The Tukey trend test: Multiplicity adjustment using multiple marginal models

Frank Schaarschmidt*, Christian Ritz, Ludwig A Hothorn

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


In dose–response analysis, it is a challenge to choose appropriate linear or curvilinear shapes when considering multiple, differently scaled endpoints. It has been proposed to fit several marginal regression models that try sets of different transformations of the dose levels as explanatory variables for each endpoint. However, the multiple testing problem underlying this approach, involving correlated parameter estimates for the dose effect between and within endpoints, could only be adjusted heuristically. An asymptotic correction for multiple testing can be derived from the score functions of the marginal regression models. Based on a multivariate t-distribution, the correction provides a one-step adjustment of p-values that accounts for the correlation between estimates from different marginal models. The advantages of the proposed methodology are demonstrated through three example datasets, involving generalized linear models with differently scaled endpoints, differing covariates, and a mixed effect model and through simulation results. The methodology is implemented in an R package.

Original languageEnglish
Issue number2
Pages (from-to)789-797
Publication statusPublished - Jun 2022
Externally publishedYes


  • adjustment of p-values
  • dose–response
  • multiple endpoints
  • multivariate normal
  • toxicology
  • Multivariate Analysis
  • Computer Simulation
  • Linear Models
  • Models, Statistical


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