[R] ci.pd() (Epi) and Newcombe method

[Peter Dalgaard]

(Ted Harding) wrote:
> Greetings!
>
> I suspect that there is an error in the code for the
> function ci.pd() in the Epi package.
>   
Any particular reason not to include the maintainer among the 
recipients?? Not sure whether Bendix is subscribed.

    -p

> This function is for computing confidence intervals
> for a difference of proportions between two independent
> groups of 0/1 responses, and implements the Newcombe
> ("Nc") method and the Agrasti-Caffo "AC" method.
>
> I think there is an error in the computation for the
> Newcombe method.
>
> Specifically, where the code says
>
> # Put the data in the right form
>   x1 <- aa; n1 <- aa+cc; p1 <- x1/n1
>   x2 <- bb; n2 <- bb+dd; p2 <- x2/n2
>   pd <- x1/n1 - x2/n2
>   z <- qnorm(1-alpha/2)
>   zz <- qchisq(1-alpha/2,1)
>
> I believe zz (which is used in the Newcombe method,
> while z is used for Agresti-Caffo) should be
>
>   zz <- qchisq(1-alpha,1)
>
> (though I think they could just as well have written
> xx <- z^2), since z^2 seems to be what they want for the
> Newcombe method, and qnorm(1-alpha/2)^2 = qchisq(1-alpha,1)
>
> This was noticed as a result of comparing results from
> ci.pd() with results from the RDCI module in STATA (run
> by someone else, since I don't have access to STATA).
> With the original code in ci.pd(), the Newcombe results
> were different between ci.pd() and STATA. After making
> the above change, they agreed.
>
> I would be most grateful if anyone who has also been
> down this path could confirm whether I am correct.
> Since I don't have access to Newcombe's original
> paper at the moment either, I am not able to check
> the code against his own description of the method!
>
> With thanks,
> Ted.
>
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
> Fax-to-email: +44 (0)870 094 0861
> Date: 06-Feb-08                                       Time: 16:58:19
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-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907