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Mixed‐effects Gaussian process functional regression models with application to dose–response curve prediction
Author(s) -
Shi J.Q.,
Wang B.,
Will E.J.,
West R.M.
Publication year - 2012
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4502
Subject(s) - covariate , nonparametric statistics , gaussian process , nonparametric regression , mixed model , semiparametric regression , kriging , covariance , regression analysis , parametric statistics , semiparametric model , regression , functional data analysis , econometrics , computer science , statistics , mathematics , gaussian , physics , quantum mechanics
We propose a new semiparametric model for functional regression analysis, combining a parametric mixed‐effects model with a nonparametric Gaussian process regression model, namely a mixed‐effects Gaussian process functional regression model. The parametric component can provide explanatory information between the response and the covariates, whereas the nonparametric component can add nonlinearity. We can model the mean and covariance structures simultaneously, combining the information borrowed from other subjects with the information collected from each individual subject. We apply the model to dose–response curves that describe changes in the responses of subjects for differing levels of the dose of a drug or agent and have a wide application in many areas. We illustrate the method for the management of renal anaemia. An individual dose–response curve is improved when more information is included by this mechanism from the subject/patient over time, enabling a patient‐specific treatment regime. Copyright © 2012 John Wiley & Sons, Ltd.