Analysis of toxicology of food flavouring

This analysis concerned the toxic effects on mice of a food flavouring additive. Quantics was asked to consider the proposed procedure of Hayashi. Some amendments were necessary; in particular Quantics suggests that:

Using extra historical controls for comparisons with current data may provide more power for the statistical comparisons but has the potential for bias.
The use of the trend test at step 3 is inappropriate if there are no significant results in the initial comparison at step 2. This can affect the overall p values (for example if the trend test was positive but the tests in step 2 were negative.).
The suggested Cochran-Armitage test is for comparing trends in proportions. The experimental design must be carefully considered to ensure that this is the appropriate test. In many instances of this type of trial, this is not strictly the case as at each dose there are a number of separate, independent animals, each of which contributes a proportion. If the numbers of cells examined for toxic effects are pooled and the proportion treated as if it were binomial, the variance may be wrongly estimated by the Cochran-Armitage test because it ignores the animal-to-animal variation.