Use of the beta-binomial distribution in dominant-lethal testing for "weak mutagenic activity: part 2.

Experiments in Dominant-Lethal Testing have been simulated on the computer to estimate the type I error rates and the power of the Beta-Binomial test under various models. (1) The mating ratio is one; and p, the probability that an implant will die, is distributed over the couples. (2) The mating ratio is larger than one; and p is distributed over the males, the females mated to the same male being binomial observations of the value p supplied by the male. (3) The mating ratio is larger than one; and p is distributed over the females. The average rates of dead implants have been set at 0.08 and 0.10 for the control and treatment groups, respectively, and a nominal level of significance equal to 0.05 has been chosen. The type I error rate of the traditional chi-square test has also been estimated. A by-product of these simulations is the behaviour of the estimates alpha and beta of the beta-distribution parameters, which discloses that, in the actual experiments with mice, p is distributed over the females. Our results lead to the recommendations that, for a given number of animals per group, a mating ratio larger than one should be adopted and that the males should be considered as the experimental units for the calculations. With 300 and 450 animals per group, average powers of 0.72 and 0.85 are reached, respectively, for the chosen increment of 2% in the rate of dead implants. Under these models, the type I error rate of the traditional chi-square test may grow to 0.30 for the nominal level of 0.05.

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