ｍａｒｋ一下，
等我忙完手头的事　想一想

So here you are making inference on comparing the means of two populations, using two samples.
In this case, it's reasonable to assume the two samples are independent, right?

Usually the estimator for the mean follows normal distribution, and we do can do a z-test, if the variance is known, or a t-test, if the variance is unknown.
H0: mu1-mu2=0
z = (xbar1-xbar2-0) /square root of (Var1 + Var2)

But in this case, the estimator for the mean(Odds Ratio) follows lognormal distribution, right?
We do something similar to the above, but slightly different. Hypothesis test for lognormal distribution is not common. I can refer you to a 2003 paper which is not long, only 19 pages.
It answers your question on page 9-10.

K. Krishnamoorthy and  Thomas Mathew (2003), "Inferences on the means of lognormal distributions using generalized p-values and generalized confidence intervals", Journal of Statistical Planning and Inference 115 (2003) 103 – 121

Hope this helps.

I met with my stat professor.

1. Can take the shortcut by taking log of the lognormal distributed random variables (Odds Ratio in this case) and doing a z-test or t-test?
If the two population variances are unknown and we only have estimates of the two variances, which is a typical case, then we cannot take the shortcut by taking log and doing a t-test.
If the two population variances are known, then it's OK to do so with slight modification.

2. In case of logistic model, there is a built in command in SAS to do hypothesis test for comparing the means of two populations. But he cannot recall the command. So check SAS user guide if you don't want to go through the paper I referred.

楼上高手，学习！
请否告知是哪个学校的？

非常感谢你的回答，但是感觉似乎并没有直接解决我的问题，不知能否说得更为详细，^_^