Mixed-effects Location Scale Modeling For The Analysis Of Accelerometry Data

Abstract

PURPOSE: To introduce a statistical technique, the mixed-effects location scale model, for analysis of longitudinal accelerometer-based physical activity (PA) data. This approach jointly models both the mean (location) and within-subject variability (scale) of participants’ PA over time as a function of covariates, since within-person variability may be an important construct to explore in PA interventions. Random effects are included in both models to allow for subject-specific deviations beyond the effect of covariates. These random effects can be correlated. METHODS: Participants (N=204, 77% female, age=33±11y, BMI=28.2±7.1 kg/m2) in the Make Better Choices Study were randomized to one of two activity-related intervention arms: 1) increase moderate-to-vigorous PA (MVPA) (PA group) or 2) decrease sedentary active control (SB group). Physical activity was measured by accelerometer for 5 weeks: a 2 week baseline assessment phase and a 3 week intervention follow-up phase: week 1 (rx1) and weeks 2 and 3 (rx23). The outcome MVPA min/d was analyzed using the mixed-effects location scale model in the MIXREGLS software program in STATA. RESULTS: The mean model shows a significant group by time interaction (MVPA group by rx1: B=6.32 (95%CI: 3.93, 8.7) MVPA group by rx23: B=9.85 (95% CI: 7.59, 12.10)) indicating that those in the PA group had significantly greater MVPA min/d at rx1 and rx23 compared to the SB group. The PA group by rx23 interaction was significant in the within-subject variance model, suggesting that those in the PA group had significantly more variability in MVPA min/d during follow-up phase rx23 compared to the SB group. The random-location effect is positively associated with the within subject variance, participants with higher mean min/d MVPA tend to have higher min/d MVPA variability (τι=0.70 (95% CI: 0.60, 0.80)). The scale standard deviation is significant indicating that some participant’s MVPA min/d are significantly more dispersed than other participants even after adjusting for group and time effects (σω=0.60 (95% CI: 0.55, 0.64)). CONCLUSIONS: The location-scale mixed model provides a new approach for examining the mean and variability of min/d of MVPA in longitudinal data. To demonstrate, we applied this model to a randomized controlled trial to increase PA in inactive adults.