Variable-Domain Functional Regression for Modeling ICU Data.

Area of Science:

• Statistics
• Biostatistics
• Health Services Research

Background:

• Functional data analysis is crucial for understanding continuous variables over time.
• Existing models often struggle with subject-specific predictor domains.
• The Intensive Care Unit (ICU) Sequential Organ Failure Assessment (SOFA) score is a key metric for patient severity.

Purpose of the Study:

• Introduce novel scalar-on-function regression models accommodating subject-specific functional predictor domains.
• Develop both parametric and nonparametric approaches for fitting functional coefficients.
• Address the challenge of functional support transformation and registration.

Main Methods:

• Proposed a bivariate functional parameter dependent on the functional argument and domain width.
• Introduced parametric and nonparametric models for functional coefficient fitting.
• Demonstrated theoretical and practical invariance of the nonparametric model to support transformation.

Main Results:

• Applied the methods to analyze the association between daily ICU SOFA scores and in-hospital mortality.
• Investigated the relationship between daily ICU SOFA scores and physical impairment at hospital discharge among survivors.
• Validated the general applicability of the methods to diverse studies with continuous variables over unequal domains.

Conclusions:

• The new regression models effectively handle subject-specific functional predictor domains.
• The nonparametric approach offers robustness to functional support transformations.
• These methods provide a valuable tool for analyzing complex health-related functional data.