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Keywords: Missing data in longitudinal analysis, Interval Reported Binary Recurrent Event Data, mixed effect model, discrete survival analysis, Poisson process
Many complex studies designs involve collecting outcomes longitudinally using questionnaire items, like "Since the last time we spoke in (provided month), have you ever had fever or other symptoms?". Even though a subject could miss a few scheduled visits, such questionnaire design only captured the available longitudinal fever data across available visiting months, where the missing visits were skipped and merged into the reporting interval. Another feature is that the recurrent events of interest was observed dichotomously - only the binary status of occurrence in the reporting interval, without frequency counts information nor when they re-occur in this interval. Even though the literature on longitudinal binary data are quite comprehensive, the longitudinal models accounting for interval reported and binary recurrent event features are quite limited. We proposed two longitudinal models in this project to deal with such design, where discrete survival modeling technique and Poisson process are used to account for interval censored reporting system between longitudinal visits and binary nature of recurrent events outcomes. Simulation studies are used to compare the proposed models vs. standard longitudinal models with logit link to see how well they will capture the significant cross-sectional and longitudinal effects, especially with or without considering interval reporting nature, with or without time-varying covariates, and some other sensitivity analyses to model mis-specifications. Various simulation studies confirmed the great performance of the proposed model. Then, a real application using Baltimore Hip Study -7 is presented to end this paper. This is a joint work with Dr. Yi Huang and Dr. Larry Magder.