Accurate forecasting of intensive care unit (ICU) length of stay (LOS) is important for resource planning, yet it often requires a compromise between predictive performance and interpretability. We present Gradient-Boosted Patient Similarity (GB-PS), a hybrid framework in which XGBoost-derived global feature importance is used to guide a covariance-aware $k$-Nearest Neighbors regressor for ICU LOS prediction. Using a retrospective cohort of 10{,}000 adult ICU admissions from MIMIC-IV, we compared GB-PS with a pure XGBoost baseline. GB-PS achieved a mean absolute error (MAE) of 1.65 days (RMSE 2.79, $R^2$ 0.60), compared with 2.02 days (RMSE 2.78, $R^2$ 0.65) for pure XGBoost. Thus, the hybrid model reduced typical patient-level absolute error while explaining slightly less overall variance. Because ICU bed planning is often driven by day-level prediction error, we treated MAE as the primary operational metric and interpreted the lower $R^2$ as a trade-off rather than a contradiction. Subgroup analyses showed stable performance in elderly and high-severity patients. The interpretability offered by GB-PS is example-based: predictions can be traced to clinically similar historical cases rather than to a fully explicit global rule set. Overall, GB-PS provides a pragmatic hybrid alternative that modestly improves MAE while preserving a clinically interpretable case-based reasoning pathway.
