×

Simultaneous confidence intervals for ratios of fixed effect parameters in linear mixed models. (English) Zbl 1346.62054

Summary: In multiple comparisons of fixed effect parameters in linear mixed models, treatment effects can be reported as relative changes or ratios. Simultaneous confidence intervals for such ratios had been previously proposed based on Bonferroni adjustments or multivariate normal quantiles accounting for the correlation among the multiple contrasts. We propose Fieller-type intervals using multivariate t quantiles and the application of Markov chain Monte Carlo techniques to sample from the joint posterior distribution and construct percentile-based simultaneous intervals. The methods are compared in a simulation study including bioassay problems with random intercepts and slopes, repeated measurements designs, and multicenter clinical trials.

MSC:

62F25 Parametric tolerance and confidence regions
62J15 Paired and multiple comparisons; multiple testing

Software:

R; mvtnorm; nlme; mratios
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1214/ss/1177010123 · Zbl 0955.62552 · doi:10.1214/ss/1177010123
[2] Browne W.J., Bayesian Analysis 1 pp 437– (2005)
[3] DOI: 10.1016/j.jspi.2004.11.009 · Zbl 1090.62071 · doi:10.1016/j.jspi.2004.11.009
[4] DOI: 10.1080/03610920902859607 · Zbl 1188.62303 · doi:10.1080/03610920902859607
[5] Djira G.D., mratios: Inferences for ratios of coefficients in the general linear model (2012)
[6] DOI: 10.1214/06-BA117A · Zbl 1331.62139 · doi:10.1214/06-BA117A
[7] Gelman A., Data Analysis Using Regression and Multilevel Hierarchical Models. (2007)
[8] Genz A., mvtnorm: Multivariate normal and t distributions (2010)
[9] DOI: 10.1002/bimj.200610333 · doi:10.1002/bimj.200610333
[10] Littell R.C., SAS System for Mixed Models. (1996)
[11] DOI: 10.1198/000313005X70605 · Zbl 05680657 · doi:10.1198/000313005X70605
[12] DOI: 10.1002/sim.1450 · doi:10.1002/sim.1450
[13] Pinheiro J., nlme: Linear and nonlinear mixed effects models (2010)
[14] DOI: 10.1007/978-1-4419-0318-1 · doi:10.1007/978-1-4419-0318-1
[15] R: A language and environment for statistical computing (2010)
[16] Spiegelhalter D., OpenBUGS (2007)
[17] DOI: 10.18637/jss.v012.i03 · doi:10.18637/jss.v012.i03
[18] Verbeke G., Linear Mixed Models For Longitudinal Data. (2000) · Zbl 0956.62055
[19] DOI: 10.2307/2533546 · Zbl 1130.62351 · doi:10.2307/2533546
[20] DOI: 10.1080/00031305.1978.10479267 · doi:10.1080/00031305.1978.10479267
[21] DOI: 10.1214/088342306000000015 · Zbl 1129.62063 · doi:10.1214/088342306000000015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.