Multiply imputing missing values arising by design in transplant survival data

Recipients of organ transplants are followed up from transplantation and their survival times recorded, together with various explanatory variables. Due to differences in data collection procedures in different centres or over time, a particular explanatory variable (or set of variables) may only be recorded for certain recipients, which results in this variable being missing for a substantial number of records in the data. The variable may also turn out to be an important predictor of survival and so it is important to handle this missing-by-design problem appropriately.
Pankhurst et al. (2018) have shown that multiple imputation outperforms other methods commonly in use to handle this issue. However, there may be more than one way the imputation process could be implemented, which leads to an interesting avenue for our work. For example, a variable such as BMI is derived from height and weight, so rather than imputing the derived variable, BMI here, directly, we could instead impute the variables used to construct the derived variable, here height and weight, and then construct the derived variable based on the imputed data. It will be interesting to explore this in the missing by design context.