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From |
May Boggess <mboggess@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: standard error of the odds ratio |

Date |
Mon, 26 Sep 2005 16:45:05 -0500 |

On Monday morning Kate asked about the standard error of the odds ratio:

The epitab command -cc- reports, by default, an exact confidence interval for the odds ratio, so there is in fact no standard error when the interval is computed this way.I need to calculate the standard error of the odds ratio and use the "cc" command which reports the 95% confidence interval but does not report the standard error itself. I would appreciate it very much if anyone could let me know if there is a way or an option to specify that the standard error of the odds ratio be reported in the output as well.

One thing Kate might want to do is to use the Woolf confidence interval. One can obtain the upper and lower bounds of the interval using the option -woolf- on -tabodds-. A standard error is reported if we use the command -logistic- to obtain the Woolf confidence interval. Here is an example that shows what I mean by all of this:

clear

webuse downs

expand pop

cc case exposed

cc case exposed, wo

logistic case exposed

Now, you may notice that the interval is not symmetric so one doesn't just add and subtract 1.96*se to get the confidence interval. It is in

confidence interval of the log of the odds ratio that is symmteric.

Here is how the above interval is calculated (I'm using the option -coef- on -logistic- to show the actual coefficients of the model

as opposed to the odds ratio here):

logistic case exposed, coef

display "or = " exp(_b[exposed])

display "lb = " exp(_b[exposed]-invnorm(0.975)*_se[exposed])

display "ub = " exp(_b[exposed]+invnorm(0.975)*_se[exposed])

So what is the standard error that -logistic- reports then? The standard error of the odds ratio is

display "se(OR) = " exp(_b[exposed])*_se[exposed]

(see [R] logistic, page 67 in version 9 manuals).

--May

mmb@stata.com

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**Follow-Ups**:**Re: st: standard error of the odds ratio***From:*katsiaryna ivanova <kivanova@usc.edu>

**References**:**st: standard error of the odds ratio***From:*Kate Ivanova <kivanova@usc.edu>

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