A New Semiparametric Joint Model for Clustered Interval‐Censored Data With Informative Cluster Size

Clustered interval‐censored data frequently arise in many areas such as biomedical studies when the failure times of interest are interval‐censored and correlated within clusters. The cluster size is said to be informative if it is associated with the failure times. Most existing papers are only based on cluster‐weighted generalized estimating equations or within‐cluster resampling under marginal models, which can not estimate the associations within clusters. In this paper, we propose a new semiparametric joint model that uses a shared, unobserved frailty term to model the association within clusters as well as the association between event times and the cluster size. The nonparametric maximum likelihood approach for estimation and the EM algorithm for implementation are proposed. The estimators are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and indicates that the procedure works well. The proposed method is further demonstrated by applying it to a dental research.