# Re: p-value from confidence interval for odds ratio

On 14 May 2005 14:54:40 -0700, "milliestat" <milliestat@xxxxxxxxx>
wrote:

> Hi--
>
> I need to understand a medical paper (for a problem at work), but I
> don't know much asbout statistics. I am hoping that someone here can
> tell me how to calculate a certain p-value from what the paper says,
> and give me a reference (to a book, ideally) that explains how to do
> the calculation.
>
> The paper states that the odds ratio that a particular exposure causes
> disease is 4.90, with 95% confidence interval ranging from 0.84 to
> 50.78. This seems to mean that a person exposed is 4.90 times more
> likely to get sick than someone who wasn't exposed. Because 1 is in
> the confidence interval, you cannot conclude that the exposure causes
> disease with 95% chance of being right. What I'd like to know is which
> confidence interval would work; in other words what is the p-value for
> the null hypothesis that exposure does not cause disease? For example,
> if the 85% confidence interval does not contain 1, then p < .15

[snip, detail ... ]
> Can I compute the p-value for the adjusted values from the adjusted 95%
> confidence interval or would I need to re-do all the analysis (which I
> am too ignorant to do)?

In the usual case, the CI is an inversion of the test, or
vice-versa, so that one is directly computable from the other.

Thus, the range from the lower cutoff to the mean is 1.96
in z-units for Normal. [If their test was a t-test, the cut-off
will be larger, but the result of the whole computation
will not differ by much.]

In your data, log(.84)= -0.17, log(4.9)= 1.59.
Thus: the cutoff, log(1)=0, is about 10% away from the 1.96
extreme, and the corresponding z at 0 is about 1.76.
Then you look up the p-level of 1.76, as two-tailed.

We expect a symmetrical CI, though. For Odds ratios,
the CI is figured in terms of log-odds, which should give
numbers whose geometric mean is the mean. However,
the numbers you cite above (0.84, 50.8) are not symmetric
around 4.90.

That implies that they got their CI somewhere else, probably
from bootstrapping. Or else that they have messed up
their numbers somewhere, or you transcribed wrong.

Even if they got their CI by bootstrapping, the number
from the lower limit is all I think of, that you have
available for estimating the p-level,

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.