The Mizon-Richard Ecompassing Test For Additive And Multiplicative Rate Models Of Recurrent Events Data

In scientific research,the research object is often repeat experience the same thing or multiple failure,this event is called recurrent events.The recurrence events data included the number of recurrence events,the time of recurrence events and the influencing factors.Recurrent event data appear in the medical and public health,business and industry,reliability,social science and insurance fields.Because of the widespread existence of recurrence events,the study of recurrence events data can be of great significance and value for people in various fields.Since the 1980 s,many scholars have been involved in the study of recurrence events.So far,many different models have been proposed for different situations.In the study,there are mainly two types,one is the risk rate and the intensity function of the recurrence event,The other is the mean function or the rate function for the recurrence event.Compared with these two class of models,the mean value model and the rate model are more explanatory and more widely applied.When dealing with the actual recurrence event time data,it is very important to select a model that can best fit the actual data for different mean value and rate models.In this paper,we use the encompassing principle to test the fitting effect of the model.Under the guidance of the encompassing principle,we establish the test statistics.The size and power of the test are calculated through Monte Carlo simulation to compare the statistics presented.Finally,the test is applied to the analysis of the chronic granulomatous disease data.From Monte Carlo simulation results of recurrence event data from different data generating progress,the test statistics constructed in this paper are good,and the acceptance or rejection of the original hypothesis is consistent with the data generating progress.Therefore,the method proposed in this paper can solve the recurrent event data model selection problem.It provides a reliable statistical analysis method and theoretical basis for practical workers.