Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Contrasting Global and Patient-Specific Regression Models via a Neural Network Representation

Max Behrens, Daiana Stolz, Eleni Papakonstantinou, Janis M. Nolde, Gabriele Bellerino, Angelika Rohde, Moritz Hess, Harald Binder

TL;DR

The paper tackles the challenge of choosing between global and personalized regression models in clinical prediction by proposing a diagnostic framework that leverages an outcome-guided latent space for localized regression. An autoencoder learns a compact representation $\mathbf{Z}\in\mathbb{R}^{n\times d}$ ($d\ll p$) end-to-end with localized regression in latent space, enabling end-to-end contrast of global versus patient-specific models. In COPD data ($n=217$, $p=76$), the method yields a global latent model with $R^2\approx0.41$ and reveals two robust subgroups where local models substantially outperform the global model (RMSE reductions up to $0.16$), with findings generalizing to a test set and mapping back to original predictors via interpretable Z-score profiles. Compared with PCA and a reconstruction-focused autoencoder, the proposed approach provides markedly higher predictive power ($R^2\approx0.40$ vs. $0.19$ and $0.15$) and greater stability across random initializations, illustrating its practical potential for identifying when personalized models are warranted and for interpreting subgroup-specific relationships in high-dimensional clinical data.

Abstract

When developing clinical prediction models, it can be challenging to balance between global models that are valid for all patients and personalized models tailored to individuals or potentially unknown subgroups. To aid such decisions, we propose a diagnostic tool for contrasting global regression models and patient-specific (local) regression models. The core utility of this tool is to identify where and for whom a global model may be inadequate. We focus on regression models and specifically suggest a localized regression approach that identifies regions in the predictor space where patients are not well represented by the global model. As localization becomes challenging when dealing with many predictors, we propose modeling in a dimension-reduced latent representation obtained from an autoencoder. Using such a neural network architecture for dimension reduction enables learning a latent representation simultaneously optimized for both good data reconstruction and for revealing local outcome-related associations suitable for robust localized regression. We illustrate the proposed approach with a clinical study involving patients with chronic obstructive pulmonary disease. Our findings indicate that the global model is adequate for most patients but that indeed specific subgroups benefit from personalized models. We also demonstrate how to map these subgroup models back to the original predictors, providing insight into why the global model falls short for these groups. Thus, the principal application and diagnostic yield of our tool is the identification and characterization of patients or subgroups whose outcome associations deviate from the global model.

Contrasting Global and Patient-Specific Regression Models via a Neural Network Representation

TL;DR

The paper tackles the challenge of choosing between global and personalized regression models in clinical prediction by proposing a diagnostic framework that leverages an outcome-guided latent space for localized regression. An autoencoder learns a compact representation () end-to-end with localized regression in latent space, enabling end-to-end contrast of global versus patient-specific models. In COPD data (, ), the method yields a global latent model with and reveals two robust subgroups where local models substantially outperform the global model (RMSE reductions up to ), with findings generalizing to a test set and mapping back to original predictors via interpretable Z-score profiles. Compared with PCA and a reconstruction-focused autoencoder, the proposed approach provides markedly higher predictive power ( vs. and ) and greater stability across random initializations, illustrating its practical potential for identifying when personalized models are warranted and for interpreting subgroup-specific relationships in high-dimensional clinical data.

Abstract

When developing clinical prediction models, it can be challenging to balance between global models that are valid for all patients and personalized models tailored to individuals or potentially unknown subgroups. To aid such decisions, we propose a diagnostic tool for contrasting global regression models and patient-specific (local) regression models. The core utility of this tool is to identify where and for whom a global model may be inadequate. We focus on regression models and specifically suggest a localized regression approach that identifies regions in the predictor space where patients are not well represented by the global model. As localization becomes challenging when dealing with many predictors, we propose modeling in a dimension-reduced latent representation obtained from an autoencoder. Using such a neural network architecture for dimension reduction enables learning a latent representation simultaneously optimized for both good data reconstruction and for revealing local outcome-related associations suitable for robust localized regression. We illustrate the proposed approach with a clinical study involving patients with chronic obstructive pulmonary disease. Our findings indicate that the global model is adequate for most patients but that indeed specific subgroups benefit from personalized models. We also demonstrate how to map these subgroup models back to the original predictors, providing insight into why the global model falls short for these groups. Thus, the principal application and diagnostic yield of our tool is the identification and characterization of patients or subgroups whose outcome associations deviate from the global model.
Paper Structure (18 sections, 9 equations, 5 figures, 7 tables)

This paper contains 18 sections, 9 equations, 5 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Overview of the Proposed Approach
  4. Dimension Reduction with an Autoencoder
  5. Localized Regression
  6. Loss Function for End-to-End Training
  7. End-to-end Training Process
  8. Balancing Global and Local Models in the Learned Latent Representation
  9. Comparison with Benchmark Dimensionality Reduction Models
  10. Standard Stepwise Regression with Interaction Search
  11. Results
  12. Clinical Data from COPD Patients
  13. Establishing and Evaluating the Global Latent Model
  14. Identifying Patients Who May Need Personalized Models
  15. Comparison of Results to Test Data
  16. ...and 3 more sections

Figures (5)

  • Figure 1: Schematic overview of the proposed approach. All data is passed in batches through the encoder neural network of an autoencoder to obtain values $z_1, \ldots, z_n$ of a latent representation. Localized regression is performed for each patient individually in the latent space (one exemplary individual marked in orange). The localized regression model takes the latent dimensions as predictors and the clinical outcome as target. The values of the latent representation are passed through the decoder neural network for reconstructing the original data. The loss function compromises both a reconstruction component ($\text{Loss}_{\text{rec}}$) and a component for the localized models ($\text{Loss}_{\text{pred}}$) to promote a latent representation where the outcome can be well predicted.
  • Figure 2: Visualization of patient-specific deviations from the global regression model in the learned latent space. Each subplot displays patients according to their SGRQ score and their value on one of the four latent dimensions: (1) Airflow Obstruction & Diffusion Capacity, (2) Dynamic Vital Capacity, (3) Static Lung Volumes, and (4) Gas Trapping & Hyperinflation. The color of each point represents the difference between the patient's local coefficient ($\boldsymbol{\beta}_{\text{local}}$) and the global model's coefficient ($\boldsymbol{\beta}_{\text{global}}$) for that dimension. Yellow indicates agreement with the global model, while blue and red hues signify positive and negative deviations, respectively. Distinct patterns of deviation, which motivate the subsequent subgroup analysis, are most apparent for Dynamic Vital Capacity (Latent 2) and Gas Trapping & Hyperinflation (Latent 4).
  • Figure 3: Characterization of Subgroup 1 ($n=30$), defined by a distinct pattern of deviation from the global model. (A) The latent space plots show this group's deviation is concentrated in the second latent dimension. (B) An interaction analysis of the original predictors most associated with this latent dimension reveals significant interaction effects, confirming a differential relationship for this subgroup. B. refers to bronchodilator in the Figure. (C) The Z-score profile shows that, compared to the rest of the cohort, these patients are characterized by lower body weight, higher lung capacity percentage, and higher expiratory reserve.
  • Figure 4: Characterization of Subgroup 2 (n=20), defined by a deviation pattern concentrated in the fourth latent dimension. (A) The latent space plots, with the fourth dimension highlighted, show the specific pattern defining this group. (B) An interaction analysis of associated original predictors reveals significant interaction effects for measures of intrathoracic gas volume (ITGV), indicating a differential relationship for these patients. (C) The Z-score profile shows that this subgroup is characterized by higher lung flow measurements, lower expiratory reserve, and higher diffusion capacity.
  • Figure 5: Test patients assigned to Group 1 (n=6) and Group 2 (n=6) show similar patterns to training patients. Regression coefficients and interaction terms remained consistent, with minor changes due to increased sample size. Z-score profiles confirm that key characteristics are largely preserved in test patients. B. refers to bronchodilator in the Figure.