Simultaneous Confidence Intervals for Ratios of Fixed Effect Parameters in Linear Mixed Models

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.