# How can one invert hazard ratios and their confidence intervals?

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!

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.

• Don't invert the p-value, though. Commented Jan 9, 2019 at 19:07

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 $$(1/x_u,1/x_l)$$.

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

• 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? Commented Aug 1, 2020 at 12:05