Serial association analyses of recurrent gap time data via Kendall's tau

Recurrent event data are frequently encountered in long-term follow-up studies. In many applications, the gap times between two successive recurrent events are natural outcomes of interest. Investigation on patterns of associations among recurrent gap times within subjects is an important inferential issue. In this paper, we introduce flexible functions of previous gap times to create a class of summary measures of serial associations for a sequence of recurrent gap times through Kendall's tau. Such a general class of serial association measures provides a useful tool to quantify the predictive abilities of event history with different aspects. Non-parametric estimators of the proposed measures of serial associations are developed by generalizing the existing estimator of Kendall's tau for two serial gap times, in which inverse probability of censoring weights is used to overcome the induced dependent censoring. Various tests are further constructed for testing the constancy of serial associations over different events. Our method is applied to Denmark schizophrenia data and the results show that association structures are different for distinct ages of onset of schizophrenia.