Estimation with Recurrent Event Data under an Informative Monitoring Period
We consider a study which monitors the occurrence of a recurrent event for n subjects or units. Of interest is the problem of parametric and semiparametric estimation of the inter-event or gap-time distribution when the data is subject to informative censoring. We first address the case where the gap-times are assumed to be independent and identically distributed with some parametric survival distribution function F¯( t,theta); where theta is some p-dimensional parameter. It is further assumed that the recurrent event is observed until some random time, tau, whose distribution G depends on that of F through the relationship G¯ = F¯beta, for some beta > 0; the so-called Koziol-Green model. We present finite and asymptotic properties of the maximum likelihood estimates of beta and theta as well as the estimator F¯(t). Next, we derive Nelson-Aalen and Kaplan-Meier type estimators by embedding the problem in an appropriate counting process. Finite and asymptotic properties of the semiparametric estimators are also established. The proposed estimators in both cases are compared to those derived ignoring informative censoring to ascertain efficiency gained that results by taking into account informative censoring. It will be shown that the proposed estimators are more efficient than those derived ignoring informative censoring. Moreover, in the special case of the homogeneous Poisson process, the asymptotic relative efficiency is shown to be bounded by approximately 0.65.
A. Adekpedjou, "Estimation with Recurrent Event Data under an Informative Monitoring Period,", Jan 2007.
Mathematics and Statistics