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Open Access Research article

Regression tree construction by bootstrap: Model search for DRG-systems applied to Austrian health-data

Thomas Grubinger*, Conrad Kobel and Karl-Peter Pfeiffer

Author Affiliations

Department of Medical Statistics, Informatics and Health Economics, Innsbruck Medical University, Schoepfstrasse 41/1, 6020 Innsbruck, Austria

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BMC Medical Informatics and Decision Making 2010, 10:9  doi:10.1186/1472-6947-10-9

Published: 3 February 2010

Abstract

Background

DRG-systems are used to allocate resources fairly to hospitals based on their performance. Statistically, this allocation is based on simple rules that can be modeled with regression trees. However, the resulting models often have to be adjusted manually to be medically reasonable and ethical.

Methods

Despite the possibility of manual, performance degenerating adaptations of the original model, alternative trees are systematically searched. The bootstrap-based method bumping is used to build diverse and accurate regression tree models for DRG-systems. A two-step model selection approach is proposed. First, a reasonable model complexity is chosen, based on statistical, medical and economical considerations. Second, a medically meaningful and accurate model is selected. An analysis of 8 data-sets from Austrian DRG-data is conducted and evaluated based on the possibility to produce diverse and accurate models for predefined tree complexities.

Results

The best bootstrap-based trees offer increased predictive accuracy compared to the trees built by the CART algorithm. The analysis demonstrates that even for very small tree sizes, diverse models can be constructed being equally or even more accurate than the single model built by the standard CART algorithm.

Conclusions

Bumping is a powerful tool to construct diverse and accurate regression trees, to be used as candidate models for DRG-systems. Furthermore, Bumping and the proposed model selection approach are also applicable to other medical decision and prognosis tasks.