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Clinical Biostatistics: Geometric mean length of hospital stay exercise, suggested answer 4

4. How could the 95% confidence interval given as “8% shorter stay to 56% longer stay” have been calculated?

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Suggested answer

This comes from a 95% confidence interval for the ratio of the geometric means
of the length of stay.
The antilog or back transformation of the difference in mean log length of stay
is the ratio of the two geometric means.

A 95% confidence interval for the difference in mean log length of stay was
also calculated and the antilog of the confidence limits gives the
95% confidence interval for the ratio of geometric means.
Here they will have a 95% confidence interval for the ratio equal to 0.92 to 1.56,
which has been presented as 8% (1 – 0.92 = 0.08) to 56%.

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