Use of Functional Linear Models to Detect Associations between Characteristics of Walking and Continuous Responses Using Accelerometry Data

Various methods exist to measure physical activity. Subjective methods, such as diaries and surveys, are relatively inexpensive ways of measuring one's physical activity; however, they are prone to measurement error and bias due to self-reporting. Wearable accelerometers offer a non-invasive and objective measure of one's physical activity and are now widely used in observational studies. Accelerometers record high frequency data and each produce an unlabeled time series at the sub-second level. An important activity to identify from the data collected is walking, since it is often the only form of activity for certain populations. Currently, most methods use an activity summary which ignores the nuances of walking data. We propose methodology to model specific continuous responses with a functional linear model utilizing spectra obtained from the local fast Fourier transform (FFT) of walking as a predictor. Utilizing prior knowledge of the mechanics of walking, we incorporate this as additional information for the structure of our transformed walking spectra. The methods were applied to the in-the-laboratory data obtained from the Developmental Epidemiologic Cohort Study (DECOS).