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

TL;DR

This paper introduces a versatile framework for creating interpretable regression functions that balance simplicity, accuracy, and generalizability, with applications in clinical trials, hypothesis testing, and real-world data analysis.

Contribution

It proposes a novel, flexible framework for constructing interpretable regression models, including a new model selection measure based on Mallows's C_p, applicable to various outcomes.

Findings

Effective in adaptive clinical trial sample size estimation

Enhances interpretability with meaningful intermediate variables

Demonstrates applicability to categorical outcomes and real data

Abstract

An interpretable model or method has several appealing features, such as reliability to adversarial examples, transparency of decision-making, and communication facilitator. However, interpretability is a subjective concept, and even its definition can be diverse. The same model may be deemed as interpretable by a study team, but regarded as a black-box algorithm by another squad. Simplicity, accuracy and generalizability are some additional important aspects of evaluating interpretability. In this work, we present a general, flexible and harmonious framework to construct interpretable functions in regression analysis with a focus on continuous outcomes. We formulate a functional skeleton in light of users' expectations of interpretability. A new measure based on Mallows's $C_p$-statistic is proposed for model selection to balance approximation, generalizability, and interpretability. We apply this approach to derive a sample size formula in adaptive clinical trial designs to demonstrate the general workflow, and to explain operating characteristics in a Bayesian Go/No-Go paradigm to show the potential advantages of using meaningful intermediate variables. Generalization to categorical outcomes is illustrated in an example of hypothesis testing based on Fisher's exact test. A real data analysis of NHANES (National Health and Nutrition Examination Survey) is conducted to investigate relationships between some important laboratory measurements. We also discuss some extensions of this method.