Regression Trees Identify Relevant Interactions: Can This Improve the Predictive Performance of Risk Adjustment?

Area of Science:

• Health economics
• Biostatistics
• Social health insurance

Background:

• Risk equalization formulas are crucial for fair healthcare reimbursement but often overlook complex variable interactions.
• Existing methods struggle to systematically identify and incorporate these interactions due to their complexity.

Purpose of the Study:

• To develop and evaluate a novel method using regression trees to systematically identify and incorporate interactions in risk equalization.
• To assess the impact of including identified interactions on the accuracy of risk adjustment formulas.

Main Methods:

• A two-step approach was applied using a large German social health insurance dataset (nearly 2.9 million individuals).
• Step 1: A regression tree identified interaction effects between different morbidity groups.
• Step 2: Identified interactions were added to a traditional weighted least squares regression model, and coefficients were recalculated.

Main Results:

• The enhanced risk adjustment formula showed a marginal improvement in adjusted R-squared from 25.43% to 25.81% on the evaluation dataset.
• Analysis of predictive ratios for subgroups affected by interactions was performed.
• The inclusion of multiple morbidity interactions resulted in only a minor increase in overall accuracy.

Conclusions:

• The regression tree approach offers a systematic way to explore interactions in risk equalization.
• Despite the marginal R-squared improvement, the study suggests that not accounting for a large number of morbidity interactions does not lead to a significant loss in predictive accuracy at the sample level.