3

Also, what will tend to produce a CI in which the sample value is far above the center, or far below the center?

user1205901 - Reinstate Monica
  • 11,303
  • 26
  • 77
  • 152
  • 2
    the log odds CI will be symmetric – user20650 Mar 19 '13 at 21:25
  • 1
    In addition to @JeremyMiles good answer below, my answer here: [interpretation-of-simple-predictions-to-odds-ratios-in-logistic-regression](http://stats.stackexchange.com/questions/34636//34638#34638), may be of some help to you as well. – gung - Reinstate Monica Mar 20 '13 at 01:16

1 Answers1

6

Odds ratios are not distributed symmetrically - they can't be, because they can't go below zero, but they can go as high as infinity.

What is distributed symmetrically is the log of the odds ratio. Most stats packages give a choice of the regular regression coefficient (B), and the exponentiated regression coefficient (exp(B)), which is the odds ratio.

Here's an extreme example: B is 3, CIs are 1, 3. Exponentiate those values, and you get a point estimate for the odds ratio of 20.1, and confidence intervals of 2.72 and 148.4.

However, notice that they are not symmetrical additively, but they are symmetrical multiplicatively. That is to say: 20.1/2.72 = 7.4 and 148.4/20.1 = 7.4 as well.

The farther your point estimate of the odds ratio is from 1, the more distorted the effect will (appear to) be. To take an extreme example, a point estimate for B of 12, with CIs 10, 14 gives an odds ratio of 162,754 with CIs 22,026 and 1,202,604. The CIs cover a range over one million. But also notice that the same ratio (7.4) still holds.

Jeremy Miles
  • 13,917
  • 6
  • 30
  • 64