Tests for the fit of the linear-quadratic model to radiation isoeffect data

The linear-quadratic (LQ) model for cell survival is frequently extended to describe multifraction isoeffect data via the formula: ln(response) = -n(alpha d + beta d2), where d is the dose per fraction and n is the number of fractions. However, estimates of the quantity "alpha/beta" derived from such data are meaningless unless the use of the model is justified. Two methods are proposed for testing the fit of the multifraction LQ model to isoeffect data. If the use of the model cannot be rejected, each method also provides a new technique for estimating alpha/beta. The two methods are applied to published data from spleen, kidney, and colon. In each case, consistent results are obtained from the two methods concerning the quality of the fit.