Modeling survival data with informative cluster size

Analysis of clustered data focusing on inference of the marginal distribution may be problematic when the risk of the outcome is related to the cluster size, termed as informative cluster size. In the absence of censoring, Hoffman et al. proposed a within-cluster resampling method, which is asymptotically equivalent to a weighted generalized estimating equations score equation. We investigate the estimation of the marginal distribution for multivariate survival data with informative cluster size using cluster-weighted Weibull and Cox proportional hazards models. The cluster-weighted Cox model can be implemented using standard software. Simulation results demonstrate that the proposed methods produce unbiased parameter estimation in the presence of informative cluster size. To illustrate the proposed approach, we analyze survival data from a lymphatic filariasis study in Recife, Brazil.