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The Tukey trend test: Multiplicity adjustment using multiple marginal models

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  • Frank Schaarschmidt
  • Christian Ritz
  • Ludwig A. Hothorn

Abstract

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.

Suggested Citation

  • Frank Schaarschmidt & Christian Ritz & Ludwig A. Hothorn, 2022. "The Tukey trend test: Multiplicity adjustment using multiple marginal models," Biometrics, The International Biometric Society, vol. 78(2), pages 789-797, June.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:2:p:789-797
    DOI: 10.1111/biom.13442
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    References listed on IDEAS

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    1. Christian Bressen Pipper & Christian Ritz & Hans Bisgaard, 2012. "A versatile method for confirmatory evaluation of the effects of a covariate in multiple models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(2), pages 315-326, March.
    2. Georg Gutjahr & Björn Bornkamp, 2017. "Likelihood ratio tests for a dose-response effect using multiple nonlinear regression models," Biometrics, The International Biometric Society, vol. 73(1), pages 197-205, March.
    3. Hui Quan & Thomas Capizzi, 1999. "Adjusted Regression Trend Test for a Multicenter Clinical Trial," Biometrics, The International Biometric Society, vol. 55(2), pages 460-462, June.
    4. Christian Ritz & Rikke Pilmann Laursen & Camilla Trab Damsgaard, 2017. "Simultaneous inference for multilevel linear mixed models—with an application to a large-scale school meal study," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 295-311, February.
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    6. Signe M. Jensen & Christian Ritz, 2015. "Simultaneous Inference for Model Averaging of Derived Parameters," Risk Analysis, John Wiley & Sons, vol. 35(1), pages 68-76, January.
    7. F. Bretz & J. C. Pinheiro & M. Branson, 2005. "Combining Multiple Comparisons and Modeling Techniques in Dose-Response Studies," Biometrics, The International Biometric Society, vol. 61(3), pages 738-748, September.
    8. Bornkamp, Björn & Pinheiro, José & Bretz, Frank, 2009. "MCPMod: An R Package for the Design and Analysis of Dose-Finding Studies," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i07).
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