A modified Armitage test for more than a linear trend on proportions

Abstract

The Armitage test for linear trend in proportions can be modified using the multiple marginal model approach for three regression models with arithmetic, ordinal and logarithmic dose scores simultaneously, to be powerful against a wide range of possible dose response relationships. Moreover, it can be used for particular designs in the generalized linear (mixed) model for the three common effect sizes odds ratio, risk ratio and risk difference. The related R package tukeytrend allows simple generalizations, e.g. the analysis 2-by-k table data with a possible plateau shape or analysing overdispersed proportions. The evaluation of further real data examples are available in a vignette to that R package.

Claiming trend in toxicological and pharmacological dose-response studies: an overview on statistical methods and related R-Software

“…Not only the statistical methods are available, but also the corresponding software in form of CRAN packages. A structure like a construction kit was described above, whereby real data assays were evaluated exemplarily (further examples see [21,23,17,24]).…”

“…One can combine the advantages of both Williams (qualitative) and Tukey (quantitative) test by formulating a related joint max-T test [24], since both models belong to the class of linear models and thus the common adjustment by means of mmm is available. This test has the average best balanced power, i.e.…”

“…One connects trend with monotonous, and a downturn effect at high dose(s) is just not monotonous. Here you can use a combination of trend test and test between control and high dose: as an intersection-union tests [33], an union-intersection test with the complete power approach [24] or surprisingly just the simple pairwise (or contrast) test control vs. high dose.…”

“…Proportions are quite common in pharmacology/toxicology, such as microscopic incidences or crude mortality/ tumor rates. For both the Williams-trend test [20] and the Tukey test [24] related GLMmodifications exist, whereas the add-1 correction for common-used small n i can be recommended to control the α-level approximately [43]. Note two very different models.…”

“…Therefore adjusted proportions p * i = y i /n * i are used in the GLM instead of the crude tumor proportions p i = y i /n i . This procedure is available for the Williams test [43] and the Tukey test [24]. As a somewhat extreme example of simultaneous inference, the tumor and mortality data of the US-NTP study on the carcinogenic potential of methyleugenol for the incidence of skin fibromas used [2] (available in the CRAN package MCPAN).…”