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I have a survival data on approximately 6 million observations. The "failure" I'm dealing with is very rare - about 0.5% has the event of interest.

I have three questions:

  1. Can I perform a case-control analysis with Cox regression?
  2. If the answer is yes - do I just need to sample, let's say, 10 controls for each case, and then run a "regular" Cox regression?

Thanks!

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  1. Yes.
  2. No.

What you probably want is a case-cohort analysis, where you weight the selected observations according to their selection probabilities: a weight of 1 for cases and approximately 20 for controls. The 'approximately 20' comes from 0.5% of cases -> 5% of control -> 1 in 20 non-cases selected.

Operationally, in R you can use survival::cch or survey::twophase and survey::svycoxph and I think there are implementations in Stata and SAS.

If you just ignore the sampling, as you would with a case-control logistic regression, you get slightly biased hazard ratios and a badly biased baseline hazard curve.

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