Understanding Indepenence

[SAS_BK]

Hi,

I am trying to determine if two different predictive variables are independently associated with a binary outcome (mortality).  I have 8 covariates that I have controlled for when selecting the model using backwards selection, but want to see if these two variable act independently.

When I include an interaction term V1*V2 (or V1 | V2), then neither are significant. If the interaction term is not included then V2 is significant but V1 still is not.  This is true when the covariates are included, or when they are not.

I think that this means these two are not acting independent of one another, but am not sure. Clinically these variables are not very different, so this would make some sense, but unsure how to explain that in statistical terms.

Thanks!

[PaigeMiller]

These tests have nothing to do with independence. The way to determine if two variables are independent is if the correlation between the two estimates is zero, which would be obtained from the CORRB option in most regression procedures.

[SAS_BK]

Thank you for the response! I thought that these tests determine if the association with the variable with the outcome is effected by a separate variable (ie: if v1*v2 has a pvalue of <0.05, then they have an association and therefore are not acting independently)?

[PaigeMiller]

Interaction, and what I think of as independence between two variables, and not the same. Maybe what you think of as the meaning of independence is different that what I think of by the word independence.