# RE: st: Binomial regression

 From "Newson, Roger B" To Subject RE: st: Binomial regression Date Sun, 5 Aug 2007 17:15:53 +0100

Two suggestions re binomial regression:

Suggestion 1: For what it's worth, confidence intervals for risk differences (in some cases) can be reported using the -somersd- package, downloadable from SSC using the -ssc- command. Given 2 binary (0,1) variables x and y, the user can type

somersd x y, transf(z) tdist

and get a confidence interval for the risk difference

Pr(y==1|x==1) - Pr(y==1|x==0)

This method has the advantage (compared to -binreg-, -glm- etc) of using the Normalizing and variance-stabilizing hyperbolic arctangent or z-transformation, recommended by Edwardes (1995) for the general Somers' D for binary X-variates (including the special case where the y-variate is also binary).

If there is a categorical confounding variable w, then the user can type

somersd x y, transf(z) tdist wstrata(w)

and get a confidence interval for a within-strata risk difference for pairs of observations with the same value of w. The user can alternatively specify multiple categorical confounding w-variables, and/or w-variables which specify propensity groups based on a propensity score for x==1 calculated from multiple confounding variables.

Suggestion 2: To output confidence intervals for baseline odds with confidence intervals for odds ratios, the user can specify a baseline variate of ones, and then enter it into the model with the -noconst- option. For instance, the user can type:

gene byte baseline=1
logit y baseline x, noconst or

This trick can also be used with geometric means and their ratios. See Newson (2003).

I hope this helps.

Roger

References

Edwardes, M. D. d. B. 1995. A confidence interval for Pr(X < Y) − Pr(X > Y) estimated from simple cluster samples. Biometrics 51: 571–578.

Newson R. 2003. Stata tip 1: The eform() option of regress. The Stata Journal 3(4): 445. Download post-publication update from
http://www.imperial.ac.uk/nhli/r.newson/papers.htm

Roger 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
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:

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 Maarten buis
Sent: 04 August 2007 07:47
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Binomial regression

--- Marcello Pagano <pagano@hsph.harvard.edu> wrote:
> I agree wholeheartedly that the risk difference is sometimes
> preferable to the odds ratio. Witness what is currently going on with
> the attack on Avandia.  Rather than report a risk difference of 0.2%
> in the MI rate, we are faced with a risk INCREASE of 40% -- the
> effect of going from 0.5% to 0.7%.  If reported as a risk difference
> it would probably not have made the headlines it has nor created the
> furor it has.

At this point I think that there is room for improvement in Stata
output. When reporting odds ratios after -logit-, Stata will not report
the baseline odds (-exp(_cons)-), So Stata reports that the odds
increased with 40%, but not that the baseline odds is .005 (at these
low probabilities risks and odds are almost the same). I would like to
see the baseline odds and the odds ratios, because both give very
useful information about the size of the effect, as Marcello's
example illustrates.

-- Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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