Optimal sizing of a holdout set for safe predictive model updating

Risk models are becoming ubiquitous in healthcare and may guide intervention by providing practitioners with insights from patient data. Should a model be updated after a guided intervention, it may lead to its own failure at making predictions. The use of a `holdout set' -- a subset of the population that does not receive interventions guided by the model -- has been proposed to prevent this. Since patients in the holdout set do not benefit from risk predictions, the chosen size must trade off maximising model performance whilst minimising the number of held out patients. By defining a general loss function, we prove the existence and uniqueness of an optimal holdout set size, and introduce parametric and semi-parametric algorithms for its estimation. We demonstrate their use on a recent risk score for pre-eclampsia. Based on these results, we argue that a holdout set is a safe, viable and easily implemented solution to the model update problem.