# Poisson approximation of a binomial model with random effects - how to get robust variance estimates

I'm interested in using a Poisson approximation for modeling a common (~40% of the time) binary outcome. But my data has some clustering in it, having come from three different sites, which suggests the use of a random effects model.

Getting the actual estimates are easy enough, using something like lme4 in R:

model <- glmer(Outcome ~ Sex + Age + (1|Site), data=study, family=poisson)


The problem is that Zou G. A modified Poisson regression approach to prospective studies with binary data. Am J Epidemiol. 2004;159(7):702–706 suggests that a robust variance estimator is needed using this method, but the standard sandwich library doesn't work (by, as I understand it, design) with lme4.

Which suggests two questions:

1. Is a robust variance estimator still needed in this circumstance?
2. How does one obtain one?