Bayesian Nonparametric Regression Analysis of Data with Random Effects Covariates from Longitudinal Measurements

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 u...

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Bibliographic Details
Published in:Biometrics 2011-06, Vol.67 (2), p.454-466
Main Authors: Ryu, Duchwan, Li, Erning, Mallick, Bani K.
Format: Article
Language:English
Subjects:
Adult
Adulthood
Age Factors
Bayes Theorem
Bayesian analysis
Bayesian nonparametric regression
Bioinformatics
BIOMETRIC METHODOLOGY
Biometrics
Biometry - methods
Body mass index
Child
Childhood
Computer Simulation
Data augmentation
Data smoothing
Generalized additive model
Humans
Linear Models
Linear regression
Longitudinal data
Longitudinal Studies
Markov Chains
Mathematical models
Measurement error
Monte Carlo Method
Nonparametric models
Obesity
Regression Analysis
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Summary: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.
ISSN:0006-341X
1541-0420
DOI:10.1111/j.1541-0420.2010.01489.x