How to analyze longitudinal multilevel physical activity data with many zeros?

Abstract Background Physical activity (PA) is a modifiable lifestyle factor for many chronic diseases with established health benefits. PA outcomes are measured and assessed in many longitudinal studies, but their analyses often pose difficulties due to the presence of many zeros, extreme skewness, and lack of independence, which render standard regression methods inappropriate. Methods A two-part multilevel modeling approach is used to analyze the heterogeneous and correlated PA data. In the first part, a logistic mixed regression model is fitted to estimate the prevalence of PA and factors associated with PA participation over time. For subjects engaging in PA, a gamma mixed regression model is adopted in the second part to assess the effects of predictor variables on the repeated PA outcomes nested within clusters. Extra variations are accommodated within the modeling process by random effects assigned to each cluster and each subject in the cohort. Results The findings in a longitudinal multilevel study of a community-based PA intervention for older adults demonstrate the effectiveness of the intervention program and enable the identification of pertinent factors affecting participation and PA levels over time. Conclusions The two-part mixed regression approach provides a practical and statistically valid method to analyze the skewed and correlated PA data with many zeros. The methodology can be extended to handle complex hierarchical or multilevel settings by suitable specification of the covariance structure in the random components, model fitting of which can be performed in STATA using GLLAMM with various user-specified options.