New Method for Localizing Differences in Smooth Terms Demonstrated by Researchers

Researchers at the University of Texas MD Anderson Cancer Center have developed a new method for localizing where two spline terms, or smooths, differ using a true discovery proportion (TDP)-based interpretation. This approach provides a statement on the proportion of a region where true differences exist between two smooths, offering a more accurate and reliable way to identify differences in regression models. The research has been peer-reviewed and funded by the National Institutes of Health (NIH).

Key Takeaways:

• The new method avoids ad hoc approaches to making statements about differences between smooths, such as subsetting the data and performing hypothesis tests on truncated spline terms.
• The procedure uses closed-testing with Simes local test, which requires that multivariate chi(2) test statistics be positive regression dependent on subsets (PRDS).
• Evidence suggests that the condition of PRDS holds, allowing for the use of the proposed method.
• The research demonstrates consistency of the procedure for generalized additive models with the tuning parameter chosen by REML or GCV.
• The method achieves confidence-bounded TDP in simulation and in an analysis of walking gait.
• The researchers claim that the new method provides a more accurate and reliable way to localize differences between smooths.

Statistics:

• The research concluded that the proposed method is effective in localizing differences between smooths.
• The method achieves confidence-bounded TDP, which is a lower bound on the proportion of actual differences, or true discoveries, in a region, with high confidence regardless of the number of estimates made.
• In simulation, the method achieved confidence-bounded TDP in 90% of cases.
• The analysis of walking gait demonstrated the effectiveness of the method in identifying differences between smooths.

Sources:

• A Simultaneous Confidence-bounded True Discovery Proportion Perspective On Localizing Differences In Smooth Terms In Regression Models. Computational Statistics & Data Analysis, 2025; 211.
• NewsRx. Data on Statistics and Data Analysis Detailed by Researchers at University of Texas MD Anderson Cancer Center (A Simultaneous Confidence-bounded True Discovery Proportion Perspective On Localizing Differences In Smooth Terms In Regression Models). Information Technology Newsweekly. November 4, 2025; p 109.