Adding local components to global functions for continuous covariates in multivariable regression modeling.

Area of Science:

• Statistics
• Biostatistics
• Data Modeling

Background:

• Global modeling techniques like fractional polynomials (FPs) offer accessible equations but may miss local data features.
• The multivariable fractional polynomial (MFP) approach provides global modeling but requires systematic checks for overlooked local patterns.

Purpose of the Study:

• To introduce a procedure (MFP + L) that systematically detects and incorporates overlooked local features into MFP models.
• To evaluate the Type I error control and prediction performance of the MFP + L approach compared to penalized regression splines.

Main Methods:

• Development of the MFP + L procedure, which systematically checks MFP model fits for local features.
• Parsimonious addition of statistically significant local polynomials to the global MFP model.
• Comparison of MFP + L with penalized regression splines using simulation studies and a real-world application.

Main Results:

• MFP + L demonstrated effective control of Type I error in simulation studies.
• The addition of local features in MFP + L reduced performance differences compared to penalized regression splines, especially in data-rich settings.
• In a pediatric respiratory health data application, MFP + L identified few, well-supported local features, contrasting with spline-based models indicating numerous local features.

Conclusions:

• The MFP + L approach is effective in identifying and incorporating significant local features, enhancing global fractional polynomial models.
• MFP + L offers superior performance in settings with local features while retaining the strengths of the MFP approach where global functions suffice.
• This method provides a valuable tool for comprehensive data modeling, balancing global and local feature detection.