# How to interpret the odds ratio in a logistic regression with proportion as a response variable

I have a glm model for some data with a proportion as the outcome variable as follows:

xi: glm pos_tests i.covariate_1 covariate_2 , family(binomial total_tests)

In this model, pos_tests is the number of positive laboratory results and total_tests in the number of all tests conducted.

i.covariate_1 and covariate_2 are categorical and continuous independent variables respectively.

pos_tests  | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Icovariate_1 |   2.535989   .9193459     2.57   0.010     1.246149    5.160891
covariate_2 |    .976045   .0270064    -0.88   0.381     .9245231    1.030438

My question is how do I interpret the significant result for covariate_1.

Does it mean that the odds of all test results being positive are 2.54 time greater for those individual with covariate_1 or is there some other way of interpreting.

Thanks.

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I don't know Stata, so I don't know if you've got the code correct, but if you do, and if covariate1 is dichotomous, then yes, that is roughly what it means. More precisely, it means that the odds of a positive test are 2.54 times higher when covariate1 is 1 than when it is 0.

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Thanks @peter-flom, the model in stata is quite similar to R. No idea what the SAS equivalent is. I don't use it. In family(binomial total_tests) the total_tests is the number of Bernoulli trials. –  John Sep 22 '12 at 23:18