodigestive tract, and pericardial effusion. The comparison was on the basis of how well each representation separated the two groups of outcomes, success or failure, in each clinical series. As a measure of separation we have used a dimensionless coefficient and calculated its value as a function of the choice of recovery coefficient in the Strandqvist relations and for the Ellis formula. In general, the Strandqvist relations with an optimal value of the recovery coefficient—defined as that value which produces the maximum separation of the two groups of outcomes—give a better separation than the Ellis formula. Our method of analysis provides a unique procedure for estimating the best value for the recovery coefficient. More importantly, it shows whether the separation is sensitive to the choice of recovery coefficient. The analysis shows that the separations are poor for the data on head and neck tumours regardless of the choice of recovery coefficient and that pericardial effusion is produced when a threshold physical dose is exceeded regardless of the time and fraction number over which it is delivered. The separation coefficient shows a marked maximum when computed for data on breast cancer at values of the recovery coefficient of 0·35 (Cohen's data) or 0·40 (Friedman's data), and for the data for Hodgkin's disease at a recovery coefficient of 0·15. When treatment time and fraction number are strongly correlated, the separation coefficient is identical whether treatment time or fraction number is used in calculating the Strandqvist relations. When they are not strongly correlated, calculations based on fraction number give a better separation than those based on treatment time.