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Chunk #34 — 5.0 Asymptotic Properties

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Modification of the Sandwich Estimator in Generalized Estimating Equations with Correlated Binary Outcomes in Rare Event and Small Sample Settings.
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If assumption 2 does not hold, as Pan recommended, subjects can be classified into groups such that the Yi have the same correlation matrix. Therefore, as the sample size increases and the marginal variance of Yi is modeled correctly we expect the values of the Pan and Rogers sandwich estimators to be more similar. If assumptions 1 and 2 hold then with a large enough sample size we expect the differences in K1∕2(β^−β) to be asymptotically multivariate Gaussian with zero mean and covariance matrix (V) under the Pan and Rogers methodologies as well. In addition to these similarities, if the sample size and prevalence are both increased, we expect to see a convergence of similar values and performance in coverage probabilities from all of the sandwich estimators.