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Regression Tree Boosting to Adjust Health Care Cost Predictions for Diagnostic Mix
*John W. Robinson, John W. Robinson, M.D., Ph.D., LLC 

Keywords: boosting, case mix, data mining, health care cost, risk adjustment

Background: Systems for risk-adjusting health care cost, described in the literature, have consistently employed deterministic models to account for interactions among diagnostic groups, simplifying their statistical representation, but sacrificing potentially useful information. An alternative is to use a statistical learning algorithm such as regression tree boosting that systematically searches the data for consequential interactions, which it automatically incorporates into a risk-adjustment model that is customized to the population under study. Methods: Using administrative data for over 2 million members of indemnity, preferred provider organization (PPO), and point-of-service (POS) plans, AHRQ's Clinical Classification Software (CCS) was applied to sort diagnoses from year 2001 into 260 diagnosis categories (DCs). For each plan type (indemnity, PPO, and POS), boosted regression trees and main effects linear models were fitted to predict concurrent (year 2001) and prospective (year 2002) total health care cost per member, given DCs and demographic variables. Results: Regression tree boosting explained 49.7-52.1 percent of concurrent cost variance and 15.2-17.7 percent of prospective cost variance in independent test samples. Corresponding results for main effects linear models were 42.5-47.6 percent and 14.2-16.6 percent. Conclusions: The combination of regression tree boosting and a diagnostic grouping scheme, such as CCS, represents a competitive alternative to risk adjustment systems that use complex deterministic models to account for interactions among diagnostic groups.