I am doing multiple imputation on a database of observations on hospital patients. There is one observation of many covariates per patient. There are 2 binary outcome variables:
Alive/Dead after 30 days
Died in hospital, or survived/discharged
Two seperate analysis models (logistic regression), with identical covariates, are to be run, each with one of these outcomes as the response. There are 7 covariates in the analysis models.
There is missing data of between 3 and 11% in the covariates and the outcomes.
In addition there are 7 further covariates that are to be used in the imputation model to predict the missingness in the covariates and outcomes.
My questions concerns the imputation of the two outcome variables. They are to be used as predictors for missingness in the covariates, as per standard practice, but they are highly collinear with each other. Is this a concern for the imputation model ? Is it valid/recommended to impute them both in the same model (to generate several complete datasets all containing both outcomes) or should seperate imputations be performed for each of the outcomes (to generate two distinct sets of complete datasets, each distinct set having one of the outcomes) ? Any other suggestions for how to proceed would be welcome.