Please be advised that @graemeleehickey and others are more expert than I am in the direct, real-world application of such models, but here I am, so whatever. Read it, or don’t.
Suppose you’re just reading along in the #COAPT primary paper, found here:
nejm.org/doi/full/10.10…
when you encounter this bumfuzzle:
nejm.org/doi/full/10.10…
when you encounter this bumfuzzle:
“Analysis of the primary effectiveness end point of all hospitalizations for heart failure was performed with a joint frailty model to account for correlated events and the competing risk of death.”
You ask “What’s a *joint frailty* model? What’s wrong with regular old Kaplan-Meier curves and Cox models?”
Well: sometimes we’re interested in the effect our intervention has on a specific endpoint (hosp for heart failure) that a) patients may experience more than once and/or b) patients may cease to be at risk for because something else happened and they’re no longer at risk (death)
In traditional survival analyses with time-to-event data (Kaplan-Meier, Cox models) we follow the patient until i) they have the event or ii) are “censored” and no longer at risk for the event
Patients may be censored for several reasons: i) end study, ii) patient withdrawal or loss 2 follow-up, and most importantly iii) experienced some competing event which makes them no longer at risk (if HHF is primary endpoint, a patient who has died is no longer “at risk” of HHF)
“Doesn’t a regular survival analysis account for censoring though?”
Yes, but with an assumption of *non-informative* censoring, meaning that the censoring is not related to the probability of experiencing the event
With an outcome like “hospitalization for heart failure” there is a difference between a patient censored because they died (no longer at risk for HHF) versus a patient censored because the study ended (also no longer at risk for HHF, but with different implications than “death”)
Also, the aforementioned “regular” survival analysis only follows a patient until their first event, but that can throw away a lot of useful information & doesn’t capture the full burden when the endpoint is something like HHF (which can happen multiple times to some patients)
“What about Andersen-Gill models…” – KEEP YOUR SHIRT ON, we’ll get there
Anyways, that’s the groundwork for why we need something a little different than your traditional Kaplan-Meier-curves-with-a-regular-old-Cox-model approach for the #COAPT primary endpoint
Now, I’ll paraphrase (er, copy) a few tweets from @graemeleehickey describing the joint frailty model
We begin with a recurrent events model (Andersen-Gill) with a frailty term (random effect)
[important: the random effect / frailty term allows you to model correlations between events of the same patient by using a random component for the hazard function]
We also have a second model for the failure process (death) that includes the frailty term
The models are linked by sharing the random effect. It is a joint model for 2 separate but correlated event processes.
Does that confuse you? Probably! I don’t really have a better way to explain it without lots of mathiness and symbols. If anyone else does, I am delighted to hear/see it.
“Gee Andrew. Shouldn’t we use these instead of Kaplan-Meier / Cox models for basically any endpoint like hospitalization when mortality is a competing risk?”
It would seem so! Maybe there’s a good reason not to…again, would love to hear from someone who has studied these in more depth.
Here are some technical papers on joint frailty models:
academic.oup.com/biostatistics/…
ncbi.nlm.nih.gov/pubmed/17267392
ncbi.nlm.nih.gov/pmc/articles/P…
academic.oup.com/biostatistics/…
ncbi.nlm.nih.gov/pubmed/17267392
ncbi.nlm.nih.gov/pmc/articles/P…
Suggest consulting your friendly neighborhood statistician if you are studying an endpoint such as HHF or something else which has the conditions named above: a) multiple occurrences and b) competing risk likely to lead to noninformative censoring on your primary endpoint
All questions may be referred to @graemeleehickey
(also, #cardiotwitter and #medtwitter, you should probably be following Graeme if you’re not already)
