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I am trying to analyze time-to-event data (time to completion of a task). Looking at the KM curves, there is a distinct behavioral change around 12 months. This makes sense, because at 12 months there is a policy requiring completion of the task to meet compliance.

I wanted to perform a cox regression, but this appears to violate the hazards assumption, and I was wondering the best way to handle this. I thought I might fit two models, one between 0-12 months and one 12+ months, but I don't know if this is the best way to handle this (and how one sets up data for this analysis in r). Maybe I would use time-variant covariates instead? I'm not sure how to set the data up for that either.

I'm showing the cumulative incidence curves here: Cummulative Incidence

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  • $\begingroup$ that behavior change is not, if taken alone, a violation of proportional hazard assumptions. Cox model assumes a baseline hazard function dependent on time, which is not estimated and may take any form. Of course overlapping, differently shaped lines on the graph actually show non proportional hazard, but training two models won't solve the problem. $\endgroup$ – carlo Nov 2 '19 at 17:09
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Indeed, this is due to time dependent effects. Do you know, for each patient, the time to "completion of the task to meet compliance"? If so, you can include a binary time dependent variable that is 0 before this time, and 1 after this time, indicating that the mysterious task was completed. Most softwares are able to include this kind of variables.

Be careful when comparing two survival curves as, if there were many patients dying before the completion of the task, then you may incur into the "immortal time bias" phenomenon.

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    $\begingroup$ Oh perhaps I misrepresented my problem. What I am saying is that I have a scenario where there is only 1 event of interest: completing a task. So records are censored if they are lost to follow-up or have not completed the task at the last known status. There is no death. $\endgroup$ – Brandon Oct 31 '18 at 16:09

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