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I came across following definition of crude odds ratio in binary logistic regression:

Crude odds ratio is when you have only one independent variable

And also I heard:

Crude odds ratio is when you have only one binary independent variable (2x2 table)

Which is proper one?

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  • $\begingroup$ Well, to have an independent variable implies you must also have a dependent variable (binary) as well as a model (binary logistic regression). Both of your definitions omit this important information, so I would strike them off on those grounds. $\endgroup$
    – Isabella Ghement
    Commented Jun 17, 2018 at 17:41
  • $\begingroup$ I think a better terminology for the odds ratio you invoke is "unadjusted" (rather than "crude") - for that definition to make sense, you must also have other independent variables and/or covariates you are not adjusting for in your model. $\endgroup$
    – Isabella Ghement
    Commented Jun 17, 2018 at 17:45
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    $\begingroup$ Hi, Isabella thanks for noticing lack of "binary", I corrected that. $\endgroup$
    – mokebe
    Commented Jun 17, 2018 at 19:07

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The former definition is correct. Logistic regression gives us a notion of odds ratios for continuous regressors. In the past, we preferred binary regressors because the models could be calculated without technology. Now we have a broader perspective because of our computational power.

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  • $\begingroup$ Could you give paper or book or any other reliable source, which confirms this? $\endgroup$
    – mokebe
    Commented Jun 17, 2018 at 15:52
  • $\begingroup$ @mokebe I believe modern epidemiology by Rothman has such a discussion. The term is not a mathematical one, but rather one of causal modeling and epidemiology. $\endgroup$
    – AdamO
    Commented Jun 17, 2018 at 19:16

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