I want to explore the relationship between biological markers and cognition in healthy controls and patients. In order to determine if the relationship varies between groups, I included the interaction term in the model first as Cognition = Biological markers + Group + Group * Biological markers + other covariates and there is a lack of significant group interaction effect. Therefore, I plan to explore the relationship in all subjects as Cognition = Biological markers + other covariates. My question is should I include Group in this new model? More specifically, if there are significant group differences in Cognition and Biological markers between healthy controls and patients, Group is highly likely contributing to Cognition.
1 Answer
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An "insignificant" Group * Biological markers interaction coefficient doesn't mean that Group by itself has an "insignificant" association with outcome. The "insignificant" interaction just means that you couldn't distinguish an extra association of outcome beyond what you could explain based on Group and Biological markers individually. Certainly you should include Group as a predictor if you have reason to believe that it might be associated with outcome.
If you have enough data, I would recommend also maintaining the interaction term in your model even though it isn't "statistically significant" based on an arbitrary p-value cutoff. The interaction still might be important enough to improve the estimates of the associations of the other variables with outcome. See Frank Harrell's Regression Modeling Strategies, especially Chapter 4, for the advantages of fitting a complex model provided that you don't overfit the data.
