Hi All, I have a question regarding the choice of interaction vs subgroup analyses in the context of effect modification. If the effect modifier (e.g., sex) is highly correlated with or even deterministic of one or several covariates (e.g., parity, breastfeeding) in the regression model, would you obtain the stratum-specific estimates derived from the interaction model with the covariates controlled for, or would you report the estimates from subgroup analyses (in men and women respectively)?
If from the interaction model, how would you address the collinearity between the interaction term and the covariates? In the latter, do we need to worry about the sample selection issue (loose of sufficiency for estimating the standard error)?
1 It depends on the Research question what you report.
2 Run the model and look for multicollinearity by looking at the VIFs you have no multicollinearity unlesss the data says so.
Best, D. Booth
David Eugene Booth Thank you Dr. Booth for your suggestions!
1. To your first point, does it mean that if the two groups as defined by the effect modifier are very different from each other that we can treat them as two populations, we can restrict our analysis to each group? What if there's not enough reason to believe they come from different populations, and when the sample size is small, would you turn to interaction analyses instead? Here, the research question is whether the exposure X is associated with the outcome Y in both stratum as defined by the effect modifier Z.
2. To your second point, that was my original thinking. However, the models are GLM s, and Cox models. Can I find alternatives for VIFs to indicate cillinearity beyond a rough examination of marginal correlations?
2. yes, The RHSs of these models are like any other linear models so eg,VIFs can be calculated and studied. No difference as long as your model is linear IN THE REGRESSION COEFFICIENTS.
1.Modification and interaction are the same thing. see:
https://www.google.com/search?q=difference+between+interaction+and+moderation&rlz=1C1CHBF_enUS847US847&oq=difference+between+interaction+and+moderation&aqs=chrome..69i57.25273j0j7&sourceid=chrome&ie=UTF-8
now all that you need to do with these things can be found in a Design and Analysis of Experiments book. I recommend the one by D C Montgomery. Look at the sections on interaction and factorial designs. Be sure to look at the info in the supplemental material. Examples are very good. Now always remember that a moderation or interaction term looks like B*x1*x2 where B is the regression coefficient x1 is the IV and X2 is the variable that you are testing for interaction/moderation. interaction/moderation means the two variables act together on the DV. You can also determine interaction/moderation by looking at an interaction/moderation plot(see Montgomery for details) If the 2 lines in your plot are parallel you do not have moderation/interaction. The same is true if B=0 when you do the regression coefficient t-test. I have more information on moderation/interaction. Just ask if you want to see it. Best Wishes, D. Booth
PS for interpretation of interaction see Montgomery.