Direct analysis of quantal radiation response data.

A direct analysis is proposed for quantal (all-or-nothing) responses to fractionated radiation and endpoint-dilution assays of cell survival. As opposed to two-step methods such as the reciprocal-dose technique, in which ED50 values are first estimated for different fractionation schemes and then fit (as reciprocals) against dose per fraction, all raw data are included in a single maximum-likelihood treatment. The method accommodates variations such as short-interval fractionation regimens designed to determine tissue repair kinetics, tissue response to continuous exposures, and data obtained using endpoint-dilution assays of cell survival after fractionated doses. Monte-Carlo techniques were used to compare the direct and reciprocal-dose methods for analysis of small-scale and large-scale studies of response to fractionated doses. Both methods tended toward biased estimates in the analysis of the small-scale (3 fraction numbers) studies. The alpha/beta ratios showed less scatter when estimated by the direct method. Most important, the 95 per cent confidence intervals determined by the direct method were more appropriate than those determined by reciprocal-dose analysis, for which 18 per cent (small-scale study) or 8 per cent (large-scale study) of the confidence intervals did not include the 'true' value of alpha/beta.