A latent variable approach to jointly modeling longitudinal and cumulative event data using a weighted two-stage method.

Ecological momentary assessment (EMA), a data collection method commonly employed in mHealth studies, allows for repeated real-time sampling of individuals' psychological, behavioral, and contextual states. Due to the frequent measurements, data collected using EMA are useful for understanding both the temporal dynamics in individuals' states and how these states relate to adverse health events. Motivated by data from a smoking cessation study, we propose a joint model for analyzing longitudinal EMA data to determine whether certain latent psychological states are associated with repeated cigarette use. Our method consists of a longitudinal submodel-a dynamic factor model-that models changes in the time-varying latent states and a cumulative risk submodel-a Poisson regression model-that connects the latent states with the total number of events. In the motivating data, both the predictors-the underlying psychological states-and the event outcome-the number of cigarettes smoked-are partially unobservable; we account for this incomplete information in our proposed model and estimation method. We take a two-stage approach to estimation that leverages existing software and uses importance sampling-based weights to reduce potential bias. We demonstrate that these weights are effective at reducing bias in the cumulative risk submodel parameters via simulation. We apply our method to a subset of data from a smoking cessation study to assess the association between psychological state and cigarette smoking. The analysis shows that above-average intensities of negative mood are associated with increased cigarette use.