Lack-of-fit tests for assessing mean structures for continuous dose-response data

We review a range of lack-of-fit tests suitable for assessing the appropriateness of the mean function in dose-response models. The review encompasses both well-known tests and new tests based on recent developments in statistics, which we have extended to the dose-response case. We argue that the classical methods are inadequate in certain situations, where the new tests may be applied. Power comparisons are carried out by means of extensive simulation studies, covering both designs with and without replicates at small and large sample sizes. Three datasets from dose-response applications illustrate differences and similarities between the tests. The results suggest that the new tests perform better and exhibit a wider applicability.