Adding a variable's effect (from literature) to an estimated Cox model I have a Cox model (estimated with coxph), built using "some" variables. There is an extra variable that I have not measured, so it is not in my dataset, but I do know the effect of that variable on cohort's similar to mine from literature (let's say the effect is well-established). If I want to "adjust" my model by including this effect, how do i do it?
My previous conviction was that this will lead to a biased model as we do not know about the interactions of this variable with the others in the cohort. But, I have seen some papers do something similar, such as Wishart 2012, where the author's adjusted their prognostic model for an extra variable that wasn't available in their cohort.
I am open to changing the base model (to a parametric or Bayesian), if that makes any difference.
Edit (for context): My goal is similar to Predict, to create a nomogram, which ideally I would like to adjust for an effect that is not in my dataset (large population level data, >10,000 observations, >500 events), but is well-established in literature.

The only thing you could do is simulate values for the variable you don't have, but you would need to also consider published correlation values of that variable with your other variables, which may not be available.  If the variable you don't have is normally distributed, then you need to vary the correlation of the simulated quantiles (values of the variable you don't have) with your other inputs during simulations.  Another complexity is that interaction is not correlation, it's a mean difference in the outcome over certain ranges of the interaction variables.
Consider the typical plot of SBP vs age, but two regression lines - one for males, one for females.  A significant interaction between gender and age implies slope inequality - i.e., the fitted regression lines cross.  That is, the predicted regression line for males has a slope that's significantly different from females.
Overall, this is a simulation problem.  Everything you mentioned could be simulated, considering you know the mean and s.d. of each of the interaction variables.
Reason I raised the correlation issue is because if the variable you don't know correlates with one of your predictors, there will be redundancy of information and your model won't be parsimonious.
