Details
| Original language | English |
|---|---|
| Pages (from-to) | 609-628 |
| Number of pages | 20 |
| Journal | Statistical Methods and Applications |
| Volume | 26 |
| Issue number | 4 |
| Publication status | Published - 20 Jun 2017 |
Abstract
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.
Keywords
- Confidence bands, Generalized linear model, Multiple contrasts, Multiple ratios, Simultaneous confidence intervals, Treatment covariate interaction
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Statistical Methods and Applications, Vol. 26, No. 4, 20.06.2017, p. 609-628.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Multiple treatment comparisons in analysis of covariance with interaction
T2 - SCI for treatment covariate interaction
AU - Schaarschmidt, Frank
N1 - Funding information: 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.
PY - 2017/6/20
Y1 - 2017/6/20
N2 - 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.
AB - 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.
KW - Confidence bands
KW - Generalized linear model
KW - Multiple contrasts
KW - Multiple ratios
KW - Simultaneous confidence intervals
KW - Treatment covariate interaction
UR - http://www.scopus.com/inward/record.url?scp=85021171102&partnerID=8YFLogxK
U2 - 10.1007/s10260-017-0383-1
DO - 10.1007/s10260-017-0383-1
M3 - Article
AN - SCOPUS:85021171102
VL - 26
SP - 609
EP - 628
JO - Statistical Methods and Applications
JF - Statistical Methods and Applications
SN - 1618-2510
IS - 4
ER -