Can confidence interval be equal to zero? Good day!
I'm doing a study on appropriateness of empiric therapy, and did a logistic regression using the outcome (death or survival) as dependent variable with age and blood culture result as independent variables. The results showed that the odds ratio for age is 2.97E006 CI:0. I asked the technical support of the software I'm using if this was an error result. I only have 107 cases and there were no cell values with zero frequencies in the 2 independent variables.
The tech support reply was, it is an undefined confidence interval.
What does it mean to have an undefined CI? Is it safe to report a result of a zero CI, in medical field.  
 A: In a remarkable paper, Gleser and Hwang showed that, for some models, confidence intervals must have infinite expected length for any positive confidence level $\alpha$ to be attained. More precisely, there is a subset of observations with positive measure for which the length of the confidence interval is infinite. Examples include error-in-variable models and the Fieller-Creasy problem, where one estimates the ratio of two normal means.
Conversely, a confidence interval may have zero length for a subset of observations with positive measure without jeopardising the (overall) coverage probability. For instance, in the normal $X\sim\mathcal{N}(\theta,1)$ case, if we pick an empty confidence interval with probability .01 and the interval $(x-2.054,x+2.054)$ with probability .99, we end up with an overall coverage probability of
$$
\mathbb{P}_\theta(|X-\theta|<2.054)\times .99 = .96\times .99 = .95
$$
A: An odd ratio of 2.97E006 (if you mean 2970000) seems odd to me, since it is way too high. Given your sample size it could be that some categories of the independed variables have a low frequency (e.g. a 1). Based on the information you provided it is indeed not safe to report the CI. I think no journal will expect a CI of zero, if it is zero there is no interval! 
The ci for a logit is calculated as   $ln(OR)-(Z*SE)\leq\theta \leq ln(OR)+(Z*SE)$
If this results in zero, something is wrong.
