When the outcome is compositional - a method for conducting compositional response linear mixed models for physical activity, sedentary behaviour and sleep research

Abstract Time use is compositional in nature because time spent in sleep, sedentary behaviour and physical activity will always sum to 24 h/day meaning any increase in one behaviour will necessarily displace time spent in another behaviour(s). Given the link between time use and health, and its modifiable nature, public health campaigns often aim to change the way people allocate their time. However, relatively few studies have investigated how movement-behaviour composition changes longitudinally (with repeated measures) due to experimental design elements or participant characteristics. This may be because most mixed-model packages that account for the random effects of repeated measures do not natively allow for a multivariate outcome such as movement-behaviour composition. In the current paper we provide a practical framework of how to implement a multivariate response linear mixed model to investigate how movement-behaviour compositions change with repeated measures. In an example we show how time is reallocated in children across the school year. Competing Interest Statement The authors have declared no competing interest. Funding Statement The life on Holidays study was funded by the National Health and Medical Research Council [grant number APP1143379] (2018 to 2022). The funding body played no role in the design, collection, analysis and interpretation of data or in writing the manuscript. AM is supported by an Australian Government RTP research scholarship and by the Centre of Research Excellence in Driving Global Investment in Adolescent Health funded by NHMRC APP1171981. DD is supported by an Australian Research Council (ARC) Discovery Early Career Researcher Award (DECRA) DE230101174 and by the Centre of Research Excellence in Driving Global Investment in Adolescent Health funded by NHMRC APP1171981. CM is supported by a Medical Research Future Fund Investigator Grant APP1193862. JAMF is supported by the Spanish government under the project PID2021 123833OB I00 and by the Catalan government under the project 2021SGR01197. Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: Ethical approval was obtained from The University of South Australia Human Research Ethics Committee (200980), the South Australian Department of Education and Child Development (2008-0055) and the Adelaide Catholic Education Centre (201820) for the original Life on Holidays study. I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes Data Availability All data produced in the present study are available upon reasonable request to the authors