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st: Applicability of Logistic Regression for modelling rare events & collinearity problems.


From   stephen.kay@adelphigroup.com
To   statalist@hsphsun2.harvard.edu
Subject   st: Applicability of Logistic Regression for modelling rare events & collinearity problems.
Date   Thu, 22 Apr 2004 11:49:33 +0100

Hi,

I've got to write a statistical analysis plan for measuring the differences
between certain drugs on various event measures. For the binary events
logistic regressions seem appropriate - whether the event occurs is the
response and the predictors would include confounding factors measured at
baseline (such as various severity measures). 
as well as dummy variables representing the drugs. 
I'm worried about two things related to the above:
	(1) It is quite possible that the events are rare. I believe that P
values derived from logistic regressions may be unreliable for rare events
(the asymptotic approximation isn't accurate) - reason why Exact Logistic
Regressions are used. Unfortunately I don't have access to any Exact
Logistic algorithms and even if I did I'm not sure they can run with 2000
observations and 6 predictors. Does anyone have any guidance on how rare
events have to be before the logistic runs into such problems - I imagine it
may be dependent with how many observations there are and the number of
predictors?
	(2) The various severity predictors (confounding variables) in my
logistic regressions may well be fairly highly correlated. I'm not actually
interested per se in any of the beta's attached to these predictors - I just
want to remove their effect when comparing the drugs. I know I could
potentially do a PCA on these severity variables or drop some of them, etc.
However I wonder if I don't even need to do any of these multicolinearity
adjustments - will the multicollinearity problems of the severity measures
actually impact on the drug coefficient beta's and their P values? I've
never found this out from a text book - my inclination is that it probably
does given the inaccuracy that can occur in inverting matrices that are
nearly singular.

Any help on the above two points would be much appreciated.

Kind regards,

Stephen

Stephen Kay

Adelphi Group Products
www.adelphigroup.com

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