Some methodological problems in estimating radiobiological parameters from clinical data. Alpha/beta ratios and electron RBE for cutaneous reactions in patients treated with postmastectomy radiotherapy.

A number of biological, dosimetric, and statistical problems encountered in the determination of alpha/beta ratios and the relative biological efficiency (RBE) of high energy electrons are discussed. The analysis is based on isoeffect dose determination from logit analysis of dose-response data. Monte Carlo simulations of the logit analysis show that the estimated isoeffect dose may be treated as a normally distributed random variable. Under this assumption, formulae for the standard error of the derived radiobiological parameters are presented. The importance of specifying not only parameter estimates but also their confidence limits is emphasized. As a practical example, the dose-response relationships for severe erythema and subcutaneous fibrosis are discussed in two series of patients treated with postmastectomy irradiation with electrons and photons in two fractionation schedules. Because of a different dose per fraction in the electron and photon fields, a determination of RBE requires a fraction size correction. This is performed using the alpha/beta formalism. The present analysis suggests a high energy electron RBE for severe erythema of 0.93 (95% confidence limits 0.89 and 0.96) and for subcutaneous fibrosis of 0.84 (95% confidence limits 0.77 and 0.92).