General outlier detection and goodness of fit for recurrent event data

A general mathematical framework for outlier detection and goodness of fit testing for recurrent event data is considered under a fully parametric specification for the baseline hazard function. The tests were examined under no-frailty and with-frailty assumptions. Asymptotic properties of the goodness of fit tests were examined, while exact and bootstrapping methods were proposed for outlier detection test in lieu of the asymptotic result. Closed form expressions and small sample properties were obtained under the Homogeneous Poisson Process (HPP) model. Examples using an engineering and biomedical recurrent event data are given.