A general, flexible, and harmonious framework to construct interpretable functions in regression analysis

Area of Science:

• Statistics
• Machine Learning
• Biostatistics

Background:

• Interpretability in models is crucial for reliability, transparency, and communication.
• Defining and evaluating interpretability remains subjective, with factors like simplicity, accuracy, and generalizability being key.
• Existing methods may not offer a unified approach to constructing interpretable functions.

Purpose of the Study:

• To present a general, flexible framework for constructing interpretable functions in regression analysis, focusing on continuous outcomes.
• To introduce a new model selection measure based on Mallows's Cp-statistic.
• To demonstrate the framework's application in clinical trial design and Bayesian decision-making.

Main Methods:

• Formulation of a functional skeleton guided by user expectations of interpretability.
• Development of a new model selection criterion using Mallows's Cp-statistic to balance approximation, generalizability, and interpretability.
• Application of the framework to derive sample size formulas for adaptive clinical trials and analyze operating characteristics in Bayesian Go/No-Go designs.

Main Results:

• A novel framework for building interpretable regression models is established.
• A new Mallows's Cp-based statistic is proposed for effective model selection.
• The framework is successfully applied to adaptive clinical trials, Bayesian Go/No-Go paradigms, and hypothesis testing for categorical outcomes.

Conclusions:

• The proposed framework offers a harmonious approach to constructing interpretable functions in regression analysis.
• The new model selection measure aids in balancing key aspects of model evaluation.
• The method demonstrates broad applicability across various statistical and biomedical applications, including real-world data analysis.