Event history data is comprised of the times of repeated events and can be found throughout the social and behavioral sciences, including investigations of substance abuse, child behavior, criminology, social unrest, and organizational ecology. Using methods collectively known as Ecological Momentary Assessment (EMA), recent advances in electronics have made it possible to collect richer kinds of event history data and at a much higher volume, improving the quality of data and offering challenges and opportunities for statistical research. In particular, methods are required for modeling the impact of time-varying covariates on the timing of repeated events, complex dependence relationships among repeated events, and variation among subjects in their responses to time-varying covariates. A probability-sampling framework will be developed for modeling the impact of time-varying covariates on event history data, supporting the construction of point process and survival models for data from an EMA of smoking behavior. The proposed framework may be applied whenever the estimating equations for a statistical model involve the integration of some function (e.g., hazard) of time-varying covariates over a sampling domain. The sampling domain is treated as a population of points, and the covariates are taken to be unknown but deterministic functions of time. A probability-based sampling design is used to sample the covariates from which a design unbiased estimator for the integrated function of the covariates may be obtained. Substituting this design-unbiased estimator into the estimating equations and solving for the parameter yields the proposed parameter estimator. This research aims to investigate the inferential properties of the estimator, to develop point process and survival models for event history data with random subject effects, and to investigate efficient probability-sampling designs for time-varying covariates.
New statistical methods will be developed for analyzing the impact of time-varying covariates such as psychological state and the subject's environment on the pattern of repeated behavioral events using observations collected by electronic devices. This research will support the development of models designed to improve our understanding of the mechanisms underlying addictive behaviors. Aside from the behavioral models considered here, the statistical framework may be applied more broadly in time series, geospatial statistics, and spatial epidemiology. The research is supported by the Methodology, Measurement, and Statistics Program and a consortium of federal statistical agencies as part of a joint activity to support research on survey and statistical methodology.
