Robust estimation of the variance in moment methods for extra-binomial and extra-Poisson variation

When faced with data in the form of overdispersed counts or proportions, moment methods allow consistent parameter estimation when only the form of the mean and variance is specified. If the variance form is misspecified, these methods still yield consistent parameter estimates, though with lower efficiency, and the variances of the estimates will be inconsistent. A variance correction is available that yields consistent variance estimates in these circumstances. The asymptotic and small-sample efficiencies of this correction are calculated, and its performance under variance misspecification is studied. A group-randomized breast self-examination prevention study that is now underway serves as a focal point for the study of these properties. The use of the variance correction in modelling is illustrated on a teratology data set.