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?
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$\begingroup$ See Interpretation of simple predictions to odds ratios in logistic regression. $\endgroup$– Scortchi ♦Commented Apr 19, 2016 at 10:56
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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.
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1$\begingroup$ Can you confirm that from the estimated mean and variance of a regression coefficient I can not estimate the associated odds ratio? $\endgroup$– DonbeoCommented Apr 19, 2016 at 13:08
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$\begingroup$ (!) 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. $\endgroup$ Commented Apr 19, 2016 at 13:14
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2$\begingroup$ 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. $\endgroup$ Commented Apr 20, 2016 at 3:26
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$\begingroup$ hey don't kill the messenger: en.wikipedia.org/wiki/Confidence_interval $\endgroup$ Commented Apr 20, 2016 at 8:16
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2$\begingroup$ 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. $\endgroup$ Commented Apr 20, 2016 at 12:16