  Metabolic Syndrome (MetS) is a serious condition that can be an early warning
sign of heart disease and Type 2 diabetes. MetS is characterized by having
elevated levels of blood pressure, cholesterol, waist circumference, and
fasting glucose. There are many articles in the literature exploring the
relationship between physical activity and MetS, but most do not consider the
measurement error in the physical activity measurements nor the correlations
among the MetS risk factors. Furthermore, previous work has generally treated
MetS as binary, rather than directly modeling the risk factors on their
measured, continuous space. Using data from the National Health and Nutrition
Examination Survey (NHANES), we explore the relationship between minutes of
moderate to vigorous physical activity (MVPA) and MetS risk factors. We
construct a measurement error model for the accelerometry data, and then model
its relationship between MetS risk factors with nonlinear seemingly unrelated
regressions, incorporating dependence among MetS risk factors. The novel
features of this model give the medical research community a new way to
understand relationships between MVPA and MetS. The results of this approach
present the field with a different modeling perspective than previously taken
and suggest future avenues of scientific discovery.
