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The basic methods statistical packages, using K-M or Cox regression, are both to handle both recurrent events and competing risks. This setting is very common in medicine, where we have recurring illnesses, for example cancer, and the terminal events, like deaths.

Of course censoring the terminal even is nonsensical and ignoring recurrent events is also unrealistic. So we need to model them together.

I learned, that joint frailty models (extending the Cox for random-effect-like terms) or multi-state model can handle both at the same time. Also, the Fine-Gray handles competing risks, and Andersen-Gill handles recurrent events.

But why do we need them all, if the simple routines, like Cox and Kaplan-Meier already present can handle that together? What was the reason for introducing multi-state models and joint frailty models?

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Cox and Kaplan-Meier can't handle it all. Competing risk models are hard to interpret. Fine-Gray makes a proportional hazards assumption that Therneau has shown can't usually be satisfied. None of these methods handle ordinal severity of outcomes. The most general approach which respects the raw data that goes into all of the analytical methods is a multi-state transition model. Easier to interpret, more flexible, and handles ordinal states and recurrent events. For detailed case studies see https://hbiostat.org/proj/covid19. Think about longitudinal ordinal outcome models as flexible, unifying approaches. You can do a lot with Markov proportional odds models, either in discrete time (easier) or in continuous time, as shown in the reports linked from the above link. You can also throw random effects into longitudinal models if you have clustering and don't just need to handle serial correlation.

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  • $\begingroup$ Thank you, Sir Professor Harrell. I just learned the frailty models are nothing but a multi-level, mixed-effects models, where the recurrence of events and competing risks are treated as random effects. I was confused as I read the documentation for the survival package in R and they handled both recurrent events (by re-shaping the data, splitting the period into sub-periods, called "counting process") and competing risks (added additional categories to the event outcome and used the time to either of them).I asked myself - if they did it with just the "survival" package, why do I need others? $\endgroup$ Commented Apr 24, 2021 at 20:07
  • $\begingroup$ The usual recurrent event models don't handle absorbing states (interrupting events) and competing risk models are hard to interpret. State transition respect all the raw data and are much easier to interpret. They also allow for the flow to be interrupted by other events. $\endgroup$ Commented Apr 24, 2021 at 20:15
  • $\begingroup$ Thank you Sir Professor Harrell. I found this article, where it's shown, how the multi-state problem is "aggregated" in the Fine-Gray and how they both can be handles by the Cox procedure (after some "tweaking") and relationship to the Aalen-Johansen estimator. cran.r-project.org/web/packages/survival/vignettes/compete.pdf $\endgroup$ Commented Apr 25, 2021 at 11:45
  • $\begingroup$ That is a fantastic article. But the methods covered there don't extend to the general cases I mentioned. $\endgroup$ Commented Apr 25, 2021 at 12:53

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