Include mortality as feature in lactate/albumin imputation models?

[finncatling]

As discussed in #43 , not including mortality as a feature in our imputation models may bias the coefficients of the final mortality model. We have fixed this for MICE / categorical imputation.

Is there a way to include mortality in the lactate & albumin imputation models, given that we want to use them at the point of care? One (convoluted) way would be to:

• Train our lactate / albumin imputation models with on the training fold, using mortality as a feature
• On the test data (simulating prospective use where mortality labels are obviously unavailable):
  • Make an initial point prediction p of mortality risk using a prediction model which excludes lactate and albumin
  • Use p to parameterise a Bernoulli that we can sample mortality labels from for use as inputs to the lactate/albumin imputation models, allowing us to obtain a distribution of imputed lactate/albumin values
  • Input all features (including lactate/albumin where required) to a final mortality model that includes lactate and albumin

If we don't do the above in production, perhaps we should at least test (in the paper) whether excluding mortality has biased the model coefficients?

[finncatling]

Explored in sensitivity analysis from #106