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Clinical Biostatistics: The ESPRIT Trial, suggested answer 5

5. The hazard ratio = 0·80 with 95% CI 0·66–0·98.
The centre of this confidence interval would be 0.82.
Why is the hazard ratio point estimate not in the centre of its confidence interval?

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Suggested answer

The hazard ratio and its confidence interval are calculated on the logarithmic scale.

We estimate the log hazard ratio and its standard error.
From these we find a 95% confidence interval for the log hazard ratio
by subtracting or adding 1.96 standard errors.
At this point, the confidence interval is symmetrical around the point estimate.
Finally, we antilog to get back to the ratio on the natural scale.
This makes the lower limit closer to the estimate than is the upper limit.

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