Number of Animals Required in the Bio-assay of Pathogens.

Experimental designs which prescribe either too few or too many animals per assay are wasteful, and it is important that experimenters in planning bio-assays use the number of animals coDsistent with the statistical precision actually desired in the results. The general philosophical treatment of experimental design, as noted by Fisher (1949), places controls on treatments, treatment combinations, randomization, and replication. Wilson and Miles (1955), in their application of statistics to bacteriology, accept these principles, as do numerous other writers. Experimental designs in the field of bio-assay, as treated by Finney (1952a, b), Bliss (1952), and Perry (1950), are somewhat specialized due to the use of two or more dose levels and of a standard preparation. A satisfactory experimental design for bio-assays estimates a mean effect, a slope, the degree of slope linearity, and some measure of error. To meet this bio-assay requirement at least 3 doses of "standard" and 3 doses of "unknown" culture must be used, as well as a number of animals for each separate dose. Therefore, treatment arrangements including dose, randomization, and total number of animals used are all essential parts of the bio-assay. The results of a bio-assay express the "unknown" in terms of the "standard" by a ratio (called potency ratio) of dosages that manifest equal response from the host. The reliability of this ratio depends upon the length of its confidence interval (Fieller, 1940), a statistic the size of which is dependent upon assay variance, and the total number of animals per assay. The length of the confidence interval of the estimated parameter, therefore, is an objective criterion of the success of the bio-assay, and usually is proportional to the parameter value itself. The number of animals required in a bio-assay to obtain the desired or essential precision must be determined if efficient experimentation is to be conducted. In a collaborative paper evaluating uniformity of response in different strains of animals to pathogenic organisms, we (Lincoln and DeArmon, 1959) determined the number of animals of each strain required to obtain a selected bio-assay precision. This paper derives simple equations useful in estimating the approximate animal requirements for bio-assays generally used in the study of organism pathogenicity. The animal requirements depend primarily upon the desired confidence interval the experimenter wishes to place on a LD50, or the potency ratio as determined either by the quantal or graded response assays. The equations are derived independent of number of doses used and will estimate the approximate total animal requirements per assay; therefore, this number should be proportioned equally among the doses used.