Can the confidence interval of an odds ratio be negative?

Question

I am running logistic regression.

The odds ratio estimate I got is positive but the lower bound of my 95% CI is negative (close to -1) and the upper bound is greater than 1. Would this mean that my result is not statistically significant?

In a hypothetical case that the odds ratio 95% CI is something like (-1, .5), would this also mean it is not statistically significant? The odds ratio in this hypothetical situation is not 0 or negative.

I used stargazer in R to get the 95% CIs, and these are the optional arguments I put in stargazer: apply.coef = exp,ci = TRUE, ci.level = .95

@jbowman one more question, first thanks for your response! according to the stargazer documentation the p-values calculated are with normal distribution since I specified apply.coef = exp. My question is, regarding a negative value in the lower bound of the CIs, would the same interpretation hold true for binomial or poisson distributions? — ineedhelp, May 21 '23 at 02:14
Yes, doubly so with the binomial probability parameter as it's bounded both above and below. — jbowman, May 21 '23 at 02:22

score 0 · Answer 1 · answered May 21 '23 at 02:24

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Odds ratios cannot be negative.

An odds ratio of 1.0 is the no-difference null hypothesis value. Values between 0 and 1 denote an effect in one direction. Values greater than 1 denote effects in the other direction.

Negative values are not possible, so the values you are looking at are not odds ratios. Maybe they are logarithms of odds ratios?

answered May 21 '23 at 02:24

Harvey Motulsky

20,456

My odds ratio (the result itself) is not negative but the 95% CI contains a negative lower bound, I apologize for the confusion. – ineedhelp May 21 '23 at 02:26
1

@ineedhelp. Your question was clear. But a properly constructed confidence interval only includes plausible values. Negative values are not plausible so something is wrong. – Harvey Motulsky May 21 '23 at 02:32
two more questions, first thanks for pointing that out.
1. regardless of the distribution type, negative 95% CIs for odds ratios cannot exist?
2. I checked with the MASS library in R (https://www.r-bloggers.com/2011/11/example-9-14-confidence-intervals-for-logistic-regression-models/) using its confint.default and got realistic 95% CIs, not sure if you use R but do you know why stargazer (https://cran.r-project.org/web/packages/stargazer/stargazer.pdf) would give those answers?
– ineedhelp May 21 '23 at 04:41
@ineedhelp. I know only a bit about R and never heard of StarGazer before. But I pulled up the link you referred to, and searched for "logistic". It doesn't appear in the document. So it appears that StarGazer does not do logistic regression. – Harvey Motulsky May 21 '23 at 15:06

Can the confidence interval of an odds ratio be negative?

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