Multi-Level Micro-Randomized Trial: Detecting the Proximal Effect of Messages on Physical Activity

Technological advancements in mobile devices have made it possible to deliver mobile health interventions to individuals. A novel intervention framework that emerges from such advancements is the just-in-time adaptive intervention (JITAI), where it aims to suggest the right support to the individual "just in time", when their needs arise, thus having proximal, near future effects. The micro-randomized trial (MRT) design was proposed recently to test the proximal effects of these JITAIs. In an MRT, participants are repeatedly randomized to one of the intervention options of various in the intervention components, at a scale of hundreds or thousands of decision time points over the course of the study. However, the extant MRT framework only tests the proximal effect of two-level intervention components (e.g. control vs intervention). In this paper, we propose a novel version of MRT design with multiple levels per intervention component, which we call "multi-level micro-randomized trial" (MLMRT) design. The MLMRT extends the existing MRT design by allowing multi-level intervention components, and the addition of more levels to the components during the study period. We apply generalized estimating equation type methodology on the longitudinal data arising from an MLMRT to develop the novel test statistics for assessing the proximal effects and deriving the associated sample size calculators. We conduct simulation studies to evaluate the sample size calculators based on both power and precision. We have developed an R shiny application of the sample size calculators. This proposed design is motivated by our involvement in the Diabetes and Mental Health Adaptive Notification Tracking and Evaluation (DIAMANTE) study. This study uses a novel mobile application, also called "DIAMANTE", which delivers adaptive text messages to encourage physical activity.