A shared-parameter location-scale mixed model to link the responsivity in self-initiated event reports and the event-contingent Ecological Momentary Assessments.

We address the issue of (non-) responsivity of self-initiated assessments in Ecological Momentary Assessment (EMA) or other mobile health (mHealth) studies, where subjects are instructed to self-initiate reports when experiencing defined events, for example, smoking. Since such reports are self-initiated, the frequency and determinants of nonresponse to these event reports is usually unknown, however it may be suspected that nonresponse of such self-initiated reports is not random. In this case, existing methods for missing data may be insufficient in the modeling of these observed self-initiated reports. In certain EMA studies, random prompts, distinct from the self-initiated reports, may be converted to event reports. For example, such a conversion can occur if during a random prompt a subject is assessed about the event (eg, smoking) and it is determined that the subject is engaging in the event at the time of the prompt. Such converted prompts can provide some information about the subject's non-responsivity of event reporting. Furthermore, such non-responsivity can be associated with the primary longitudinal EMA outcome (eg, mood) in which case a joint modeling of the non-responsivity and the mood outcome is possible. Here, we propose a shared-parameter location-scale model to link the primary outcome model for mood and a model for subjects' non-responsivity by shared random effects which characterize a subject's mood level, mood change pattern, and mood variability. Via simulations and real data analysis, our proposed model is shown to be more informative, have better coverage of parameters, and provide better fit to the data than more conventional models.