test interactions in adjusted models or unadjusted models

[pierre martin]

Hi all,

I have always wondered if it is better to test interactions in adjusted models (at least for demographics) or in unadjusted models? I assume in adjusted models to have potentiel confounders included in the model? Are there any recommandations on the best approach? What do people usually do?

Thank you for your advice,
Best, Pierre

[George Ford]

adjusted/unadjusted in what sense?

[pierre martin]

Hi George,

Let's say for example I am interested in investigating the association of air pollution on cancer and my model is adjusted for age, sex, education, physical activity. If I want to test the interaction of air pollution and age on cancer (I want to know if the risk of cancer when exposed to air pollution is greater in young vs old individuals), am I supposed to test the interaction in the fully adjusted model for instance regress cancer air pollution##age sex education physical activity? OR just regress cancer air pollution##age and get the p value of the interaction from this model?

Hope it's clearer, thank you!
Pierre

[George Ford]

nonlinear model?

[pierre martin]

Hi George, no linear regression models or linear mixed models
best, Pierre

[Dave Airey]

If I have a multiple linear regression model like Y = A + B + A#B + Cat_Cov1 + Cat_Cov2, we are assuming the interaction plot for A#B has the same shape over the levels of the covariates. If true, then motivated inclusion of the covariates can make the interaction test more powerful. However, your model is likely predicting a binary cancer variable so is a logistic regression model. Treatment of covariates of an interaction of interest is indeed more complicated than in linear regression. Covariates are mostly about efficiency of estimation in linear regression, but in logistic regression they are about efficiency and estimand definition. For example, adding a covariate changes the interaction estimate even without confounding in logistic regression, but does not do so in linear regression. Interactions are scale dependent, so you need to be explicit about the log odds versus probability scales. I think the Stata bookstore just added an introductory applied textbook on logistic regression. One of the chapters covers interaction. I do not work for Stata.

[George Ford]

If linear, which should be ok if you're not predicting, then use the interactions.

Also see:

 https://www.statalist.org/forums/forum/general-stata-discussion/general/1711822-marginal-effects-and-interactions

[pierre martin]

thank you all for the very insightful comments! P.