Multiple treatment comparisons in analysis of covariance with interaction
- 179 Downloads
When multiple treatments are analyzed together with a covariate, a treatment-covariate interaction complicates the interpretation of the treatment effects. The construction of simultaneous confidence bands for differences of the treatment specific regression lines is one option to proceed. The application of these methods is difficult because they are described as a collection of special cases and the implementation requires additional programming or relies on non-standard or proprietary software. If inferential interest can be restricted to a pre-specified set of covariate values, a flexible alternative is to compute simultaneous confidence intervals for multiple contrasts of the treatment effects over this grid. This approach is available in the R software: next to treatment differences in the linear model, approximate simultaneous confidence intervals for ratios of expected values and asymptotic extensions to generalized linear models are straightforward. The paper summarizes the available methodology and presents three case studies to illustrate the application to different models, differences and ratios, as well as different types of between treatment comparisons. Simulation studies in the general linear model, for different parameters and different types of comparisons are provided. The R code to reproduce the case studies and a hint to a related R package is provided.
KeywordsMultiple contrasts Simultaneous confidence intervals Treatment covariate interaction Generalized linear model Multiple ratios Confidence bands
I thank Prof. L.A. Hothorn, Dr. M. Hasler and two anonymous referees for their helpful comments on earlier versions of the manuscript. The work was partly supported by the German Science Foundation Grant DFG-HO1687.
- Djira GD, Hasler M, Gerhard D, Schaarschmidt F (2011) mratios: inferences for ratios of coefficients in the general linear model. R package version 1(3):16Google Scholar
- Genz A, Bretz F, Miwa T, Mi X, Leisch F, Scheipl F, Hothorn T (2011) mvtnorm: multivariate normal and t distributions. R package version 0.9-9991Google Scholar
- Core Team R (2014) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, AustriaGoogle Scholar
- Westfall PH, Tobias RD, Wolfinger RD (2011) Multiple comparisons and multiple tests using SAS, 2nd edn. SAS Institute Inc, CaryGoogle Scholar