Variable selection with P-splines in functional linear regression: Application in graft-versus-host disease

Area of Science:

• Statistics
• Functional Data Analysis

Background:

• Functional linear regression models (FLM) are crucial for analyzing data with functional responses and scalar covariates.
• Challenges exist in simultaneous variable selection and parameter estimation within FLM.

Purpose of the Study:

• To propose P-splines as a robust tool for variable selection and parameter estimation in FLM.
• To evaluate and compare penalized (L1, L2) and non-penalized regression approaches combined with response variable smoothing.

Main Methods:

• A functional LASSO approach using basis representation for the response variable.
• A penalized FLM incorporating a P-spline penalty into the least squares fitting criterion.
• Comparison of six distinct methods, including penalized/non-penalized regression and presmoothing techniques (regression splines, P-splines).

Main Results:

• P-splines demonstrate effectiveness for simultaneous variable selection and functional parameter estimation.
• The study identified the most competitive approach through simulation schemes.
• The chosen method was successfully applied to real-world graft-versus-host disease data.

Conclusions:

• P-splines offer a powerful and integrated solution for estimation and variable selection in functional linear regression.
• The findings provide practical insights for analyzing complex functional data, particularly in medical applications like allogeneic stem-cell transplantation.