  There are very different statistical methods for demonstrating a trend in
pharmacological experiments. Here, the focus is on sparse models with only one
parameter to be estimated and interpreted: the increase in the regression model
and the difference to control in the contrast model. This provides both
p-values and confidence intervals for an appropriate effect size. A combined
test consisting of the Tukey regression approach and the multiple contrast test
according to Williams is recommended, which can be generalized to the
generalized linear (mixed effect) model. Thus numerous variable types occurring
in pharmacology/toxicology can be adequately evaluated. Software is available
through CRAN packages. The most significant limitation of this approach is for
designs with very small sample sizes, often in pharmacology/toxicology.
