A nonparametric approach to isotemporal substitution regression

A number of large health surveys such as the UK Biobank and the National Health and Nutrition Examination Survey (NHANES) include both health related measurements and accelerometer based estimates of how participants allocate their time between physical activities, sedentary behaviors, and sleep. Those time allocations add up to 24 hours for each participant, and parametric regression techniques such as isotemporal substitution analysis and compositional data analysis have been previously developed to estimate how reallocation of time from one activity to another associates with an expected health outcome. This paper develops a novel nonparametric approach. We apply the method to data from NHANES to examine the association between time allocation and body mass index (BMI). The nonparametric approach reveals that the associations between increased activity and BMI depend on both the amount of activity and how the rest of a person’s time is spent. That type of conclusion is not easily available from existing methods.