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How can you compute the confidence intervals for a ratio of risk ratios? For example: RRa = 0.52 (95% CI 0.25 to 1.08) RRb = 0.68 (95% CI 0.52 to 0.89)

If I take the natural logarithm of each RR (RRa = -0.65, RRb = -0.39), then my ratio is 0.39/0.65 = 0.6

But I don't have confidence intervals for this number (0.6)...

Assume I don't have the raw data used to develop the original risk ratios

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Shortly before he died, John Pezzullo wrote an Excel spreadsheet that calculates the ratio and confidence interval (and p value) for a comparison of either 1 two ratios and their confidence intervals or 2 two means and their confidence intervals.

The Excel spreadsheet (with one tab for means and another for ratios) is here.

With an explanation here.

For the example in the question, using the Ratios tab in the Excel spreadsheet for 0.52 (95% CI 0.25 to 1.08) compared to 0.68 (95% CI 0.52 to 0.89) we get 0.76 (0.35-1.67) for A/B and 1.31 (0.60-2.85) for B/A, with p = 0.50.

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    $\begingroup$ Thanks. Any formulas and citations behind the John Pezzullo's spreadsheet? $\endgroup$
    – Krantz
    Commented Dec 7, 2018 at 11:08

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