Estimation and Efficiency with Recurrent Event Data under Informative Monitoring.

This article deals with studies that monitor occurrences of a recurrent event for n subjects or experimental units. It is assumed that the i(th) unit is monitored over a random period [0,tau(i)]. The successive inter-event times T(i1), T(i2), ..., are assumed independent of tau(i). The random number of event occurrences over the monitoring period is K(i) = max{k in {0, 1, 2, ...} : T(i1) + T(i2) + ... + T(ik) </= tau(i)}. The T(ij)s are assumed to be i.i.d. from an unknown distribution function F which belongs to a parametric family of distributions C={F(;theta):thetain subsetRep}. The tau(i)s are assumed to be i.i.d. from unknown distribution function G. The problem of estimating theta, and consequently the distribution F, is considered under the assumption that the tau(i)s are informative about the inter-event distribution. Specifically, 1 - G = (1 - F)(beta) for some unknown beta > 0, a generalized Koziol-Green (cf., Koziol and Green (1976); Chen, Hollander, and Langberg (1982)) model. Asymptotic properties of estimators of theta, beta, and F are presented. Efficiencies of estimators of theta and F are ascertained relative to estimators which ignores the informative monitoring aspect. These comparisons reveal the gain in efficiency when the informative structure of the model is exploited. Concrete demonstrations were performed for F exponential and a two-parameter Weibull.