Exploring the variable importance in random forests under correlations: a general concept applied to donor organ quality in post-transplant survival.

Random Forests are a powerful and frequently applied Machine Learning tool. The permutation variable importance (VIMP) has been proposed to improve the explainability of such a pure prediction model. It describes the expected increase in prediction error after randomly permuting a variable and disturbing its association with the outcome. However, VIMPs measure a variable's marginal influence only, that can make its interpretation difficult or even misleading. In the present work we address the general need for improving the explainability of prediction models by exploring VIMPs in the presence of correlated variables. In particular, we propose to use a variable's residual information for investigating if its permutation importance partially or totally originates from correlated predictors. Hypotheses tests are derived by a resampling algorithm that can further support results by providing test decisions and p-values. In simulation studies we show that the proposed test controls type I error rates. When applying the methods to a Random Forest analysis of post-transplant survival after kidney transplantation, the importance of kidney donor quality for predicting post-transplant survival is shown to be high. However, the transplant allocation policy introduces correlations with other well-known predictors, which raises the concern that the importance of kidney donor quality may simply originate from these predictors. By using the proposed method, this concern is addressed and it is demonstrated that kidney donor quality plays an important role in post-transplant survival, regardless of correlations with other predictors.