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st: RE: CI for a difference in proportions


From   "Newson, Roger B" <r.newson@imperial.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: CI for a difference in proportions
Date   Wed, 27 Feb 2008 21:54:00 -0000

I can think of 2 possibilities. One is to use -glm-, with the options
-family(binomial) link(identity)-, to get estimation results for a
proportion for Group 1 and a Group 2 - Group 1 difference between
proportions. As in:

glm event group2, family(binomial) link(identity)

where event is the binary outcome variable (with values 0 and 1), and
group2 is an indicator (with values 0 an 1) indicating membership of
group 2 rather than group 1. The parameter named _cons will be the
proportion of individuals for which the event happened in group 1, and
the parameter labelled group2 will be the difference between the
proportion of individuals for which the event happened in group 2 and
the proportion of individuals for which the event happened in group 1.
Both of these parameters have estimates and standard errors, which can
be extracted for further processing, using -parmby-, -statsby-,
-estout-, -outreg- etc.

A better alternative is probably to use the -somersd- package,
downloadable from SSC. This can calculate differences between
proportions, and confidence intervals for these, because a difference
between proportions is a special case of Somers' D when both the
Y-variable and the X-variable are binary. The -somersd- package has the
advantage of offering Normalizing and variance-stabilizing
transformations for differences between proportions, allowing confidence
intervals in which we can probably be more confident. In our case, we
might type

somersd group2 event, transf(z) tdist

and 2 confidence intervals will be displayed, one for the hyperbolic
arctangent (or z-transform) of the difference between proportions, and
one for the difference between the proportions itself. Again, the
estimates and standard errors of the z-transformed difference can be
extracted using -statsby-, -parmby-, -parmest-, -estout- etc. and then
back-transformed  using the -tanh()- function.

I hope this helps.

Best wishes

Roger


Roger B Newson
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk 
Web page: www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/pop
genetics/reph/

Opinions expressed are those of the author, not of the institution.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Antoine
Terracol
Sent: 27 February 2008 19:19
To: statalist@hsphsun2.harvard.edu
Subject: st: CI for a difference in proportions

Dear _all,

This might be a silly question, but I currently have no access to 
Stata's user manuals or stats textbook.

I have data on two independant samples (of different sizes), each 
observed over 20 periods. I wish to draw a graph representing, for each 
period, the difference in the proportion of some event between the two 
groups, together with the 95% CI for this difference.

I first wanted to use -prtest- for each period, store/compute the 
differences and CI bonds in new variables, and graph them against
periods.

However, I am a bit confused over which standard error to use (and how 
to get them) when computing the CI bounds.

-prtest- gives two standard errors, the one under H0 can be easily 
computed from stored results r(P_1), r(P_2) and r(z). The standard 
errors for each proportion (se1 and se2) are not stored, and I do not 
know if the fact that my calculation of sqrt(se1^2 + se2^2) differs from

the reported standard error for the difference (not under H0) is caused 
by rounding errors or if my formula is incorrect...

I thought of using -proportion- to get the standard errors as stored 
results, but it actually gives standard errors for each proportion that 
differ from -prtest-, but are identical to the ones computed by -mean-.

Any advice would be appreciated.

Antoine



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