# Constructing CI for log OR based on OR

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.

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 : $\overline{lor}\pm1.96 se_{\overline{lor}}$