# [R] Coefficients, OR and 95% CL

Frank E Harrell Jr f.harrell at vanderbilt.edu
Tue Sep 23 14:37:02 CEST 2008

```Eik Vettorazzi wrote:
> l.mod<-glm(menarche~age,binomial)
>
> you will get odds-ratios by exponentiating the coefficients of this
> model, so
>
> exp(coef(l.mod))
>
> will do this job. You may notice that this will produce an "OR" for the
> intercept part as well - which is not interpretable.
> For the confidence intervals for this odds ratio you have to
> exponentiate the borders of the "standard" confidence intervals for the
> log-odds-ratios,
>
> exp(confint(l.mod))
>
> hth.

The approach of anti-logging a coefficient only works in the simple case
in which the variable is binary (or a one-unit change is of interest and
the variable is linear), doesn't interact with another variable, and the
reference cell desired equals the reference cell coded.

Frank

>
> Luciano La Sala schrieb:
>> Dear R-users,
>>
>> After running a logistic regression, I need to calculate OR by
>> exponentiating the coefficient, and then I need the 95% CL for the OR
>> as well. For the following example (taken from P. Dalaagard's book),
>> what would be the most straightforward method of getting what I need?
>> Could anyone enlight me please?
>> Thank you!
>> Lucho
>>
>>> summary(glm(menarche~age,binomial))
>>>
>>
>> Call:
>> glm(formula = menarche ~ age, family = binomial)
>>
>> Deviance Residuals:      Min        1Q    Median        3Q       Max
>> -4.68654  -0.13049  -0.01067   0.09608   2.35254
>> Coefficients:
>>             Estimate Std. Error z value Pr(>|z|)    (Intercept)
>> -17.9175     1.7074  -10.49   <2e-16 ***
>> age           1.3549     0.1296   10.45   <2e-16 ***
>> ---
>> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>> (Dispersion parameter for binomial family taken to be 1)
>>
>>     Null deviance: 974.31  on 703  degrees of freedom
>> Residual deviance: 223.95  on 702  degrees of freedom
>>   (635 observations deleted due to missingness)
>> AIC: 227.95
>>
>> Number of Fisher Scoring iterations: 9
>>
>>
>>
>>
>>
>>
>> ______________________________________________
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>> and provide commented, minimal, self-contained, reproducible code.
>>
>

--
Frank E Harrell Jr   Professor and Chair           School of Medicine
Department of Biostatistics   Vanderbilt University

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