We propose a new probability-based framework for modeling the impact of time-varying covariates on the timing of repeated discrete behavioral events to support collaborative efforts to model two existing data sets involving Ecological Momentary Assessment (EMA) of smoking. EMA involves the use of electronic diaries to monitor the real-time behavior of subjects in their environments, avoiding recall biases inherent to retrospective questionnaires. Although EMA is increasingly important in the health sciences, aside from our own work little if any attention has been given to EMA in the statistics literature.
The specific aims of the proposed collaborative research between a biostatistician and a psychologist are to: 1) Develop a general probability-sampling framework for estimating the impact of time varying- covariates on the pattern of ad-lib smoking, lifetimes to lapse following a designated quit date, and the post-lapse pattern of cigarettes that takes into account temporal dependence among these smoking events with general applications to ecological momentary assessment;2) Construct joint models for the effects of time-varying covariates and time-of-day, accounting for circadian cycles in addictive behavior;3) Develop a model for variation among subjects with respect to baseline smoking rates, effects of time-covariates, and time of day, from which clusters of subjects showing similar smoking behaviors may be identified;and 4) Construct models in which the hazard of smoking a cigarette at a given instant in time depends not only on the current values of time-varying covariates, but also on an integrated function of past values of those covariates. To obtain a better understanding of the mechanisms underlying success or failure of attempts to quit smoking, point process and survival models will be constructed to describe the impact of temporal variation in smokers'psychological states and environments on the pattern of ad lib smoking, lifetime to lapse following smoking cessation and the post lapse pattern of cigarettes leading to relapse. A common feature of both point process and survival models is that the full likelihood involves the integration of a function (intensity or hazard) of the time- varying covariates over the sampling domain. The proposed framework treats the sampling domain as a population of points, and assumes that the covariates are an unknown but deterministic function of time. A probability-based design is used to sample the covariates, from which a design-unbiased estimator of the integrated function of the covariates may be obtained. Substituting this design-unbiased estimator into the likelihood yields an objective function that may be maximized to obtain the proposed estimator for the model parameters. Design-based inference for the integrated function of the covariates is offered as an alternative to a hierarchical modeling approach based on joint modeling of the time-varying covariates and the timing of repeated behavioral events. In contrast to the hierarchical approach, no model assumptions are required regarding the time-varying covariates.
To obtain a better understanding of the mechanisms underlying success or failure of attempts to quit smoking, we propose to develop new statistical methods for analyzing two existing data sets involving the use of electronic diaries to monitor the moods and environments of smokers in real time. Beyond the smoking data considered here, the proposed methods have broad applications in public health, ranging from analysis of addictive behaviors to investigations of patterns of asthma attacks, epileptic seizures, recurrent tumors in cancer patients, and more.
| Rathbun, Stephen L; Shiffman, Saul (2016) Mixed effects models for recurrent events data with partially observed time-varying covariates: Ecological momentary assessment of smoking. Biometrics 72:46-55 |
| Neustifter, Benjamin; Rathbun, Stephen L; Shiffman, Saul (2012) Mixed-Poisson Point Process with Partially-Observed Covariates: Ecological Momentary Assessment of Smoking. J Appl Stat 39:883-899 |
| Shiffman, Saul; Rathbun, Stephen L (2011) Point process analyses of variations in smoking rate by setting, mood, gender, and dependence. Psychol Addict Behav 25:501-10 |
