What is the distribution of OR (odds ratio)? I have a bunch of articles presenting "OR" with a- 95% CI (confidence intervals).
I want to estimate from the articles the P value for the observed OR.  For that, I need an assumption regarding the OR distribution.  What distribution can I safely assume/use?
 A: Generally, with a large sample size it is assumed as reasonable approximation that all estimators (or some opportune functions of them) have a normal distribution.  So, if you only need the p-value corresponding to the given confidence interval, you can simply proceed as follows:


*

*transform $OR$ and the corresponding $(c1,c2)$ CI to $\ln(OR)$ and
$(\ln(c1),\ln(c2))$
[The $OR$ domain is $(0,+\infty)$ while $\ln(OR)$ domain is $(-\infty,+\infty)$]

*since the length of every CI depends on its level alpha
and on estimator standard deviation, calculate
$$
d(OR)=\frac{\ln(c2)-\ln(c1)}{z_{\alpha/2}*2}   
$$
$[\text{Pr}(Z>z_{\alpha/2})=\alpha/2; z_{0.05/2}=1.96]$

*calculate the p-value corresponding to the (standardized normal) test statistic $z=\frac{\ln(OR)}{sd(OR)}$
A: The estimators $\widehat{OR}$  have the asymptotic normal distribution
around $OR$. Unless $n$ is quite large, however, their distributions are highly
skewed. When $OR=1$, for instance, $\widehat{OR}$ cannot be much smaller than $OR$ (since $\widehat{OR}\ge0$), but it could be much larger with non-negligible probability. The log transform, having an additive rather than multiplicative structure, converges more rapidly to normality. An estimated Variance is: 
$$
\text{Var}[\ln\widehat{OR}]=\left(\frac{1}{n_{11}}\right)+\left(\frac{1}{n_{12}}\right)+\left(\frac{1}{n_{21}}\right)+\left(\frac{1}{n_{22}}\right).
$$
The confidence interval for $\ln OR$:
$$
\ln(\hat{OR})\pm z_{\frac{\alpha}{2}}\sigma_{\ln(OR)}
$$
Exponentiating (taking antilogs) of its endpoints provides a confidence interval for $OR$.
Agresti, Alan. Categorical data analysis, page 70.
A: The log odds ratio has a Normal asymptotic distribution :
$\log(\hat{OR}) \sim N(\log(OR), \sigma_{\log(OR)}^2)$
with $\sigma$ estimated from the contingency table.  See, for example, page 6 of the notes:


*

*Asymptotic Theory for Parametric Models
A: Since the odds ratio cannot be negative, it is restricted at the lower end, but not at the upper end, and so has a skew distribution. 
