Analysis of late effects data using dose-response models: application to human skin telangiectasia data.

The clinical data for skin telangiectasia from previous prospective studies at the Radiotherapy Department in Gothenborg are reanalyzed using two dose-response models - the general formulations of the well known linear-quadratic (LQ) and NSD isoeffect models. Assuming that essentially no repopulation appears in the vessel endothelium for overall treatment times up to 68 days, the alpha/beta-value of 2.75 Gy is obtained for the LQ-model. The time factor is found not to be significant by the NSD-model for the treatment times used (less than or equal to 68 days) at the 95% level of confidence. The estimated value of the exponent of the number of fractions, A, is 0.321. The obtained values of the alpha/beta-ratio and of A show high sensitivity of the vessel endothelium to changes in the dose per fraction. Our results show that within the interval of the number of fractions used, 10-35 fractions, the NSD-model gives predictions comparable to those of the LQ-model. For number of fractions smaller than 5, a high discrepancy occurs between the two models, the NSD-model predicting higher values of the isoeffective total dose. The maximal deviation between the models appears for N = 1; 25% and 27% at the 5 and 50% level of effect, respectively. For large N and especially at low effect probabilities the NSD-model again predicts higher isoeffective doses: the dose predicted by the NSD-model for a regimen with 40 fractions and for 5% probability of telangiectasia is 7.5%, higher than that predicted by the LQ-model. Based on the estimated dose-response curves, considering the telangiectasia as the decisive late tissue effect, the requirement for the combined uncertainty in the dose delivery is estimated between 3 and 4.5%.