Semiparametric regression analysis for recurrent event interval counts

This paper deals with analysis of data from longitudinal studies where the rate of a recurrent event characterizing morbidity is the primary criterion for treatment evaluation. We consider clinical trials which require patients to visit their clinical center at successive scheduled times as part of follow-up. At each visit, the patient reports the number of events that occurred since the previous visit, or an examination reveals the number of accumulated events, such as skin cancers. The exact occurrence times of the events are unavailable and the actual patient visit times typically vary randomly about the scheduled follow-up times. Each patient's record thus consists of a sequence of clinic visit dates, event counts corresponding to the successive time intervals between clinic visits, and baseline covariates. We propose a semiparametric regression model, extending the fully parametric model of Thall (1988, Biometrics 44, 197-209), to estimate and test for covariate effects on the rate of events over time while also accounting for the possibly time-varying nature of the underlying event rate. Covariate effects enter the model parametrically, while the underlying time-varying event rate is modelled nonparametrically. The method of Severini and Wong (1992, Annals of Statistics 20, 1768-1802) is used to construct asymptotically efficient estimators of the parametric component and to specify their asymptotic distribution. A simulation study and application to a data set are provided.