st: Testing equality of odds ratios outside of logistic regression

["Michael I. Lichter" <MLichter@Buffalo.EDU>]

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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