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Given the formula $OR=\frac{P_1(1-P_2)}{P_2(1-P_1)}$ for calculating the odds ratio ($OR$). How can I calculate the standard error of $OR$ based on the standard errors of $P_1$ and $P_2$?

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If you have the cell counts you can get the standard error for the $\ln(OR)$ (see for exampel here) :

$\sqrt{\frac{1}{n_{11}}+\frac{1}{n_{10}}+\frac{1}{n_{01}}+\frac{1}{n_{00}}}$

Using the delta method, you can approximate the standard error of the $OR$ as:

$OR \times \sqrt{\frac{1}{n_{11}}+\frac{1}{n_{10}}+\frac{1}{n_{01}}+\frac{1}{n_{00}}}$

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  • $\begingroup$ But I haven't cell counts: n11, n10, n01 & n00 $\endgroup$ – Ehsan Razzaghi Oct 27 '14 at 10:08

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