Interpretation of the p-value of a variable involved in an interaction

[deleted_user]

Dear all,

I have checked all the day on the internet without having found anything... that's why I would need your input!
I perform logistic regression. Due to a confounding effect, a non-significant covariate was kept in the model. Following the test of all possible 2*2 interactions between covariates: this variable (initially non-significant) is included in a significant interaction!! And, this variable is now significant.

For example:
- Step 1: selection on covariates
P
Covariate A >0.05
Covariate B >0.05
--> these variables were kept in the model due to their confounding effect
- Step 2:
P
Covariate A <0.001
Covariate B >0.05
Inter A*B <0.001

According to you: what does it mean?
I know that when there is a significant interaction, we cannot interpret the corresponding coefficients independently. But, is it the same for the p-values?
In particular, could I conclude: "covariate A is significantly associated with Y"???
Or do you think that I can only say that there is a significant interaction between covariates A and B?

Thanks so much in advance for your answer. I will be a great help!
Best regards,

Violaine

[Doc_Duke]

You are actually going to have to read a book (you know, those dusty things on shelves) for this one. I think the phenomenon is described in Frank Harrell's regression book.

What you saw is why we check interactions first.

All of the p-values are for the variable after considering all the other effects, so you can't say that A is significantly associated with Y. What you can say is that A has a different effect on Y depending on the value of B.

If you look at the coefficients for A in model 1 and model 2, you are likely to see that the coefficient is very different (maybe even changes sign).

Doc Muhlbaier
Duke

[deleted_user]

Thanks so much for your answer! It's the very beginning of the morning in France... so, thanks to you, I will be able to work on my statistical report today! Thanks again! BR, Violaine

[plf515]

doc gave a very good reply.

Here's another take: This is further evidence for NOT using p-values as the basis for much of anything. They rarely, if ever, answer the question you are interested in.

[Doc_Duke]

plf515: If you were a journal editor, your advice would me more credible. I've had a paper that the editor would not accept until I put p-values on the univariate analyses. Like it our not, p-values are a necessary part of getting published in a journal in most applied fields.

[plf515]

Doc, I know how you feel.

I actually am a statistical reviewer for one journal, and, while I do not (yet) campaign to eliminate p-values, I do insist on measures of effect size.