Marginal incidence trend with clustered observations ($\log \mathbb{E}[Y_{it}]=\log P_{it}+{\beta }_0+{\beta }_{1}t$)

A population-averaged log-rate model with exposure $P_{it}$ gives an annual rate ratio $e^{{\beta }_1}$. A generalized estimating equation can account for repeated observations within clusters through a working correlation and sandwich covariance matrix. Independent Poisson standard errors do not account for clustering. An exposure-weighted population rate and an equally weighted average of cluster rates are different estimands.