We consider nonparametric regression analysis in a generalized linear model (GLM) framework for data with covariates that are the subject-specific random effects of longitudinal measurements. The usual assumption that the effects of the longitudinal covariate processes are linear in the GLM may be unrealistic and if this happens it can cast doubt on the inference of observed covariate effects. Allowing the regression functions to be unknown, we propose to apply Bayesian nonparametric methods including cubic smoothing splines or P-splines for the possible nonlinearity and use an additive model in this complex setting. To improve computational efficiency, we propose the use of data-augmentation schemes. The approach allows flexible covariance structures for the random effects and within-subject measurement errors of the longitudinal processes. The posterior model space is explored through a Markov chain Monte Carlo (MCMC) sampler. The proposed methods are illustrated and compared to other approaches, the "naive" approach and the regression calibration, via simulations and by an application that investigates the relationship between obesity in adulthood and childhood growth curves. © 2010, The International Biometric Society.
|Original language||English (US)|
|Number of pages||13|
|State||Published - Sep 28 2010|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The research of D. Ryu and B. Mallick was partially supported by Award Number KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST), and was partially supported by the DOE NNSA under the Predictive Science Academic Alliances Program by grant DE-FC52-08NA28616. B. Mallick's research was also partially supported by National Science Foundation grant NSF DMS 0914951 and National Cancer Institute grant CA 57030. The authors are thankful to M. Pepe and K. Seidel for the child growth data, and S. Berry for the Fortran source code of the Bayesian smoothing splines.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.