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st: calculating AUROC when odds ratio cannot be defined


From   Ashwin Ananthakrishnan <ashwinna@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: calculating AUROC when odds ratio cannot be defined
Date   Mon, 16 May 2011 08:24:37 -0700 (PDT)

Hi, 

I'm trying to calculate the area under the ROC for a model where the outcome is 
binary (disease 1 vs. disease 2) and the predictors are response rates at 
various time points (also binary variables - for example, response at 2 months - 
Y/N, response at 3 months - Y/N). 


For the 3 month cut off point, all patients with disease 1 respond (100%) while 
about 40% of those with disease 2 respond. Obviously, I can't calculate an odds 
ratio for this time point. Is it possible to calculate an AUROC with disease 1 
vs. disease 2 as the outcome of interest and response at 3 months as the 
predictor variable? Or because there are no events in one of the 2x2 boxes, is 
it that an AUROC cannot be calculated?

Thanks, 

Ashwin

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