Semiparametric Estimation with Recurrent Event Data under Informative Monitoring.

Consider a study where the times of occurrences of a recurrent event for n units are monitored. For the ith unit, T(i1), T(i2), …, denote the successive event interoccurrence times and this unit is monitored over a random period [0, τ(i)] with τ(i) independent of the T(ij)s. Over this monitoring period, [Formula: see text] is the random number of event occurrences. The T(ij)s are independent and identically distributed (IID) from an unknown continuous distribution function F and the τ(i)s are IID from a distribution function G. A generalized Koziol-Green (GKG) structure wherein 1-G = (1-F)(β) for some β > 0 is assumed. Under this model, Nelson-Aalen and product-limit type estimators of Λ = -log(1-F) and F are obtained, as well as an estimator of β. Asymptotic and small-sample properties of these estimators are obtained and the estimator of F is compared to the fully nonparametric estimator in Peña et al. (2001) in terms of their finite-sample and asymptotic efficiency. The performance of the estimators of F are also examined when the GKG structure does not hold through a simulation study.