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

arXiv: https://arxiv.org/abs/2608.12885 · HTML: https://mlsanity.com/paper/2608.12885/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Investigating a domain adaptation approach for integrating different measurement instruments in a longitudinal clinical registry](https://mlsanity.com/paper/2312.00616/) (2023)
- [A novel approach for identifying and addressing case-mix heterogeneity in individual participant data meta-analysis](https://mlsanity.com/paper/1908.10613/) (2019)
- [CausalMetaR: An R package for performing causally interpretable meta-analyses](https://mlsanity.com/paper/2402.04341/) (2024)
- [Contrasting Global and Patient-Specific Regression Models via a Neural Network Representation](https://mlsanity.com/paper/2601.18658/) (2026)

## Abstract (arXiv)

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.