Availability of accelerometer data has made it possible to objectively and continuously monitor sedentary behavior. Various summaries of the extensive accelerometer data have been used to understand the relationship between sedentary behavior and health. However, the widely used summary measures on sedentary bouts, average bout length or its derivatives, fail to reveal patterns of accumulated sedentary behavior over time. Studies have suggested that prolonged uninterrupted sedentary behavior can be an important metric that is related to health states. Yet existing measures to capture the prolonged sedentary patterns either rely on parametric assumptions on the underlying distribution of sedentary bout length or have to categorize sedentary bout length into somewhat arbitrary categories. Gini index was also used; however, it only measures the variability in bout lengths but not the actual length. To overcome these limitations, we proposed a non-parametric weighted survival function to characterize uninterrupted sedentary behavior over time in a continuous fashion and used the area under the survival curve as a new summary measure to quantify sedentary behavior. We showed that this measure is a weighted average of bout length and contains the information on both the mean and variability of bout lengths. We demonstrated in the simulation studies that the proposed measure could better identify prolonged uninterrupted sedentary behavior and predict health outcomes. We applied this new measure and existing sedentary measures to data from the Hispanic Community Health Study/Study of Latinos to examine the association between sedentary behavior and overweight/obesity.
Keywords: Gini index; Lorenz curve; Sedentary bout length; survival function.