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I've seen this done in NICE HTA submissions where a hazard ratio from a meta-analysis has been applied to a range of survival functions. More generally, are you able to apply a hazard ratio, however it was estimated, to any survival curve? With this, are you then able to get survival probabilties by converting it to the survival function?

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Yes. Once you have a reference survival function, say, by digitalizing a published Kaplan-Meier plot from a low-risk of bias, larger cohort, you can:

  1. Calculate the hazard function from the survival function (reference hazard function).
  2. Multiply the reference hazard function by the hazard ratio.
  3. Convert back the new hazard function to survival function
  4. Plot the two survival functions.

This procedure assumes, inherently, proportional hazards.

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  • $\begingroup$ Can you share the NICE reports using this approach? $\endgroup$
    – Jacob
    Commented Jul 7, 2023 at 1:02
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    $\begingroup$ You do have to be sure that the reference hazard function from the other cohort represents the reference situation for the new cohort of interest, however. This is a situation where you certainly can do the calculations in the way you suggest, but you would have to be very cautious in interpreting the details of the survival curves. $\endgroup$
    – EdM
    Commented Jul 7, 2023 at 12:24

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