How does the hazard ratio change when the exposure is doubled? I am a medical student who somehow ended up having to do a meta-analysis. I have no knowledge about statistics.
For example, if the cardiovascular mortality hazard ratio associated with a 5μg/m3 change in PM2.5 is 1.5, what would be the hazard ratio for a 10μg/m3 change in PM2.5??
Thanks a lot!!

If the hazard ratio associated with a given change in circumstances is $1.5$, then this change multiplies the original hazard rate by $1.5$
Assuming this hazard ratio stays constant in different circumstances (this is a strong assumption) then making the same change a second time would multiply the new hazard rate by a further $1.5$,
so double the original change in circumstances would multiply the original hazard rate by $1.5^2$ i.e. by $2.25$, and this is the hazard ratio for the double change
