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

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.

Eliciting associations between clinical variables from LLMs via comparison questions across populations

The training data of large language models (LLMs) comprises a wide range of biomedical literature, reflecting data from many different patient populations. We investigate how it might be possible to recover information on correlation and causal links between patient characteristics, as a key building block for medical decision making. To avoid the pitfalls of direct elicitation, we propose an approach based on structured comparison questions, specifically patient comparison triplet questions. This is combined with a statistical model for the LLM representation that provides estimates of correlations without access to activations or model internals. Intuitively, we consider how similarity decisions of LLMs based on a first variable are affected by providing information on a second variable for one of the patients being assessed. We then induce prompt-level environment shifts to obtain correlation estimates for different subpopulations, which enables an invariant causal prediction (ICP) approach to obtain conservative candidate parent links. We demonstrate the method in two clinical domains, chronic obstructive pulmonary disease (COPD) and multiple sclerosis (MS). Across prompted environments, the elicited correlations are smooth, stable, and clinically interpretable, yet vary in a statistically significant way that supports downstream invariance testing, such that ICP provides a small set of candidate invariant parent links. These results show that indirect elicitation via triplet comparisons can recover meaningful association structure from LLMs and offer a cautious route from implicit correlations to causal statements that are congruent with LLM answering patterns.

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

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.