Statistical evaluation of toxicological assays: Dunnett or Williams test-take both

The US National Toxicology Program recommends the use of the parametric multiple comparison procedures of Dunnett and Williams for the evaluation of repeated toxicity studies. For endpoints where either increasing or decreasing effects are of toxicological relevance, we recommend the use of the two-sided Dunnett test exclusively. For the many other endpoints, where a priori only one direction is of toxicological relevance, however, we recommend the combination of Dunnett and Williams test. In particular, we recommend the so-called Umbrella-protected Williams test which offers insights for all interesting monotone and non-monotone alternatives while only suffering a marginal loss in power compared to the Dunnett test. We illustrate the power difference analytically and compare the approach for different endpoint types using three real data examples to alternative tests available. Nonparametric tests, which are suitable for the evaluation of skewed distributed or scores data, are also considered. Particular attention is given to the different interpretations of the findings revealed by the different test. R programs used for the analyses are provided.