# Why odds ratio less than lower limit of 95% confidence interval?

Can there be a situation where odds ratio is less than lower limit of 95% confidence interval? If yes then what could be the possible reason for this? The formula I used to calculate confidence interval is exp(log(OR)+/-(1.96*SE)).

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Assuming your talking about the sample odds ratio - No, because $\exp$ is a monotone function. If you found this happening then it must be a mistake. Can you provide more details? –  Macro Oct 9 '12 at 16:05
@Macro The odds ratio = 0.806, standard error = 0.061 and 95% CI = (0.808 - 1.0262) –  Ismeet Kaur Oct 9 '12 at 16:10
I'm getting a different confidence interval from the one you wrote there. On the log scale, the confidence interval is $\log(.806) \pm 1.96 \cdot .061 = (-.335, -.096)$. Exponentiate that and you have $(.715, .908)$. As I said, since on the log scale the lower bound must be smaller than the point estimate, and $\exp$ is a monotone function, it's impossible for the sample odds ratio to be less than the lower bound of the confidence interval. –  Macro Oct 9 '12 at 16:16
@Macro You are taking natural log that why you are getting this value, where as i am taking log to the base 10 –  Ismeet Kaur Oct 9 '12 at 16:55
You need to use the natural log if you want your results to make sense and be comparable. If you use a different base for the log and the exponential then you are scaling the results, kind of like having a mean in inches, then computing a CI in centimeters and wondering why the mean is outside the CI. –  Greg Snow Oct 9 '12 at 18:01