Is it advisable to include variables that are not in the full model in the imputation model? I have a dataset with several missing values. I know that the missing is MNAR. I'm trying to use MICE to impute the data; then apply a survival model on the imputed data. The MICE paper advises that all variables in the full model (the survival model) must be included in the imputed model, but it says nothing about whether variables not in the full model can be used to impute the missing data. Any thought or reference on this will be appreciated.
 A: Another R package for multiple imputation is Amelia. According to its vignette (version 1.7.4; December 5, 2015), including additional variables in your imputation model can be beneficial.
On page 4:

Note that the MAR assumption can be made more plausible by including additional variables in the dataset D in the imputation dataset than just those eventually envisioned to be used in the analysis model.

"MAR" is of course "missing at random".
On page 10:

In fact, it is often useful to add more information to the imputation model than will be present when the analysis is run. Since imputation is predictive, any variables that would increase predictive power should be included in the model, even if including them in the analysis model would produce bias in estimating a causal effect (such as for post-treatment variables) or collinearity would preclude determining which variable had a relationship with the dependent variable (such as including multiple alternate measures of GDP).

You should however note that if the missing data is "missing not at random" (MNAR) then it does not satisfy the assumptions of multiple imputation.
