Optimal design of multifraction assays of colony survival in vivo

Certain fractionation protocols for multifraction in vivo colony assays permit the use of a statistical method to test the hypothesis that equal dose fractions produce equal decrements in cell survival and to obtain an estimate of the number of clonogens initially capable of structure regeneration. The essential requirement is that common doses per fraction be given in two or more regimens consisting of different fraction numbers. It is shown that the accuracy of the method is dependent upon the particular selection of common-dose regimens used in the assay. Calculations with theoretical data were used to determine guidelines for selecting the optimal experimental design. It was found that the fraction number pairs (n, m) which result in observable levels of survival tend to lie in a triangular region when plotted in the plane. Use of regimens corresponding to points along the lower edge of this triangle can substantially improve the results of the statistical method. It was also found to be optimal to use a minimal dose for each regimen, subject to the constraint that survival levels lie in the observable range. An application of the main ideas to data from assays of mouse jejunal crypt cell survival illustrates that use of a near-optimal design would have produced better results with 80 mice than were obtained with 140 mice.