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While there is wide agreement that physical activity is an important component of a healthy lifestyle, it is unclear how many people adhere to public health recommendations on physical activity. The Physical Activity Guidelines (PAG), published by the CDC, provides guidelines to American adults, but it is difficult to assess compliance with these guidelines. The PAG further complicates adherence assessment by recommending activity to occur in at least 10 min bouts. To better understand the measurement capabilities of various instruments to quantify activity, and to propose an approach to evaluate activity relative to the PAG, researchers at Iowa State University administered the Physical Activity Measurement Survey (PAMS) to over 1000 participants in four different Iowa counties. In this paper, we develop a two-part Bayesian measurement error model and apply it to the PAMS data in order to assess compliance with the PAG in the Iowa adult population. The model accurately accounts for the 10 min bout requirement put forth in the PAG. The measurement error model corrects biased estimates and accounts for day-to-day variation in activity. The model is also applied to the nationally representative National Health and Nutrition Examination Survey.

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.