Interpretable Prediction Rule Ensembles in the Presence of Missing Data

Abstract

Prediction Rule Ensembles (PREs) are robust and interpretable statistical learning techniques with potential for predictive analytics, yet their efficacy in the presence of missing data is untested. This study uses multiple imputation to fill in missing values, but uses a data stacking approach instead of a traditional model pooling approach to combine the results. We perform a simulation study to compare imputation methods under realistic conditions, focusing on sample sizes of $N=200$ and $N=400$ across 1,000 replications. Evaluated techniques include multiple imputation by chained equations with predictive mean matching (MICE PMM), MICE with Random Forest (MICE RF), Random Forest imputation with the ranger algorithm (missRanger), and imputation using extreme gradient boosting (MIXGBoost), with results compared to listwise deletion. Because stacking multiple imputed datasets can overly complicate models, we additionally explore different coarsening levels to simplify and enhance the interpretability and performance of PRE models. Our findings highlight a trade-off between predictive performance and model complexity in selecting imputation methods. While MIXGBoost and MICE PMM yield high rule recovery rates, they also increase false positives in rule selection. In contrast, MICE RF and missRanger promote rule sparsity. MIXGBoost achieved the greatest MSE reduction, followed by MICE PMM, MICE RF, and missRanger. Avoiding too-course rounding of variables helps to reduce model size with marginal loss in performance. Listwise deletion has an adverse impact on model validity. Our results emphasize the importance of choosing suitable imputation techniques based on research goals and of advancing methods for handling missing data in statistical learning.