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Modeling longitudinal binomial responses: implications from two dueling paradigms

The generalized estimating equations (GEEs) and generalized linear mixed-effects model (GLMM) are the two most popular paradigms to extend models for cross-sectional data to a longitudinal setting. Although the two approaches yield well-interpreted models for continuous outcomes, it is quite a different story when applied to binomial responses. We discuss major modeling differences between the GEE- and GLMM-derived models by presenting new results regarding the model-driven differences. Our results show that GLMM induces some artifacts in the marginal models at assessment times, making it inappropriate when applied to such responses from real study data. The different interpretations of parameters resulting from the conceptual difference between the two modeling approaches also carry quite significant implications and ramifications with respect to data and power analyses. Although a special case involving a scale difference in parameters between GEE and GLMM has been noted in the literature, its implications in real data analysis has not been thoroughly addressed. Further, this special case has a very limited covariate structure and does not apply to most real studies, especially multi-center clinical trials. The new results presented fill a substantial gap in the literature regarding the model-driven differences between the two dueling paradigms.