Multivariate Regression value higher than univariate?

[Robert Frykberg]

This is a simple question: I have done a small research study where I had a significant (Logistic regression) association with outcome by treatment group. When doing further analysis only one other variable was significant with outcome. Putting the second confounding explanatory variable into the model with the primary treatment variable, my OR actually increased. Usually it is reduced somewhat. Is this a common event? Have we potentially done something wrong with this rather simple model of two covariates? Thanks!

[Marcos Almeida]

I wonder whether there is some sort of correlation between both predictors.

[Mike Lacy]

What you describe is not especially common, but is almost always interesting and not a sign of something wrong. In my world, we'd call this a "suppressor" variable, and can occur if your variable of interest has direct and indirect (through another variable) effects in opposite directions. As so often is true, Richard Williams offers some nice instructional material: https://www3.nd.edu/~rwilliam/stats2/l35.pdf

[Richard Williams]

Suppressor effects are possible, but the fact that logistic regression is being used raises other possibilities. See

https://www3.nd.edu/~rwilliam/xsoc73994/Nested01.pdf

https://www3.nd.edu/~rwilliam/xsoc73994/Nested02.pdf

You may want to use the KHB method described in the 2nd handout.

[Robert Frykberg]

Thank you for your comments. The severity covariate was significantly in favor of the active treatment group that itself was also positively associated with outcome. We achieved similar effects on outcome when doing a Cox analysis as well.

[Marcos Almeida]

Maybe you should think about a shared frailty model.

[Jeff Wooldridge]

This seems like a good argument for focusing on average partial (marginal) effects, which automatically adjust to scale.