Public health program evaluation often relies on routinely collected aggregated data. In resource-limited settings, cluster-stratified sampling, in which clinics are sampled and data on all patients in the selected clinics is collected, is a cost-efficient way to overcome the loss of information in group-level data. Given data from a cluster-stratified design, Cai et al. (2001) proposed estimation for a marginal model using inverse-probability weighted generalized estimating equations. Towards performing inference, however, the expression for variance of the resulting estimator presented by Cai et al. (2001) ignored covariance in the cluster-specific selection indicators. We provide a corrected variance expression, as well as a consistent plug-in estimator. Furthermore, we provide expressions for small-sample bias corrections to both the point estimates and the standard errors in the context of outcome-dependent sampling. Simulations are conducted to examine the operating characteristics of the proposed methods. The proposed methods are illustrated using birth data from 18 clinics in Rwanda, collected via a cluster-stratified scheme.