Mixture analysis of heterogeneous physical activity outcomes

The health benefits of physical activity (PA) are well established. PA outcomes, being semicontinuous in nature, often exhibit a large portion of zero values together with continuous positive values that are right-skewed. We propose a novel two-part mixture regression model with random effects to characterize heterogeneity of the clustered PA data.

In the binary part, the odds of PA participation are modeled with the use of a logistic mixed regression model. In the continuous part, the PA intensity conditional on those individuals engaging in PA is assessed by a gamma mixture regression model. Random effects are incorporated within the two parts to account for correlation of the observations.

Model fitting and inference are performed through the Gaussian quadrature technique, which is implemented conveniently in the SAS PROC NLMIXED. The development of mixture methodology for analyzing PA is motivated by a study of PA in the daily life of patients with chronic obstructive pulmonary disease.

The findings demonstrate the usefulness of the mixture analysis, which enables the separate identification of pertinent factors affecting PA participation and PA intensity for different patient subgroups.