Standard single-cell differential expression (DE) analysis identifies genes that change across conditions, but it usually overlooks two key sources of heterogeneity that single-cell data are uniquely positioned to reveal: how disease-associated expression varies among cells within a donor, and how expression contrasts depend on cell state or subject-level context. Assigning every cell the diagnosis of its donor can contaminate DE signal when disease penetrance is partial, while modeling each gene with a single disease effect cannot capture heterogeneous responses across cell populations. We present PRISM (Phenotype-Resolved Inference in Single-cell Mixed models), a negative-binomial mixed-effects framework that augments standard DE analysis with three outputs: a context-DE vector \theta_g that tests whether disease effects vary along a biological axis z_ij (such as cell state, sex, or age); regularised cell-state responsibilities q_ij for a putative disease-associated expression component; and a subject-level state summary \rho_i. Naive likelihood-only inference of q_ij can align with nuisance variation (batch, cell-cycle, or dominant subtypes) rather than the intended disease axis. We therefore introduce PRISM-OT, a closed-form 1-D Wasserstein-2 projection that regularises the disease-arm posterior toward an affected/unaffected marginal while preserving the likelihood-derived rank ordering of cells. In simulations, PRISM accurately recovers simulated latent-state assignments and detects context-dependent DE at P_ctx = 95.7% while controlling \mathrmFPR_α= 2.0%. Applied to 73,830 ROSMAP microglia from 420 subjects, PRISM recovers Alzheimer’s-consistent microglial biology in a single joint analysis. On a Perturb-seq benchmark with ground-truth cell-level labels, PRISM transfers without tuning and recovers per-construct penetrance estimates consistent with an independent proxy. PRISM is available on PyPI as prism-de.

Clinical decision-making often simplifies continuous risk data into discrete levels using round-number thresholds. These simplifications can distort risk assessments. To systematically uncover these distortions, we develop an interpretable machine learning model that identifies anomalies caused by threshold-based practices. Through simulations, real-world data, and longitudinal studies, we demonstrate how round-number thresholds can lead to discontinuities and counter-causal paradoxes in mortality risk. Despite advances in medicine, these anomalies persist, underscoring the need for dynamic and nuanced risk assessment methods in healthcare. Our findings suggest continuous reassessment of clinical protocols, especially in critical settings like intensive care, to improve patient outcomes by aligning thresholds with the continuous nature of risk.

Cancers are shaped by somatic mutations, microenvironment, and patient background, each altering gene expression and regulation in complex ways, resulting in heterogeneous cellular states and dynamics. Inferring gene regulatory networks (GRNs) from expression data can help characterize this regulation-driven heterogeneity, but network inference requires many statistical samples, limiting GRNs to cluster-level analyses that ignore intracluster heterogeneity. We propose to move beyond coarse analyses of predefined subgroups by using contextualized learning, a multitask learning paradigm that uses multiview contexts including phenotypic, molecular, and environmental information to infer personalized models. With sample-specific contexts, contextualization enables sample-specific models and even generalizes at test time to predict network models for entirely unseen contexts. We unify three network model classes (Correlation, Markov, and Neighborhood Selection) and estimate context-specific GRNs for 7,997 tumors across 25 tumor types, using copy number and driver mutation profiles, tumor microenvironment, and patient demographics as model context. Our generative modeling approach allows us to predict GRNs for unseen tumor types based on a pan-cancer model of how somatic mutations affect gene regulation. Finally, contextualized networks enable GRN-based precision oncology by providing a structured view of expression dynamics at sample-specific resolution, explaining known biomarkers in terms of network-mediated effects and leading to subtypings that improve survival prognosis. We provide a SKLearn-style Python package https://contextualized.ml for learning and analyzing contextualized models, as well as interactive plotting tools for pan-cancer data exploration at https://github.com/cnellington/CancerContextualized

Models which estimate main effects of individual variables alongside interaction effects have an identifiability challenge: effects can be freely moved between main effects and interaction effects without changing the model prediction. This is a critical problem for interpretability because it permits “contradictory" models to represent the same function. To solve this problem, we propose pure interaction effects: variance in the outcome which cannot be represented by any subset of features. This definition has an equivalence with the Functional ANOVA decomposition. To compute this decomposition, we present a fast, exact algorithm that transforms any piecewise-constant function (such as a tree-based model) into a purified, canonical representation. We apply this algorithm to Generalized Additive Models with interactions trained on several datasets and show large disparity, including contradictions, between the apparent and the purified effects. These results underscore the need to specify data distributions and ensure identifiability before interpreting model parameters.