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I have a dataset that I'm trying to model using Cox proportional hazard models. The data include patient IDs and several attributes about the patients (including time till failure). Due to the nature of the data, a patient could fail and then fail again later several times. This means that some of the patients are repeated in the data due to multiple failures. However, patients aren't all repeated and when they are, they aren't all repeated the same number of times.

My questions are:

  1. How should this be handled in cox proportional hazard modeling?
  2. Should each instance be treated as independent? (I don't think that would make too much sense.)
  3. Should the patient data be aggregated in some way so that each patient is being included once in the model while still utilizing his/her data from the multiple failures?
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This is more of a recurrent events or count data scenario and there is a huge literature on this topic.

In general, you will have to assume a dependence across observations from the same object / patient / unit.

Whether you aggregate or not is dependent on what questions you are trying to answer and what assumptions you are willing to make.

One extension to recurrent events that is close to the Cox model that allows for within-patient correlation of event times is the Anderson-Gill model that is often modified to suit a particular application (e.g. allowing for time-dependent covariates, changing hazard rates after the first or after each event etc.). Other approaches include Negative Binomial regression and joint frailty modeling of the count process plus time to a terminal event (e.g. for recurrent heart failure related hospitalization and time to death).

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  • $\begingroup$ Yes and Wayne nelson has written a book in the SIAM/ASA series on this very subject. $\endgroup$ – Michael R. Chernick Dec 26 '16 at 19:33
  • $\begingroup$ Also Cook and Lawless have a book on this in the Wiley series. There is also a book by Therneau and Grambsch on extensions to The Cox model that may be relevant. Bjorn has given an excellent and I would only add some references. $\endgroup$ – Michael R. Chernick Dec 26 '16 at 19:42
  • $\begingroup$ For complete citation: 1 W. B. Nelson Data Analysis for Product Repairs, Disease Recurrences, and Other Applications (2003) SIAM/ASA. $\endgroup$ – Michael R. Chernick Dec 26 '16 at 20:02
  • $\begingroup$ 2, T.M. Therneau and P. M. Grambsh Modeling Survival Data: Extending the Cox Model (2000) Springer-Verlag. $\endgroup$ – Michael R. Chernick Dec 26 '16 at 20:07
  • $\begingroup$ 3 R.J.Cooke and J.F. Lawless The Statistical Analysis of Recurrent Events (2007) Springer-Verlag. $\endgroup$ – Michael R. Chernick Dec 26 '16 at 20:10

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