The Fitting of Multi-Hit Survival Curves

Because of the rapid growth of research in the field of atomic energy for both military and civilian uses, biologists are placing more and more emphasis on the study of the effects of radiation on living organisms. The use of microorganisms in radiation studies has increased steadily since they are in general easier and cheaper to work with than higher forms of life and since the results of such research may be used to define areas of investigation with more expensive material. For the most part data from experiments with microorganisms are survival proportions of cultures exposed to different experimental conditions, frequently varying amounts or intensities of radiation. For this reason the interpretation of survival curves plays a very important role in the field of modern radiobiology. Among research wiTorkers who have realized this fact are Atwood and Norman (1949) wjTho have discussed rather thoroughly the theoretical approach to survival curves from several different points of view. Graphical methods of estimating parameters have been suggested by these and other authors, but the problem of estimating sampling errors seems to have been overlooked. The purpose of this paper is to present some statistical methods for obtaining parameter estimates and their standard errors. Although the analysis of a single-hit curve is simple and straightforward, it will be presented first for completeness.