Solved – Calculate of standard deviation for an Odds Ratio by standard deviations of probabilities

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 $P_2$?

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


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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