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What is the relationship between the confidence interval and odds ratio of a regression coefficient in multivariable logistic regression?

Is there a one to one relationship? i.e. Can I measure one from the other?

Frank Harrell
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Donbeo
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the confidence interval aka CI (typ. at 95% ) is two numbers = (za, zb). Given an odds ratio = z, the prob that the actual z falls outside the (za, zb) interval is less than the (confidence) 95%. You cannot measure one from the other at all. The only thing you know is that the z is inside the interval.

Jose Berengueres
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    Can you confirm that from the estimated mean and variance of a regression coefficient I can not estimate the associated odds ratio? – Donbeo Apr 19 '16 at 13:08
  • (!) regression coefficients do not have mean or variances, they are parameters of a model that can be more or less accurate (read useful). The estimated odds ratio depends on the coeff. that is all. – Jose Berengueres Apr 19 '16 at 13:14
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    This is not a proper definition of a confidence interval Jose. In the frequentist world there is no probability associated with a parameter. A parameter is either inside or outside an interval. CIs deal with long-run operating characteristics. This complexity turns many of us to Bayesian statistics. – Frank Harrell Apr 20 '16 at 03:26
  • hey don't kill the messenger: https://en.wikipedia.org/wiki/Confidence_interval – Jose Berengueres Apr 20 '16 at 08:16
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    The definition given in the Wikipedia article is different from yours. It's a fine point but shows weaknesses in the frequentist approach to inference, or at least the difficulty of teaching frequentist methods. – Frank Harrell Apr 20 '16 at 12:16