Compositional Data Analysis of Relative Body Mass and Physical Function Using the Relative Shift Approach

ABSTRACT Objective The purpose of this study was to present the novel relative shift approach for compositional data analysis of body composition as a predictor for gait speed and to compare it to existing methods. Methods Body composition was quantified from dual‐energy x‐ray absorptiometry in 145 older adults living with obesity. Gait speed was measured from a fast‐paced 400‐m walk. The associations between speed and body composition used separate least squares regression models with absolute (kg) mass and compositional methods based on isometric log‐ratio (ILR) transformations and the relative shift approach. Results All methods found significant associations between gait speed and body composition. The ILR approach was fit three times, once for each component variable (lean, fat, and bone mass). Predictions differed for the same magnitude of 5% composition change due to total body mass differences (+4.4 [0.8 to 8.0] vs. +5.0 [1.2 to 8.8] cm/s). The absolute mass model ignored the relative nature of the components. The relative shift model required no transformation and provided consistent predictions for 5% change (+4.6 [1.0 to 8.2] cm/s). Conclusions Our data suggest the relative shift model may provide simpler estimation and interpretation than ILR for models with compositional covariates. Trial Registration ClinicalTrials.gov identifier NCT04076618