Standard Error – How to Calculate SE of an Odds Ratio

odds-ratiostandard error

If one is calculating odds ratio with a,b,c and d counts, I believe variance of log(OR) is given by

var_log_OR = (1/a + 1/b + 1/c + 1/d)

Hence one can calculate 95% confidence intervals of OR as follows:

SE_log_OR = sqrt(var_log_OR)

CI_lower_log_OR = log(OR) - 1.96*SE_log_OR
CI_upper_log_OR = log(OR) + 1.96*SE_log_OR

CI_lower_OR = exp(CI_lower_log_OR)
CI_upper_OR = exp(CI_upper_log_OR)

But how can we calculate SE of OR?

Best Answer

@FrankHarrell is right that the standard error for an odds ratio is a problematic number in the sense that you can do better by testing on the corresponding log(odds ratio) scale, as the sampling distribution of the log(odds ratio) is more likely to be normally distributed.

Nonetheless, the standard error of the odds ratio does exist, even if it is not that useful. One possible estimate is to use the delta method to move from the standard error of the log(odds ratio) to an approximation of the standard error of the odds ratio.

$\sqrt{(1/a + 1/b + 1/c + 1/d)}\times\frac{a\times d}{b\times c}$

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