Page 369 - Contributed Paper Session (CPS) - Volume 4

CPS2292 Roger S. Zoh, PhD et al.
1. Introduction
It is estimated that about 20% of the U.S. child population suffer from
obesity and the percentage of childhood obesity has more than tripled in the
last 40 years (CDC, 2017). The consequences of childhood obesity include
reduced healthy physiological, behavioural and psychological development
during childhood. Obesity in children and adolescents also leads to adverse
health outcomes such as type 2 diabetes and cardiovascular diseases in
adulthood. To combat this epidemic, targeted environmental and behavioural
school-based interventions designed to increase physical activity among
school-aged children have gained widespread interest. Examples of these
school-based interventions include activity permissive learning environments
and the use of stand-biased desks in classrooms (Lanningham, 2008;
Benden,2011).
In a recent study, stand-biased desks were introduced to a Texas school
district as a means of increasing school day physical activity. A research
question of interest was to quantify the association between daily energy
expenditure and subsequent progression toward obesity among children. The
children were given accelerometer armbands to approximate their daily
energy expenditure. Since the levels of true daily energy expenditure is not
directly observable, it is calculated as a function of the observed physical
activity behaviour from the devices. In this manuscript, we assume that the
objective measures of energy expenditure obtained from physical activity
monitors are prone to measurement error and develop a method of analysis
that calibrates the measurement error and is easily applicable for assessing
the effects of daily energy expenditure on 18-month change in BMI.
In determining the role of energy expenditure in obesity development
among children, we consider the linear scalar-on-function regression model
with a scalar-valued outcome Y and an imprecisely observed function-valued
covariate, X(t). In this setting, X(t) is a latent function-valued covariate that is
not directly observable. Instead, it is unbiasedly measured by W(t) prone to
some measurement error. Linear scalar-on-function regression models extend
classical regression methods to allow function-valued covariates with scalar-
valued outcomes in regression settings and many statistical methods have
been proposed to estimate the model (Silverman, 2005) when the covariate is
measured with no or negligible error. In this paper, we propose a different
approach to incorporate measurement errors and allow unspecified error
structures. A function-valued instrumental variable belonging in the same
parameter space as X(t) is used for model identification, and the generalized
method of moments-based approach is proposed to consistently estimate the
functional coefficient, $\beta(t)$, in the presence of functional measurement
errors. Our proposed method for functional measurement errors do not treat
the imprecisely observed function-valued covariate as longitudinal or time

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