Nonparametric Estimation of the Conditional Bivariate Distribution Function of Censored Gap Times

A major goal in recurrent events analysis is to estimate the bivariate distribution function. This estimation is crucial across various fields and applications, as it helps clarify the patterns of recurring events and their underlying patterns. ‘Gap time’ refers to the duration between consecutive occurrences of an event, while the bivariate distribution function represents the joint probability distribution of two such gap times. Despite significant advancements in this area, most existing methods assume independent censoring and neglect the impact of covariates. Therefore, the primary aim of this paper is to develop and introduce nonparametric estimation methods for the bivariate distribution function that incorporate covariate measures. This study seeks to provide more precise and applicable tools for analyzing recurrent event data, thereby enhancing the understanding and interpretation of such events in practical scenarios.