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Imagine that when we compare treatment A to treatment B there is an associated hazard ratio of 0.56 (95% CI: 0.36 to 0.87). Let's say that instead of this, I want the hazard ratio associated with comparing treatment B to treatment A. Do I simply invert the HR (1/0.56 = 1.79) and invert the CI limits (1/0.36 = 2.78, 1/0.87 = 1.15) to obtain an "inverted HR" of 1.79 (95% CI: 1.15 to 2.78)?

Or must I use a more complicated formula?

My apologies if this is an overly simplistic question, but I can't find an answer to this anywhere. Thank you kindly!

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3 Answers 3

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Yes, you can just use the inverse of the HR point estimate and the confidence interval endpoints.

As the name suggests, the hazard ratio is a ratio of hazard rates in the two groups. So if the groups are switched, so can be the nominator and the denominator of HR.

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    $\begingroup$ Don't invert the p-value, though. $\endgroup$
    – AdamO
    Commented Jan 9, 2019 at 19:07
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Yes, you can invert both the point estimate and the confidence limits. If the original point estimate is $x$ with a 95% confidence interval $(x_l,x_u)$ you can invert it to get estimate $1/x$ and a 95% confidence interval $(1/x_u,1/x_l)$.

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HR= exp(x2B)/exp(x1B), so one can directly invert the point estimate

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    $\begingroup$ This does not seem to add anything to the existing answer. Can you edit it to include any details missing, in your view, from the other answer? $\endgroup$
    – mdewey
    Commented Aug 1, 2020 at 12:05

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