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# RE: st: RE: Poisson Regression

 From "Visintainer, Paul" To "'statalist@hsphsun2.harvard.edu'" Subject RE: st: RE: Poisson Regression Date Tue, 15 Feb 2011 08:44:32 -0500

```Very good point.  But you also moved the discussion from ratio measures to difference measures (excess risk).  And this is the essence of the discussion.  There are subtleties of these measures that are not discussed in clinical articles, particularly when the measure -- like the odds ratio -- is not intuitive (even if it's only superficial).  If the measure is not understood, the focus is on significance testing (which is also poorly understood in the clinical world).  So the focus is not where it should be -- the clinical relevance.  IMO, more frequent use of log-binomial and Poisson approaches in these specific types of clinical studies (common outcomes) can only help to refocus the discussion to the content that is relevant for the clinician.

Regards,

-p

________________________________________________
Paul F. Visintainer, PhD
Baystate Medical Center
Springfield, MA 01199

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Brendan Halpin
Sent: Tuesday, February 15, 2011 5:41 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RE: Poisson Regression

On Mon, Feb 14 2011, Visintainer, Paul wrote:

> My frustration is that when the outcome is common and logistic
> regression is used, there virtually no discussion of clinical relevance
> -- only statistical significance, (e.g., is a significant odds ratio of
> 2.5 clinically relevant? Perhaps if the base risk is 2%; perhaps not if
> the base risk 73%.

Your underlying point about substantive significance is well taken, but
this is a bad example. Here is a simulation (code below):

Case 1:
|        outcome
class |        No        Yes |     Total
-----------+----------------------+----------
Controls |       980         20 |     1,000
Treatment |       951         49 |     1,000
-----------+----------------------+----------
Total |     1,931         69 |     2,000

Case 1:
RR  2.450
OR  2.525
N extra outcomes   29

Case 2:
|        outcome
class |        No        Yes |     Total
-----------+----------------------+----------
Controls |       270        730 |     1,000
Treatment |       129        871 |     1,000
-----------+----------------------+----------
Total |       399      1,601 |     2,000

RR  1.193
OR  2.497
N extra outcomes  141

In both cases the OR is 2.5, and the rate for controls is respectively
2% and 73%. The RR is much lower with the 73% base rate. However, the
"clinical" significance is *higher* with the 73% base rate, with 14.1%
excess "outcomes" in the treatment group compared with 2.9% when the
base rate is 2%.

In other words, the relative rate seems a poorer, not a better estimate
of clinical significance than the odds ratio. (In fact, a probit model
looks even better with a 2% effect of 0.40 and a 73% effect of
0.52.)

Brendan

--8<-----
clear
input class outcome n
0 0 980
0 1  20
1 0 951
1 1  49
end

label define class 0 "Controls" 1 "Treatment"
label define outcome 0 "No" 1 "Yes"
label values class class
label values outcome outcome

noi tab class outcome [freq=n], matcell(t)
scalar relrate = (t[2,2]/(t[2,1]+t[2,2]))/(t[1,2]/(t[1,1]+t[1,2]))
scalar OR      = (t[2,2]/(t[2,1]       ))/(t[1,2]/(t[1,1]       ))
scalar D       = t[2,2] - t[1,2]

noi di "Case 1:" _newline "RR " %6.3f relrate _newline "OR " %6.3f OR _newline "N extra outcomes" %5.0f D
expand n
noi probit outcome class

clear
input class outcome n
0 0 270
0 1 730
1 0 129
1 1 871
end

label define class 0 "Controls" 1 "Treatment"
label define outcome 0 "No" 1 "Yes"
label values class class
label values outcome outcome

noi tab class outcome [freq=n], matcell(t)
scalar relrate = (t[2,2]/(t[2,1]+t[2,2]))/(t[1,2]/(t[1,1]+t[1,2]))
scalar OR      = (t[2,2]/(t[2,1]       ))/(t[1,2]/(t[1,1]       ))
scalar D       = t[2,2] - t[1,2]

noi di "Case 2:" _newline "RR " %6.3f relrate _newline "OR " %6.3f OR _newline "N extra outcomes" %5.0f D
expand n
noi probit outcome class

--8<-----
--
Brendan Halpin,  Department of Sociology,  University of Limerick,  Ireland
Tel: w +353-61-213147 f +353-61-202569 h +353-61-338562; Room F1-009 x 3147
mailto:brendan.halpin@ul.ie  http://www.ul.ie/sociology/brendan.halpin.html
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