Elasticity in time to the event

I wanted to comment on a concept that is used a lot in engineering but I have not seen it much in medicine, the elasticity of time to the event.

What I thought I knew before I read this was that the hazard rate is a rate of events per unit of time.
Therefore, the reciprocal (1/ hazard rate) is the average time in which the events occur.
Now, I have seen RCTs in which 100/HR is interpreted similarly to a “time ratio”, as the ratio of the average time to the event for the two levels of the variable.
I wanted to ask why this elastic function of engineers is not popular in medicine.
Thank you.

1/\lambda is only the mean \mu in the special case of the simple exponential distribution: S(t) = e^{-\lambda t}. The exponential distribution tends to be used in sample size calculations but not in actual study analysis.

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Yes, that’s what I knew about this.
My doubt is when this is brought to the result of an RCT evaluated with the Cox model, where S(t)= So(t)^ e^{-bX}. How can I interpret 100/HR = 100/exp(bX) in a Cox model… ?

You cannot interpret that.

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