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Abstract
Many extensions of survival models based on the Cox proportional hazards approach
have been proposed to handle clustered or multiple event data. Of particular note
are five Cox-based models for recurrent event data: Andersen and Gill (AG); Wei, Lin
and Weissfeld (WLW); Prentice, Williams and Peterson, total time (PWP-CP) and gap
time (PWP-GT); and Lee, Wei and Amato (LWA). Some authors have compared these models
by observing differences that arise from fitting the models to real and simulated
data. However, no attempt has been made to systematically identify the components
of the models that are appropriate for recurrent event data. We propose a systematic
way of characterizing such Cox-based models using four key components: risk intervals;
baseline hazard; risk set, and correlation adjustment. From the definitions of risk
interval and risk set there are conceptually seven such Cox-based models that are
permissible, five of which are those previously identified. The two new variant models
are termed the 'total time - restricted' (TT-R) and 'gap time - unrestricted' (GT-UR)
models. The aim of the paper is to determine which models are appropriate for recurrent
event data using the key components. The models are fitted to simulated data sets
and to a data set of childhood recurrent infectious diseases. The LWA model is not
appropriate for recurrent event data because it allows a subject to be at risk several
times for the same event. The WLW model overestimates treatment effect and is not
recommended. We conclude that PWP-GT and TT-R are useful models for analysing recurrent
event data, providing answers to slightly different research questions. Further, applying
a robust variance to any of these models does not adequately account for within-subject
correlation.
Copyright 2000 John Wiley & Sons, Ltd.