Page 184 - Contributed Paper Session (CPS) - Volume 4

CPS2169 Carmen D. Tekwe et al.
et al. 2013). However, more complex statistical data reduction techniques such
as functional principal components analysis (FPCA) or polynomial basis
expansions for approximating the mean of the curves data have also been
used (Silverman, et al. 2005). Polynomial basis expansions approximate curves
by describing their shapes by a few main features. Thus, an advantage of using
polynomial splines is that they summarize the information contained within
the curves into basis functions that adequately capture their patterns. Unlike
summary statistics, such as the mean, which accounts for only one source of
variation in the data, each basis function accounts for a different source of
variation in the data. An example of such basis functions includes the B-splines
(deBoors, 1978). B-splines do not assume a specific form for the shape of the
curves but rather they assume that the individual curves can be approximated
by spline functions with random coefficients (Rice, et al. 2001). In Figure 1,
nonparametric smoothing was used to approximate the mean of the SDEE. By
smoothing the mean, we uncover underlying patterns in the data while also
retaining some of its important features (Rice, et al. 2001).
The objectives of this manuscript are two-fold. First, we examine the
relationship between SDEE obtained at baseline and future progression
towards obesity indicated by measures of body mass indexes at 18 months
post-baseline. Secondly, we describe the use of conditional functional quantile
regression models to study the relationship between SDEE and BMI, by
treating SDEE as a curve or functionvalued covariate after adjusting for
relevant socio-demographic variables. Through empirical comparisons, we
determine if results obtained from standard approaches used in obesity
research such as the multiple linear regression provide notably different
results from those obtained from either functional linear regression models or
conditional functional quantile regression models. To the best of our
knowledge, this is the first comparative analyses focused on determining the
usefulness of SDEE as a predictor for subsequent progression towards obesity
among elementary school-aged children. The manuscript is organized as
follows. In the first section, we briefly describe the data from our motivating
example and discuss some limitations of the use of standard regression
approaches to assess the association between objective measures of physical
activity behaviour and BMI. Next, we provide descriptions of statistical models
considered in our applications. We then present the results from our analyses
and end with some concluding remarks.

2. Methodology
The stand-biased desks study was conducted from 2012 to 2014 in three
elementary schools within the College Station Independent School District
(CSISD) (Benden, et al. 2014). The cluster randomized study has been
described elsewhere, but briefly, at the beginning of the 2012-2013 academic

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