Mixed effects models for recurrent events data with partially observed time‐varying covariates: Ecological momentary assessment of smoking. Issue 1 (27th September 2015) - Rathbun, Stephen L.; Shiffman, Saul
Summary: Cigarette smoking is a prototypical example of a recurrent event. The pattern of recurrent smoking events may depend on time‐varying covariates including mood and environmental variables. Fixed effects and frailty models for recurrent events data assume that smokers have a common association with time‐varying covariates. We develop a mixed effects version of a recurrent events model that may be used to describe variation among smokers in how they respond to those covariates, potentially leading to the development of individual‐based smoking cessation therapies. Our method extends the modified EM algorithm of Steele (1996) for generalized mixed models to recurrent events data with partially observed time‐varying covariates. It is offered as an alternative to the method of Rizopoulos, Verbeke, and Lesaffre (2009) who extended Steele's (1996) algorithm to a joint‐model for the recurrent events data and time‐varying covariates. Our approach does not require a model for the time‐varying covariates, but instead assumes that the time‐varying covariates are sampled according to a Poisson point process with known intensity. Our methods are well suited to data collected using Ecological Momentary Assessment (EMA), a method of data collection widely used in the behavioral sciences to collect data on emotional state and recurrent events in the every‐day environments of study subjects using electronic devices such as Personal Digital Assistants (PDA) or smart phones.