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I have been wracking my brain for several weeks now, trying to figure out the best way to model the following type of data:

I am helping to set up a clinical trial. We are testing a new type of sealant for sealing wounds after lung surgery, and comparing it to an existing sealant on the market. Since this is a lung surgery, residual air may be leaking out after the surgery is over, even after applying a sealant. Patients can experience an air leak after surgery (this is fairly common), but they also might not. The duration of this air leak is our endpoint of interest.

An air leak is a negative symptom, therefore a sealant is better if the air leak duration is shorter. Intuitively, a lower incidence of air leak is also better, though a simple analysis (e.g t-test) of our current chosen endpoint (duration of air leak) may not reflect this additional information.

Additionally, patients may be sent home while still experiencing an air leak. Therefore, some observations may be censored.

As you can see, it's not a traditional 'time-to-event' analysis, since the duration itself is conditional on whether patients experience the air leak. It's almost like we have a double time-to-event analysis... 'time to air leak' (and corresponding censoring if no air leak occurs) and then 'duration of air leak' (and corresponding censoring if patient goes home before air leak ends).

Also, I think it's unwise to treat as a simple continuous endpoint (as most papers have done in their analysis) as you lose the information regarding the amount of patients actually experiencing the event.

One last thing - I would like to present the result as a difference in median duration and corresponding 95% confidence interval (rather than hazard ratio or whatever), since this 'difference in duration' is what I based my sample size off of.

Do you have any suggestions on how to best model this endpoint? Are recurrent event analysis methods appropriate here (e.g Anderson-Gill)? Is there some weird zero-inflated survival analysis? Am I overthinking this, and should I just treat it as continuous?

If you have any ideas or suggestions I would REALLY appreciate to hear them :) Thank you!

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    $\begingroup$ Seeking some off-the-shelf model that will convert data from this trial into 'results' for a publication wastes precious scientific opportunities. Rather than to model the data, you might rather model the phenomena underlying the scientific and clinical questions at issue. Consult the surgeons. Some surely expect the new sealant is superior: WHY? Others will have their doubts: WHY? You're dealing with at least 2 phenomena: the intraoperative leak formation, and its postoperative healing. Might a sealant reduce probability of any leak, yet delay healing of leaks that do occur? $\endgroup$ Jun 27, 2017 at 20:19

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I can just give you a short suggestion. Have you looked into Poisson regression models? They are based on the Poisson distribution to model count data. Here you should find some information about these types of models, but I am thinking this would suit to your problem best.
There exists also extensions for censored data if this is a big deal within your given data.

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