# Logistic Regression with Unreasonable Odds Ratio

I am building a logistic regression of TREATED (yes/no) and BLOODLOSS_PERCENT (continuous, skewed right). I have also built a multivariate logistic regression to control for possible confounders, but the issue is the same. I am getting an odds ratio for BLOODLOSS_PERCENT to be 50000+. Looking at the effect plot and the histogram of deviance residuals, the model appears to be fitting well, but there is obviously an issue I can't identify. Do you have any suggestions?

PROC LOGISTIC DATA=DATA PLOTS=EFFECT; MODEL TREATED(EVENT='1')=BLOODLOSS_PERCENT; RUN;

• seems to make sense that...if patients have large percent of their blood lost...that they will be treated Jun 22, 2023 at 19:23
• Maximum likelihood estimates of logistic regression coefficients are biased. Use Firth logistic regression. See Kosmidis (2014) or Rainey & McCaskey (2015) for a review.
– Noah
Jun 22, 2023 at 19:39
• Please can you add more medical details to your question. What do you expect the odds ratio to be? What is meaningful blood loss. I am guessing the issue you have is non linearity (with no untreated over 0.8% blood loss. Splines would help and perhaps a nonlinear transformation of bloodloss, that better captures relationship to log odds. Treatment Jun 22, 2023 at 20:12
• RE seanv507: the analysis is exploratory, so there is not an expected odds ratio. That being said, we would not expect the odds to increase by more than say 100% per unit of BLOODLOSS_PERCENT. I attempted cubic spines, and it seems to make the problem worse. The OR for each paramter tended even more toward infinity. Jun 22, 2023 at 20:30
• Depending on the other covariates in your model, your 'unreasonable' odds ratio could be a sign of near-perfect separation. Jun 22, 2023 at 22:05

A multivariate logistic regression is another story. After more and more variables are added, it is hard to visualize the changes to the OR. A fininte OR becomes subject to separation. Separation means your OR = $$\infty$$. Of course, the estimate comes from a numerical solver so they just stop at a "big value", but it might not be as unreasonable as you say. OR=$$\infty$$ means the S shaped curve becomes a step function, with 0% probability of event prior to the step and 100% probability of the event after the step.