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I run a multivariable logistic regression in SAS using the main effect/independent variable as continuous and categorical. As a continuous variable the confidence intervals of the odds ratios were extremely wide, i.e. >0.001 to <999,99999. I tried using the Firth correction but it didn't work, I got the same wide CIs. However, when I categorize the main effect variable into tertiles I get tighter CIs without a problem. How is this happening?

I run the same predictor variable with two different continuous outcome and I get the fit diagnostics below:

[Fit diagnostics]1

[Fit diagnostics 2]2

Parameter Estimate for 2nd image: -342.57, 95%CIs -1033.52, 340.37 - similar results for the first image as well.

Thanks.

Patsy
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    *Extremely wide*? A better word would be *infinite*. Is there only one independent variable? If so, then it is linearly related with the dependent variable. If not, then it is collinear with another IV in the model. Since you're using SAS and their logistic regression module doesn't offer traditional regression diagnostics such as VIF or the collinearity index, run your model in the OLS module and include the diagnostics. That will provide good insight into what's going on. –  Jun 07 '20 at 13:18
  • See also: https://stats.stackexchange.com/questions/45803/logistic-regression-in-r-resulted-in-perfect-separation-hauck-donner-phenomenon and https://stats.stackexchange.com/questions/5354/logistic-regression-model-does-not-converge?rq=1 – Sycorax Jun 07 '20 at 15:10
  • I have read all the comments on the other similar posts, but haven't found a solution or answer yet. You suggest to run it in the OLS model, but the outcome is binary? I'm not sure how to run the binary outcome in the OLS model, but I have attached the fit diagnostics for a continuous variable and the same predictor (bivariate regression). This time the CI's are not infinity but very large. Your help would be greatly appreciated, thanks – Patsy Jun 11 '20 at 15:24

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