Effective simultaneous confidence bands for repeated measurements in linear mixed-effect models

Abstract

Linear mixed-effect (LME) models have been extensively accepted to analyse repeated measurements due to their flexibility and ability to handle subject-specific matters. The inclusion of random effects has resulted in much benefit with respect to estimation, but it is complicated to measure their impact on hypothesis testing. While the same complication is present in the construction of simultaneous confidence bands (SCBs), degrees of freedom (df) for SCBs have rarely been discussed unlike those for test statistics. This motivates us to propose the adoption of approximate df to construct SCBs in LME models. Simulation studies were performed to compare the performances of different calculations for the df. The results of simulations demonstrate the efficacy of the use of approximate df. In addition, our proposal allows linesegment SCBs developed under covariance models to function with LME models. Applications with real longitudinal datasets present consistent results with the simulation study.

Assessing bias, precision, and agreement in method comparison studies

“…This has already been observed by others in the setting of longitudinal data and mixed models. 19,20 However, in these studies focus was on developing confidence bands for the population average curve and not for the individual profiles. Thus, they did not have to deal with the tricky issue of a predicted latent variable as one of the regressors.…”

Use of clinical tolerance limits for assessing agreement

“…This result has already been observed in Taffé 5 and by others in the setting of longitudinal data and mixed models. 18 , 19 However, in the latter studies, the authors did not have to deal with the tricky issues posed by the use of a predicted latent variable as one of the regressors. Further research should strive to improve this.…”