A Random Intercepts–Functional Slopes Model for Flexible Assessment of Susceptibility in Longitudinal Designs
Article first published online: 21 JUL 2010
© 2010, The International Biometric Society
Volume 67, Issue 2, pages 486–494, June 2011
How to Cite
Coull, B. A. (2011), A Random Intercepts–Functional Slopes Model for Flexible Assessment of Susceptibility in Longitudinal Designs. Biometrics, 67: 486–494. doi: 10.1111/j.1541-0420.2010.01461.x
- Issue published online: 20 JUN 2011
- Article first published online: 21 JUL 2010
- Received October 2008. Revised February 2010. Accepted March 2010.
- Laird–Ware model;
- Latent variable;
- Penalized spline;
- Random intercepts–random slopes model;
- Semiparametric regression
Summary In many biomedical investigations, a primary goal is the identification of subjects who are susceptible to a given exposure or treatment of interest. We focus on methods for addressing this question in longitudinal studies when interest focuses on relating susceptibility to a subject's baseline or mean outcome level. In this context, we propose a random intercepts–functional slopes model that relaxes the assumption of linear association between random coefficients in existing mixed models and yields an estimate of the functional form of this relationship. We propose a penalized spline formulation for the nonparametric function that represents this relationship, and implement a fully Bayesian approach to model fitting. We investigate the frequentist performance of our method via simulation, and apply the model to data on the effects of particulate matter on coronary blood flow from an animal toxicology study. The general principles introduced here apply more broadly to settings in which interest focuses on the relationship between baseline and change over time.