Modelling Obesity as a Function of Weekly Physical Activity Profiles Measured by ActiGraph Accelerometers

Introduction Epidemiological studies for investigating physical activity as a predictor for a health outcome such as obesity often use average daily moderate to vigorous physical activity (MVPA) as a summary of the highly dimensional actigraph measurements. The problem with using a single summary statistics such as MVPA is that it ignores the pattern of the physical activity measurements. In addition, it relies on setting cut-points for moderate and vigorous activity with the cut-points being arbitrary or based on expensive calibration studies. Also, cut-points may change with age. Our objective is develop a statistical tool for exploring the relationship between physical activity and fat mass which allows to take the whole range and pattern of physical activity into account.

Methods The data is from the The Avon Longitudinal Study of Parents and Children (ALSPAC). Fat mass, the outcome, was derived using a Lunar Prodigy DEXA scanner. Physical activity, the predictor, is a time series of 10080 minute by minute accelerometer measurements of counts per minute over 7 days available at three time points (ages 12, 14 and 16). We summarised these profiles by a histogram, this makes the profiles comparable between individuals and reduces the dimension of data, while still being easy to interpret. Then we fitted a generalised version of a regression model with fat mass as the outcome and the profile histogram as one of the predictors. The model is a generalisation of a regression model, allowing the use of functions of highdimensional predictors rather than just univariate predictors.

Results The histogram is a useful summary for exploring characteristics of highly dimensional physical activity profiles aiding in classifying individuals into groups with similar profile characteristics. Our preliminary model results back up the cut-point used for MVPA at 3600 counts per minute set by a calibration study [1] and confirm that moderate and vigorous activity has a negative effect on fat mass. In addition, we find that light physical activity ranging around 500 counts per minute has a significant positive effect on fat mass.

References [1] Mattocks C, Ness A, Leary SD, Tilling K, Blair S, Shield J, Deere, K, Saunders J, Kirkby J, Smith GD, Wells J, Wareham N, Reilly J, and Riddoch C (2008). Use of accelerometers in a large field based study of children: Protocols, design issues, and effects on precision. Journal or Physical Activity and Health, 5:S94–S107.