A direct method for estimating the alpha/beta ratio from quantitative dose-response data.
A one-step optimization method based on a least squares fit of the linear quadratic model to quantitative tissue response data after fractionated irradiation is proposed. Suitable end-points that can be analysed by this method are growth delay, host survival and quantitative biochemical or clinical laboratory data. The functional dependence between the transformed dose xn (dn) = n (alpha dn + beta dn2) and the measured response is approximated by a polynomial. The method allows for the estimation of the alpha/beta ratio and its confidence limits from all observed responses of the different fractionation schedules. Censored data can be included in the analysis. A method to test the appropriateness of the fit is presented. A computer simulation illustrates the method and its accuracy as examplified by the growth delay end point. A comparison with a fit of the linear quadratic model to interpolated isoeffect doses shows the advantages of the direct method.
Stuschke
M
M
Department of Radiotherapy, University of Essen.
D006801:Humans; D011880:Radiotherapy Planning, Computer-Assisted; D011881:Radiotherapy, Computer-Assisted