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st: pseudo r2 and confidence limits


From   joe ragg <joeragg@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: pseudo r2 and confidence limits
Date   Fri, 13 Jun 2008 00:31:11 -0700 (PDT)

Dear all,
I wonder if somebody would so kindly help me with a statistical question, rather than with the more technical stata aspects which this forum is more often addressing.
I have a multivariate logistic regression model assessing risk factors for adverse outcome in human subjects, and have obtained adjusted odds ratios, along with predicted risks and their associated confidence limits. 
My question is firstly in relation to the confidence limits of predicted risk (which seem relatively wide given sample size near 700 and only 3 significant variables retained in the model obtained by a forward stepwise techniqe) and secondly in discussing strength of association between risk factors and outcome. 
My question is: Were the model hypothetically to have a greater pseudo R2 would the confidence limits then be narrower? (eg were pseudo R2 be 0.40 rather than the 0.23 that model 1 has for an outcome A (of 5% observed incidence) or 0.07 for second model 2 for outcome B (of 20%  observed incidence), HL gof and AU ROC satisfactory). 
Further, what sort of pseudo R2 figure might demonstrate low, medium and high levels of strength of association between risk factor and adverse outcome given the model is addressing biologic subjects? Few papers give the pseudo R2 statistic so that I might compare. Is there a reference(s) to a succinct paper(s) that may help me on such matters? 
Unfortunately my institution has not furnished me with access to expert statistical advice, and nor am I likely to have access to specialised statistical texts but I am very interested in trying to best explain the nature of the data that I have, and can bear the purchase costs of individual articles. 
Thank you all for your kind consideration of these questions.   
PS 
I am aware of the controversial nature of pseudo R2, given there are different ways to calculate, that it does not have the literal meaning that R2 has in OLS, and that most warn that caution is required in interpreting the pseudo R2 figures. 
I referred to McFaddens pseudo R2 above as I think it is the STATA default. On that, I cannot find a specific reference to McFaddens ps R2 in the STATA ref manual (for logistic) – I have seen it elsewhere mentioned that it was published in 1974, but I cannot find the original reference / paper.
Finally, I did assess for model interactions to optimise the model, and there were significant interactions, but I rejected those given considerations of fit / complexity (BIC figures) particularly given I wanted to retain the main effect variable.
Thank you all again


      

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