Regression Trees and Ensemble for Multivariate Outcomes

Area of Science:

• Biostatistics
• Machine Learning in Healthcare
• Data Mining

Background:

• Tree-based methods are powerful for complex data analysis.
• Biomedical research frequently involves multivariate outcomes (e.g., multiple blood pressure measures).
• Current methods inadequately address correlations within multivariate outcomes.

Purpose of the Study:

• To develop novel goodness-of-split measures for multivariate regression trees.
• To build trees that effectively handle continuous multivariate outcomes with inherent correlations.
• To enhance prediction accuracy through ensemble methods.

Main Methods:

• Proposed two approaches: minimizing within-node homogeneity and maximizing between-node separation.
• Utilized Mahalanobis distance, determinant of variance-covariance matrix, Euclidean distance, and standardized Euclidean distance for split measures.
• Extended single trees to ensembles of multivariate trees for improved prediction.

Main Results:

• Developed and evaluated new goodness-of-split measures for multivariate regression.
• Simulations demonstrated the properties of the proposed measures.
• Methods were successfully applied to clinical datasets in neuropathy and pediatric cardiac surgery.

Conclusions:

• The new methods provide a robust framework for analyzing correlated multivariate outcomes in biomedical studies.
• The proposed techniques enhance the utility of tree-based methods in complex health data analysis.
• Ensemble multivariate regression trees show promise for improving predictive accuracy in clinical research.