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I have in my data the mean OR and its standard deviation (computed by Delta method). I have a question about constructing a 95% CI for the log OR based on this data (based on asymptotic normality assumption).

Can I first construct a 95% CI for the OR and then take the log of that?

Or, should I compute the mean log OR and the standard deviation of the log OR (standard deviation of OR/mean OR), and then construct a 95% CI based off of that?

Currently, I am leaning towards the latter approach.

Thanks.

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I assume you are doing a meta analysis. The simplest way of doing this is:

  1. Go back to all log(odds ratios) and their standard errors: $lor = ln(or)$ and $se_{lor} = \frac{se_{or}}{or}$
  2. compute weights for each observation/study: $w=\frac{1}{se_{lor}^2}$
  3. The average effect size is the weighted average: $\overline{lor} = \frac{\sum_i w_i lor_i}{\sum_i w_i}$
  4. The standard error is $se_{\overline{lor}}= \sqrt{\frac{1}{\sum_i w_i}}$
  5. Compute the confidence interval using : $\overline{lor}\pm1.96 se_{\overline{lor}}$
  6. transform those back to the odds ratio metric by exponentiating the effect size and the confidence interval boundaries.
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  • $\begingroup$ The approach I am using is based in the confidence distribution framework, and I'm combining MH odds ratios based on this framework. The 'gmeta' package in R allows me to input 2x2 table data and gives me the meta-analysis odds ratio mean and its standard error. However, I want to turn these statistics for the odds ratios into statistics for the log odds ratios. $\endgroup$ Nov 27 '14 at 14:35
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    $\begingroup$ Than you need to look into the documentation of that package (or in the code) to see what it does exactly, and base your next action on that. $\endgroup$ Nov 27 '14 at 14:45

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