Received: 12 May 2016 Revised: 7 November 2017 Accepted: 12 November 2017
Dynamic prediction in functional concurrent regression
with an application to child growth
Department of Biostatistics, Johns
Hopkins University, Baltimore, MD 21205,
Department of Statistics, North Carolina
State University, Raleigh, NC 27606, USA
School of Medicine, Johns Hopkins
University, Baltimore, MD 21205, USA
Luo Xiao, Department of Statistics, North
Carolina State University, Raleigh, NC
Bill and Melinda Gates Foundation,
Grant/Award Number: OPP1114097 and
OPP1148351; National Institute of Health,
Grant/Award Number: R01NS060910 and
In many studies, it is of interest to predict the future trajectory of subjects based
on their historical data, referred to as dynamic prediction. Mixed effects models
have traditionally been used for dynamic prediction. However, the commonly
used random intercept and slope model is often not sufficiently flexible for
modeling subject-specific trajectories. In addition, there may be useful expo-
sures/predictors of interest that are measured concurrently with the outcome,
complicating dynamic prediction. To address these problems, we propose a
dynamic functional concurrent regression model to handle the case where both
the functional response and the functional predictors are irregularly measured.
Currently, such a model cannot be fit by existing software. We apply the model
to dynamically predict children's length conditional on prior length, weight, and
baseline covariates. Inference on model parameters and subject-specific trajec-
tories is conducted using the mixed effects representation of the proposed model.
An extensive simulation study shows that the dynamic functional regression
model provides more accurate estimation and inference than existing methods.
Methods are supported by fast, flexible, open source software that uses heavily
tested smoothing techniques.
covariance function, face, fPCA, longitudinal data, mixed effects, penalized splines, sparse func-
In many biological and epidemiological studies, sampling is conducted at multiple time points resulting in longitudinal
data that exhibit within-subject correlation. Traditionally, longitudinal data have been analyzed using either marginal
or conditional mixed effect models.
Both approaches are parametric and are not designed to account for subtle
or strong departures from the assumed parametric trends. This problem can manifest in a number of ways in longitudinal
data, including autocorrelation in the residuals of random intercept/slope models.
To address such challenges, one may
consider using methods for functional data, which allow more flexible modeling of subject-specific random curves. A
random functional intercept model can be understood as a special case of a broader class of models referred to as functional
mixed effects models. However, functional mixed models are complex, and the computational burden for fitting them is
A computationally feasible approach to estimating functional mixed effects models is to combine semiparamet-
ric regression techniques
with functional data analysis.
Arguably, the functional mixed effects framework was first
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the
original work is properly cited.
© 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.
1376 wileyonlinelibrary.com/journal/sim Statistics in Medicine. 2018;37:1376–1388.