Disclaimer: This manuscript reflects the views of the authors and should not be construed to represent the FDA's views or policies. Matthew Guerra began this work while he was a PhD student in the Department of Biostatistics at the University of Pennsylvania, and was supported by a grant from the National Cancer Institute (T32 CA93283). With permission from the journal, we note that an earlier version of this paper was submitted to {\it The American Statistician} on May 2, 2011, and a shorter version was tentatively accepted on May 28, 2013. The authors are also very grateful to their friend and mentor Professor Thomas Ten Have for suggesting that they work on this manuscript and dedicate this paper to his memory.


We propose a straightforward approach for simulation of discrete random variables with overdispersion, specified marginal means, and product correlations that are plausible for longitudinal data with equal, or unequal, temporal spacings. The method stems from results we prove for variables with first-order antedependence and linearity of the conditional expectations. The proposed approach will be especially useful for assessment of methods such as generalized estimating equations, which specify separate models for the marginal means and correlation structure of measurements on a subject.



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