I am reading a paper on how the authors calculate the variance/standard deviation of what appears to be log(odds).

The paper is a medical paper (Discontinuation of Oral Antivirals in Chronic Hepatitis B: A Systematic Review).

In the paper, it seems that they are doing something equivalent of log(odds) by using $\log(p/(1-p))$.

However, I don't understand how they get the variance to be $1/[Np(1-p)]$.

I am confused by other sources stating that the standard deviation of log odds is supposed to be $\sqrt{1/a+1/b+1/c+1/d}$. For instance, How do I calculate the standard deviation of the log-odds?.

Are the two approaches the same or different? Which is correct?

cited text as pdf


1 Answer 1


$$\hat Var(log(\frac p{1-p})) \approx \frac 1 {Np(1-p)}$$

$$\hat Var\left[log\left(\frac {p_1/(1-p_1)}{p_2/(1-p_2)}\right)\right] \approx \frac 1 a + \frac 1 b+ \frac 1 c +\frac 1 d$$ where $p = X/N$ is estimate of parameter $\pi$ in $X\sim Bin(\pi,n)$

First one is for log ODDS, and second one is for log ODDS RATIO. In the linked page, OP misused ODDS.


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