Distinguishing case-mix from context heterogeneity in prognostic regression model synthesis settings

2026-08-13

AI Summary

This study addresses the challenge of disentangling whether coefficient heterogeneity in multicenter prognostic models arises from differences in case-mix or site-specific contextual effects. The authors propose the first diagnostic framework capable of decoupling these sources: leveraging an autoencoder to construct a low-dimensional latent space that emphasizes local prognostic relationships, combined with a tailored loss function, site-specific local regressions, and coefficient surface decomposition. This approach separates heterogeneity into a cross-site reference and site-specific deviations, which are then mapped onto the outcome scale to generate both observation-level and site-level summaries. In a two-center COPD trial, the dominant source of slope heterogeneity in key latent variables was attributed to context, while observation-level variance was primarily driven by case-mix; site-level summaries highlighted contextual differences. Negative-control permutation tests confirmed the authenticity of the contextual signal, offering empirical guidance for choosing between unified or localized modeling strategies.

Abstract

Prognostic regression models often synthesize data from multiple sites, whether within a multi-site study, across federated settings, or in individual participant data meta-analysis. Here, a site is any data source, such as a hospital, registry, trial, or study, and need not be a physical center. Analysts must then decide whether one regression model represents all sites or whether site-specific models are needed. Established measures such as coefficient-level tau^2 quantify heterogeneity but do not distinguish its source. We focus on diagnosing whether coefficient heterogeneity reflects case-mix or site-specific context effects. Case-mix heterogeneity can arise when linear regression terms approximate multivariable non-linear relationships in populations with different covariate distributions. Contextual heterogeneity arises when comparable patients require different regression relationships across sites. We do this by fitting site-specific local regressions in a dimension-reduced space and partitioning the smoothed coefficient surfaces into a cross-site reference and site-specific deviations. An autoencoder and custom loss structure the latent space around local prognostic relationships. We then project this partition onto the outcome scale to derive observation- and site-level summaries. We demonstrate the approach on a COPD trial with two sites. In the three leading latent slope coordinates, coefficient-surface variation was predominantly contextual. The derived observation-level outcome-scale variance partition was case-mix-leading, whereas its between-site aggregation was concentrated in contextual differences rather than case-mix shifts. A permuted-site negative control assesses whether the contextual summary can arise when site labels carry no signal. This diagnostic distinction can inform whether joint or site-specific regression models should be evaluated.

Problem

• case-mix
• context heterogeneity
• prognostic regression
• coefficient heterogeneity
• multi-site data

Innovation

• case-mix heterogeneity
• contextual heterogeneity
• prognostic regression
• latent space modeling
• coefficient surface partitioning