The Mean, Variance and Correlation for Bivariate Recurrent Event Data with a Terminal Event

Abstract

Summary Recurrent events in the presence of a terminal event are often encountered in a biomedical setting. The marginal mean of the number of recurrent events in a specified time period is a useful non-parametric summary of recurrent events data also in the presence of a terminal event. Other useful non-parametric summaries, that are simple to compute, are the distribution function of the number of recurrent events for each point in time and the variance of the number of recurrent events. For bivariate recurrent events, still in the presence of a terminal event, we suggest a simple non-parametric estimator of the covariance or correlation of the marginal number of events for both processes. When there is no terminal event the correlation is useful, but when there is an important terminal event we suggest an adjustment for correlation induced by the terminal event to obtain a measure that reflects the dependence in the recurrent event processes among survivors only. Our estimators can be used for deciding whether the two recurrent events are correlated and in what way. We provide large sample properties of our estimators and show their performance in small samples by simulations. The estimators are applied in a study of catheter complications among patients receiving home parenteral nutrition through a central venous catheter, and we show a positive correlation between the number of infections and the number of occlusion defects.