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Event history data, including competing risks and more general multistate process data, are commonly encountered in biomedical studies. In practice, such event history data are often subject to intra-cluster correlation in multicenter studies and are complicated due to informative cluster size, a situation where the outcomes under study are associated with the size of the cluster. In addition, outcomes or covariates are frequently incompletely observed in real-world settings. Ignoring these statistical issues will lead to invalid inferences. In this dissertation, I develop a series of marginal regression methods to address these statistical issues with competing risks and more general multistate process data. The motivation for this research comes from a large multicenter HIV study and a multicenter randomized oncology trial.