Vuataz L, Sotek J
Mutat Res. 1978 Nov;52(2):211-30. doi: 10.1016/0027-5107(78)90143-4.
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.
已在计算机上模拟了显性致死试验中的实验，以估计在各种模型下β-二项式检验的I型错误率和检验功效。（1）交配比例为1；植入物死亡的概率p在各对之间分布。（2）交配比例大于1；p在雄性中分布，与同一雄性交配的雌性是该雄性提供的p值的二项式观察值。（3）交配比例大于1；p在雌性中分布。对照组和治疗组的植入物平均死亡率分别设定为0.08和0.10，并选择了名义显著性水平等于0.05。还估计了传统卡方检验的I型错误率。这些模拟的一个副产品是β分布参数估计值α和β的行为，这表明在实际的小鼠实验中，p在雌性中分布。我们的结果得出以下建议：对于每组给定数量的动物，应采用大于1的交配比例，并将雄性视为计算的实验单位。对于每组300只和450只动物，对于选定的植入物死亡率2%的增量，检验功效分别达到0.72和0.85。在这些模型下，对于名义水平0.05，传统卡方检验的I型错误率可能会增至0.30。
