[R] exact 95% confidence intervals

[Frank E Harrell Jr]

Peter Dalgaard wrote:
> Frank E Harrell Jr <f.harrell at vanderbilt.edu> writes:
> 
>> Peter Dalgaard wrote:
>>> "XinMeng" <xmeng at capitalbio.com> writes:
>>>
>>>> Hello sir:
>>>> As to the 2*2 table format for reporting results comparing a new
>>>> test to true diagnosis,when I got the sensitivity and
>>>> specificity,how can I calculate the exact 95% confidence intervals
>>>> (based on the binomial distribution) for sensitivity and specificity
>>>> via R?
>>> Just run binom.test on the data from each column (or row, depending
>>> on
>>> which way you turn the tables).
>>>
>> But beware of exact binomial intervals - they are often not very
>> accurate.  Wilson and other intervals are generally better.  For
>> example see the binconf function in the Hmisc package.
> 
> I suppose that by "accurate" you mean that they are generally better
> at getting the coverage rate right? 

Yes

> 
> The "exact" intervals are strictly conservative, but at least
> predictably so. The whole thing is largely a matter of taste to my
> mind, but I know that other people (notably Alan Agresti) have
> stronger opinions.

I tend to side with Agresti, and emphasize the expected absolute error 
in confidence coverage.

> 
> (People taking an interest in this may want to have a look at
> http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval )

nice to know!

Frank