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st: Testing equality of odds ratios outside of logistic regression

From   "Michael I. Lichter" <MLichter@Buffalo.EDU>
Subject   st: Testing equality of odds ratios outside of logistic regression
Date   Sun, 09 May 2010 19:49:02 -0400

I'm assisting on a paper where we examine the relationship between each of four dichotomous predictors variables and one dichotomous outcome variable. Prediction is our primary objective. The predictors are all measures of more or less the same thing, and we want to know whether, *without controlling for any of the others*, they predict the outcome equally well. We want to be able to say, "If you could only pick one of these variables as a predictor of the outcome, it wouldn't make any difference which one you selected."

For each of the predictors we calculate a odds ratio and a corresponding confidence interval. The odds ratios are very similar in magnitude and have confidence intervals that overlap almost entirely. We did not do any formal tests, not knowing of any offhand, and, because this isn't a central point, we didn't think it was very important. When we reported that the odds ratios were essentially equal, a reviewer objected that we had not tested for equality. Any suggestions?

In logistic regression, by the way, two of the four variables emerged as significant predictors and two did not, controlling for the others. That is of interest, but it doesn't answer my initial question. At least, I don't think it does.
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