Dropping insignificant interactions I have two general questions regarding interactions in a Cox regression.

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*I have a hypothesis that marker X has different effect in groups G. The interaction self and the marker are insignificant. When the interaction is dropped, the effect of a marker is significant. How legitimate is it in statistics in general to drop the interaction, just to show that the marker is overall a significant predictor of an outcome?


*Study participants are grouped according to other variables into groups (G). For example, when A or B is true, they are group 1, C or D they are group 2 and E, F group 3.
In the model I've left out the variables A-F. When the interaction with G is dropped, the marker overall is significant, however there is strong evidence that marker has different effect depending on A. Can one include both interactions in a model (with A and G)? Or is it advised to build a completely new model with A-F and without Group variable?

It is a mistake to test if a variable is significant and drop it is it is not. By screening this way, you distort your downstream inferences that assume a model to be fit without this kind of screening. In particular for your analysis, the confidence interval and p-value for the marker variable of interest will be wrong.
What you propose is a form of stepwise regression, which Frank Harrell  eviscerates here. While the link is for a Stata website, the content is unrelated to the particular software used, and the ideas apply more broadly than the  classical linear model framework that seems to be the big concern there.
