Statistical Inference Of Change-point Model For Recurrent Events

The problem of change-points has been a topic of permanent interest in Statisticalliterature since in the1970s. The change-points reflect the changes in the nature ofobject, which has an important application in various fields. The change-pointsstatistical analysis is one of the key to analysis the impact of emergencies on model, asan important tool to study on abrupt climate change and the effect of new drugs.Furthermore, it also occurs in the context of quality control and actuarial theory, whichbelongs to survival data. When we speak of survival analysis, we mean that we areinterested in studying the time of an event, where each individual can experience theevent only once.Recurrent events data occur frequently in business, engineering, biological andmedical fields. The conception of recurrent events is the situation in which subjects canexperience more than one of an event. To analyze recurrent event data, the focus can beplaced on three aspects: the first is the number of repeated events for each sample unit;the second is gap times between successive recurrent events; the third is the time to anevent. Recurrent events are associated with many factors, such as age, gender, heightand weight. Meanwhile, in many situations the complete observation of the recurrentevents data may not be possible since some subjects will never experience the events ofinterest up to the endpoint observation and will be censored ultimately. These subjectsare commonly referred as cure fraction or long-term survivors.In this paper, three new change-point model are considered. The first model is achange-point model for recurrent events data that accounts for long-term survivors. Thesecond model is a change-point model for recurrent events data with covariates. The lastis a change-point model for gap times. The contributions of three models is as follows.(1) We first consider the long-term survivors work for a change-point model forrecurrent events data.(2) We first consider covariates work for intensity rate function.(3) We first combine gap time with a change-point model.In this paper, we adopt parametric method and nonparametric method to estimate the unknown change-point and parameters. Meanwhile, Large-sample properties of thechange-point estimator are also discussed. Simulations and applications are carried outto evaluate the performance of the proposed models.