Should I use Cox PH regression when there is large share of observations that never 'die'?

[Li recordyao]

I'm considering model patent right transfer as a survival process. That is, when a patent is transferred, it is considered death; if not, it's survival.
I'm not using Logitic regression because I want to know whether some policy will speed up the patent transfer process, and also we don't know whether some patent will be transferred yet.

But the problem is that only a small share of patents are transferred (about 10%), and most patent will never be transfer in its patent life. Could that be a problem for using Cox regression? If I remove these never transferred patents and only keep the ones that eventually transferred, would that be a problem?

My questions are basically:

1. Can I use Cox regression when a sample with a large proportion of observations never die?
2. Would it problematic if I conduct Cox regression on only those that eventually die?

Thank you for your reply!

[Li recordyao]

Another question: do people every use difference-in-diferences in Cox PH regression?

[Mike Lacy]

By analogy to what is known in other kinds of estimation, I suspect that having a small *proportion* of "deaths" is not the issue, but rather the problem would be having a small *number* of "deaths." You'd get better advice here if you reported that number rather than the percent. Regarding the second question, analyzing only the cases that resulted in a death would be a selection bias, given that you would have a sample that distorts the true distribution of the response variable. I'm again reasoning by analogy, in this case to ordinary regression models in which there is selection on the response variable distribution. However, I have not specifically read literature on either topic, but I'd suspect it exists.

Regarding your third question, I'm not knowledgeable, but a quick bit of searching the net on /"difference in difference" cox survival/ yields quite a few hits, including a number on StataList itself. Perhaps something there might help you.