Should I keep the interaction term? I am doing research on mortality. I am running Cox regression and I am adjusting for 40 variables which are proven in the literature to be related with mortality. My main exposure is X. In my final model I have 19 variables that are significant and my exposure is non significant. Than I try the last analysis including interaction terms between my exposure and the 19 covariates that I found significant in the final model, of which only one interaction term was significant. It changes the coefficient of my main exposure around 40% and makes it significant. 
Is this a good approach, and should I keep the interaction term in the model?
 A: How did you get the "final model" which turned out not to be final (since you changed it)?  I hope it wasn't through procedure such as forward, backward, stepwise or bivariate screening.
First, with so many potential IVs, you need a lot of data; what is your N?
Second, you should base model selection first of all on substantive theory If theory says all 40 are important (note, important, not significant necessarily) and you have the N, you may want to keep all 40. Showing that what was thought to be a large effect is small in your sample can be just as important as finding a large effect. In fact, it can be more important. E.g. if you found some group of humans in which men were not much different in height from women, that would be hugely important. 
Alternatively, you could have a null hypothesis that isn't a nill hypothesis.
Third, similarly with interactions: You want to look at what would be interesting.
Finally, all this presupposes you have checked for things like collinearity and outliers and so on. 
A: I don't really know anything about Cox models, but in general you should keep an interaction term if (1) you've got a theory to interpret it, and (2) it improves AIC or BIC or some other sensible model selection criterion.  If you just report whatever happens to be ``significant,'' you run the risk of data mining.  This is why a number of disciplines require people to file pre-analysis plans.  
If you're not familiar with data mining:  its the idea that a 95% significant coefficient will actually be zero 5% of the time.  So if you've got 20 variables and 1 of them is significant...  you get the point.  
