Question on modeling repeated outcomes among single patients



I was reading about the PARAGON-HF trial design:

where rehospitalizations are being modeled using LWYY semiparametric regression instead of a time-to event analysis. Are there other suggested methods people would recommend for looking at repeated events like hospitalizations as an endpoint? I’m more familiar with two-part models. Any assumptions or limitations of LWYY I should be aware of. How would one suggest accounting for competing risk/mortality endpoints?

I now Dr. Harrell has discussed Bayesian modeling composite endpoints, but wasn’t sure how repeated endpoints would be modeled in this framework.


I think it’s worth some discussion about the criteria that an analytical method should meet in this setting. Then we can discuss particular models. Here’s a draft:

  • The statistical method must be able to distinguish a more severe outcome from a less severe outcome, with the result being that a treatment that has more benefit on more severe outcomes getting credit for this.
  • It should have a reasonable way to “score” early less severe events against later more severe events.
  • Multiple occurrences of the same event should be considered as worse than single occurrences.
  • Ideally, it should allow for competing risks by accounting for irrelevant absorbing states, e.g., non-related cause of death.

:new: The last point is tricky. A method that allows for a hierarchy of severity of events may not accommodate a cause of death such as “accidental” that interrupts the follow-up and masks other relevant events. Methods that explicitly handle competing risks don’t currently allow for multiple types of events of differing severity, and perhaps not for recurring nonfatal events.


-“How would one suggest accounting for competing risk/mortality endpoints?” rogers and pocock had a good paper illustrating advantages of joint frailty approach:
-multi state model approach:
-weighted approach: (i don’t like this at all)
-wlw criticism:

sorry for just dumping references and not contributing to discussion …! (travelling etc)


I added a bit related to this in my early note.


yeah, it becomes complicated as the different types of events interact with each other eg you can’t have an ED visit if you’re already in the hospital, or maybe they move from ED to hospital (treated as a third event-type “ED-hospital”?). Maybe then we use days-alive-and-out-of-hospital, and i guess this accounts for severity in a way because a hospital visit is lengthier than an ED visit. We described a model for multi-type recurring nonfatal events (using a joint frailty for mortality) [paper] but the event types are nominal (‘severity’ is considered only in the interpretation of results). But it does handle the competing risk of death and to distinguish between event-types…

edit: to your other point, i guess it is interesting whether you use mortality or just CV related death. I’ve heard arguments for both, but i can only ever recall a paper by yusuf [yusuf paper]. In the rogers paper i linked to above they used CV death


I think that multi-state transition models are the most flexible and interpretable. The problem is they require enormous sample sizes because of the huge number of parameters to estimate. It would be nice to have a way to place restrictions on parameters using Bayesian priors.


the multistate model doesn’t give a sense of the relatedness of events, that’s the downside i see. The multitype events random effects model gives an estimate of the correlations among event types, and the dependence between events of the same type. I have never tried to fit a multistate model, mostly ignorance but also a concern that with many recurrent events there are too many transitions and states and the model won’t converge


By multi-state do we mean state-space model? If it’s autoregressive, don’t we get a sense of how covariates are dependent on the previous time point?

I think we can do this with a linear state-space model, am I wrong?

My only issue here is that some of the observations I’m dealing with have 1-2 time points… with this approach the prior might dominate (although not “constrict” the posterior so much as regularize). There are classical solutions as well but when T is small priors would be helpful


I think that is correct, although the transition probabilities between various events give a clue. To more directly do that we are exploring Bayesian copula models. Here one specifies all the usual marginal outcome models but connects them through copulas to model dependence structure. Difficult to see how to handle events that mask other events though.


You could lump events after a certain number into the same state and allow a transition from that state to itself. E.g., Entry -> first -> second -> third_or_more -> third_or_more -> …

After the third (or fourth, or some number) event of the same type you consider the subejcts to be in the state of having had “many” events which sometimes make sense from a clinical perspective.