Statistical analysis and sample-size determinations for mutagenicity experiments with binomial responses.

Two statistical analyses are studied for their applicability to mutagenicity experiments that produce binomial responses from a control group and a single treated group. Attention is focused on experiments with (1) group sample sizes greater than 500 and (2) a probability less than .05 for a binary observation from any experimental unit being "positive." In addition, it is assumed that historical control data will not be included in the statistical analysis. The first analysis is a conditional binomial test, which has been tabulated extensively by Kastenbaum and Bowman [1970], while the second is based on a standard normal approximation to the distribution of the difference between two sample proportions. A formula is presented for each analysis that relates the associated probability of detecting a mutagen to the mutant frequencies and sample sizes of the two groups. Based on extensive numerical results, the conclusion is drawn that the normal test is the preferred analysis for experiments in which the ratio of the two sample sizes is between 0.80 and 1.25. On the further assumption that an experiment is to be conducted with equal experimental group sample sizes, recommendations are offered for values of this common sample size needed to achieve a specified power, ie, a degree of assurance of detecting a postulated level of mutagenic effect.