Joint Longitudinal and Survival Models for Intensive Longitudinal Data from Mobile Health Studies

Abstract

Mobile health (mHealth) technology enables the collection of intensive longitudinal data (ILD) and, as a result, serves as a rich source of information on both the short-term and long-term dynamics of multiple outcomes measured over time. When combined with time-to-event outcomes, ILD can provide insight into factors that elevate the risk of an event. Motivated by mHealth studies of smoking cessation in which participants report both longitudinal data on the intensity of many emotions multiple times per day and event-time information on cigarette use, this dissertation presents methods for jointly modeling multivariate ILD and time-to-event outcomes.

In the first project, we develop a dynamic factor model that summarizes ILD as a smaller number of time-varying latent factors. The evolution of these latent factors is modeled using a multivariate continuous-time Ornstein-Uhlenbeck stochastic process. We propose a block coordinate descent algorithm for maximum likelihood estimation and apply our method to mHealth data to summarize the dynamics of 18 emotions as two latent factors. These latent factors are interpreted by behavioral scientists as the psychological constructs of positive and negative affect.

In the second project, we extend this dynamic factor model to consider an event outcome. Specifically, we use the latent factors as time-varying predictors of a cumulative event outcome (e.g., the total number of cigarettes smoked across repeated intervals of time), which we model using Poisson regression. We take a two-stage approach to estimation; we use weights--based on importance sampling--to account for potential bias that could result from the two-stage approach.

In the third project, we extend this dynamic factor model to model the longitudinal process jointly with a traditional survival outcome (e.g., the time of first cigarette use after attempted quit). In this joint longitudinal-survival model, the hazard of a time-to-event outcome is a function of the low-dimensional latent process. Joint estimation of this model is challenging due to the combination of ILD and the presence of a stochastic process as a time-varying covariate in our hazard model. We fit our joint model with a Bayesian approach and use it to analyze data from another mHealth study of smoking cessation. We summarize the longitudinal self-reported intensity of nine emotions as the psychological states of positive and negative affect; these time-varying latent states capture the risk of the first smoking lapse after attempted quit.

In the fourth project, we present a model-based approach for estimating the effect of repeatedly delivered treatments in a micro-randomized trial (MRT) via an extension of our joint model. We discuss different ways that these repeated treatment effects can be incorporated into the joint model; these different model specifications correspond to different mechanisms by which treatment is assumed to impact the longitudinal and event processes. Taking a Bayesian approach to inference, we model the association between repeated app-based notifications, longitudinally-measured emotions, and recurrent events of substance use in an mHealth MRT.