A copula model for marked point processes
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Many chronic diseases feature recurring clinically important events. In addition, however, there often exists a random variable which is realized upon the occurrence of each event reflecting the severity of the event, a cost associated with it, or possibly a short term response indicating the effect of a therapeutic intervention. We describe a novel model for a marked point process which incorporates a dependence between continuous marks and the event process through the use of a copula function. The copula formulation ensures that event times can be modeled by any intensity function for point processes, and any multivariate model can be specified for the continuous marks. The relative efficiency of joint versus separate analyses of the event times and the marks is examined through simulation under random censoring. An application to data from a recent trial in transfusion medicine is given for illustration.
KeywordsCopula function Joint analysis Marks Recurrent events
This research was supported by Grants from the Natural Sciences and Engineering Research Council of Canada (RGPIN 155849) and the Canadian Institutes for Health Research (FRN 13887). Richard Cook is a Canada Research Chair in Statistical Methods for Health Research. The authors thank Professor Jerry Lawless and Professor Nancy Heddle for helpful discussions and collaboration and Ray Goodrich for helpful discussion and permission to use the data from the Mirasol Study.
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