Application of Semiparametric Mixed Models and Simultaneous Confidence Bands in a Cardiovascular Safety Experiment with Longitudinal Data

Abstract

Several pharmacological studies involve experiments aimed at testing for a difference between experimental groups wherein the data are longitudinal in nature, frequently with long sequences per subject. Oftentimes, treatment effect, if present, is not constant over time. In such situations, imposing a parametric mean structure can be too complicated and/or restrictive. A more flexible approach is to model the mean using a semiparametric smooth function, estimated using, for example, penalized smoothing splines. We formulate a series of models exhibiting how the group-specific mean profiles could possibly differ. Once an appropriate model is chosen, interest lies in identifying specific time points where the groups differ. For this purpose, we propose the use of simultaneous confidence bands around the fitted models wherein the bands take into account within and between-subject variability, as well as variability arising from smoothing.

Keywords:

• Penalized splines
• Semiparametric mixed models
• Simultaneous confidence bands
• Smoothing

ACKNOWLEDGMENTS

We would like to thank the two anonymous referees for very useful comments and suggestions in an earlier version of this article. The authors gratefully acknowledge the financial support from the IAP research Network P6/03 of the Belgian Government (Belgian Science Policy) and from the Institute for the Promotion of Innovation by Science and Technology (IWT) in Flanders, Belgium.