Joint modeling the frequency and duration of accelerometer-measured physical activity from a lifestyle intervention trial.

Physical activity (PA) guidelines recommend that PA be accumulated in bouts of 10 minutes or more in duration. Recently, researchers have sought to better understand how participants in PA interventions increase their activity. Participants can increase their daily PA by increasing the number of PA bouts per day while keeping the duration of the bouts constant; they can keep the number of bouts constant but increase the duration of each bout; or participants can increase both the number of bouts and their duration. We propose a novel joint modeling framework for modeling PA bouts and their duration over time. Our joint model is comprised of two sub-models: a mixed-effects Poisson hurdle sub-model for the number of bouts per day and a mixed-effects location scale gamma regression sub-model to characterize the duration of the bouts and their variance. The model allows us to estimate how daily PA bouts and their duration vary together over the course of an intervention and by treatment condition and is specifically designed to capture the unique distributional features of bouted PA as measured by accelerometer: frequent measurements, zero-inflated bouts, and skewed bout durations. We apply our methods to the Make Better Choices study, a longitudinal lifestyle intervention trial to increase PA. We perform a simulation study to evaluate how well our model is able to estimate relationships between outcomes.