Biostatistics

Abstract: Compartmental epidemic models conventionally treat the probability of moving between dis ease states as fixed over time, an assumption that sits uneasily with the reality of a pandemic in which lockdowns, mask mandates, vaccination roll-out, and the arrival of new variants continually reshape transmission. This paper develops a time-inhomogeneous Markov chain framework for the Susceptible-Exposed-Infectious-Removed (SEIR) process, in which each transition probability pab(t) is allowed to vary with calendar time while respecting the struc tural zeros implied by the SEIR compartmental flow. We derive the constrained maximum likelihood estimator of pab(t) under these structural constraints, establish its finite sample efficiency, asymptotic normality, and Wilson score confidence intervals, and construct a like lihood ratio test of the null hypothesis that a compartments exit probability is constant over time. We further propose a stochastic machine learning hybrid extension in which the raw, kernel smoothed transition probabilities are regressed on policy and mobility covariates using both a logistic generalized linear model and a random forest, allowing the framework to attribute time-inhomogeneity to observable interventions. The methodology is applied to a compiled daily, district level COVID-19 surveillance panel for Sierra Leone spanning March 2020 to December 2023 (16 districts, 1,401 days). The likelihood ratio test rejects time-homogeneity of the exposed to infectious transition in 15 of 16 districts and of the infectious-to-removed transition in 8 of 16 districts ( = 0.05), and the covariate augmented logistic model achieves an out of sample Brier score roughly 76 times smaller than a time homogeneous pooled baseline, with healthcare capacity and the time trend emerging as the most influential predictors in the random-forest component. These results provide statisti cal evidence that time-inhomogeneous, covariate informed Markov models offer a materially better description of district-level COVID-19 transmission in Sierra Leone than classical time homogeneous compartmental models, with implications for sub-national outbreak monitoring in resource constrained settings

Estimating the correlation between subject-specific rates of change is a common objective in longitudinal studies. A natural approach is to fit ordinary least squares regressions per subject and correlate the resulting slope estimates directly. Under complete data, this slopes-first estimator is algebraically equivalent to a contrast-based plug-in estimator derived from the joint variance-covariance matrix of the two signals across time. Under independent dropout, however, the slopes-first approach implicitly applies heterogeneous weights across missing-data patterns, introducing bias whenever the cross-covariance between the two signals is not constant over time. We formalise this result and propose an unbiased alternative that estimates the joint covariance matrix before applying the contrast. We further extend our results to include covariates as well. Simulations confirm that the slopes-first estimator is biased under non-constant cross-covariance while the proposed alternative remains unbiased. Further, we show in a real-world example that the two estimators can lead to different scientific conclusions and recommend that researchers working with longitudinal data inspect the missing data pattern to make an informed decision about the estimator of choice.

In biomedical research, multiple types of high-dimensional data, such as genomic, transcriptomic, proteomic, and metabolomic data, are increasingly collected from the same subjects. Integrating these multiple data views can improve prediction by exploiting shared or complementary information across the views. Cooperative learning provides an agreement-based framework for multiview supervised learning by encouraging predictions obtained from individual views to be similar. However, the original framework assumes independent observations and therefore does not account for clustered structures, such as repeated measurements obtained from the same subject. To address this limitation, we propose Cooperative Learning with a penalized Linear Mixed Model (CL-pLMM) for high-dimensional multiview data with a clustered structure. CL-pLMM replaces the ordinary prediction loss in cooperative learning with a covariance-weighted loss that accounts for within-cluster dependence, while retaining the agreement penalty between views and a Lasso penalty for variable selection. We further show that its objective function can be represented as a penalized linear mixed-effects model applied to augmented data, allowing existing estimation procedures to be used. The performance of CL-pLMM is evaluated through simulation studies under various signal and dependence settings and an application to longitudinal proteomic and metabolomic data for predicting the time to spontaneous labor.

Causal mediation analysis is widely used to identify biological pathways linking exposures to outcomes, but most methods assume homogeneous mediation effects across individuals. In high-dimensional omics settings, this assumption can mask important heterogeneity driven by demographic, genetic, or environmental factors. We propose the M-high-learner, a flexible framework for detecting heterogeneous mediation effects with high-dimensional mediators. The method identifies mediators with subgroup-specific indirect effects while distinguishing them from null or homogeneous signals and controlling the type I error rate. It is computationally efficient, scalable, and yields interpretable sub-types. Simulation studies show that the proposed approach achieves high power while maintaining accurate error control. Applications to the Framingham Heart Study and the Multi-Ethnic Study of Atherosclerosis reveal that the mediation role of gene expression in sexs effect on high-density lipoprotein varies across subgroups defined by body mass index and age. Our framework provides a practical tool for uncovering heterogeneous biological mechanisms in high-dimensional genomic studies. Author SummaryBiological processes linking risk factors to disease often differ across individuals, but many existing methods assume these processes are the same for everyone. This can hide important differences between groups. We developed a powerful method to identify when these pathways vary across subgroups using large-scale molecular data. Our approach detects differences in how intermediate biological factors contribute to outcomes in populations defined by characteristics such as age and body mass index. Applying our method to population studies, we found that some biological pathways operate differently across groups, suggesting that key mechanisms may be missed when differences are ignored. Our work provides a tool to better understand how disease-related processes vary across individuals, which may support more targeted and personalized approaches to health research.

Longitudinal non-Gaussian data are common in biomedical and microbiome studies, where responses may not be normally distributed. However, many existing dynamic graphical models are developed for Gaussian responses, while many non-Gaussian graphical models focus on cross-sectional dependence and do not explicitly estimate temporal transition effects. We propose a latent Gaussian dynamic graphical model for longitudinal non-Gaussian responses, including binary, count, and compositional outcomes. The proposed framework jointly estimates the contemporaneous conditional dependence network and the lag-one temporal dependence structure. We further develop a penalized Monte Carlo expectation maximization procedure for estimation. Simulation studies across multiple graph structures and outcome types show that the proposed method can recover both dependence structures, with more stable recovery for the lag-one temporal dependence structure and more structure-dependent recovery for the contemporaneous conditional dependence network. We apply the proposed method to longitudinal data from the Integrative Human Microbiome Project (HMP2) using a multinomial observation model. The results reveal persistent lag-one temporal dependence and contemporaneous conditional dependence among dominant microbial taxa, demonstrating the utility of the proposed framework for dynamic network analysis of longitudinal non-Gaussian biomedical data.

The rapid growth of technologies such as wearable devices and high-throughput sequencing has generated unprecedented volumes of longitudinal data, often with multiple correlated features. This trend highlights the need for robust clustering methods tailored to multi-feature longitudinal datasets. Although previous reviews have benchmarked clustering methods in this context, most evaluations relied heavily on simulated and overly simplified datasets, which substantially limit their interpretability and applicability to real-world data. Missing data is also ubiquitous in longitudinal data, yet understudied in the context of clustering. To address these gaps, we systematically evaluate clustering methods across three distinct types of real-world longitudinal datasets: (1) a high-dimensional, low-timepoint metagenomic study, (2) a low-dimensional, high-timepoint multi-site repeated-measure study, and (3) a high-dimensional, high-timepoint repeated-measure study. We further investigate how missing data and different imputation strategies influence clustering performance. In addition, we introduce a novel resampling framework based on the empirical cumulative distribution function (eCDF) and a copula. This framework enables us to simulate multi-feature longitudinal data that preserves the correlation structure of real datasets, while also allowing for controlled variations such as sample size. Our simulation framework naturally accommodates missing data, thereby providing a flexible tool for benchmarking and comparing clustering methods in more realistic longitudinal settings.

Understanding the causal pathways linking the gut microbiome to downstream biomarkers and clinical outcomes is central to microbiome research. When the microbiome acts as the exposure, the high dimensionality and compositional structure of the data introduce unique methodological challenges for mediation analysis. To address these challenges, we propose a latent variable mediation framework that captures variation in microbial composition through a microbial balance, defined as the log-ratio between two unknown subsets of taxa. This balance serves as a latent scalar exposure and simplifies the estimation of the overall indirect effect at the community level, while simultaneously identifying specific taxa that contribute to the overall direct and indirect effects. We describe the model's estimation and inference, and illustrate the method using data from the Multiethnic Cohort--Adiposity Phenotype Study, where we examine the mediation pathway from the gut microbiome through lipopolysaccharide-binding protein, a marker of metabolic endotoxemia, to percent liver fat.

Somatic mutations in sequenced tumors are often detected with imperfect sensitivity. They can be missed because tumor heterogeneity results in some mutations being absent in a sample at hand or present at very low frequencies which, combined with technical limitations like insufficient sequencing depth, reduces their detectability. It becomes apparent with multi-regional sequencing that some mutations confined to specific areas can be overlooked in single-region analyses. Adjusting for such sensitivity becomes critical when mutation frequencies between groups of subjects are compared, such as responders and non-responders to a given therapy. Otherwise, the estimate of the mutation prevalence, or of the difference in prevalences between the groups, can be biased, leading to inflated type I error. Here, we propose a weighted approach to adjust for imperfect sensitivity of the mutation detection and compared it to the unweighted approach. We assume that a surrogate of mutation sensitivity is observed only among patients with called mutation, and we derive its unconditional mean. Such adjustment leads to less biased estimates of mutational frequencies and better control of the type 1 error.

Spatial transcriptomics technologies enable measurement of gene expression while preserving spatial tissue organization, but they remain highly sensitive to technical variability such as library size differences, slide-level effects, and spatial artifacts. Most existing normalization approaches treat normalization as a preprocessing step and perform downstream analyses on normalized values as fixed inputs, ignoring the uncertainty introduced during normalization. We introduce GPSNorm (Gaussian Process Spatial Normalization), a Bayesian spatial normalization framework that jointly models technical variation, spatial structure, and biological signal within a unified hierarchical model. GPSNorm represents gene expression counts using a negative binomial latent Gaussian model whose spatial component is a Gaussian Markov random field approximating a Gaussian process and performs efficient approximate Bayesian inference using the Integrated Nested Laplace Approximation (INLA), producing posterior estimates that propagate normalization uncertainty into downstream differential expression analysis. In simulations anchored to empirical spatial transcriptomics data, GPSNorm accurately recovers spatial technical structure and improves log-fold change estimation compared with existing normalization methods. Applications to three spatial transcriptomics datasets--including human dorsolateral prefrontal cortex Visium data, a GeoMx COVID-19 lung damage study, and the Spatial Organ Atlas kidney dataset--demonstrate improved preservation of biologically expected spatial patterns and marker gene contrasts. These results show that jointly modeling normalization and downstream inference can improve the robustness and interpretability of spatial transcriptomics analyses.An open-source R implementation of GPSNorm is available at https://github.com/Tiny-Quant/GPSNorm.

Estimating differential gene expression is a common task in RNA-seq. Current methods mostly rely on normalization to reduce variance and increase accuracy. These methods are widely used and provide invaluable information about transcriptomic changes between biological conditions. However, widely used normalization methods are known to distort estimates of transcript differential expression when a majority of genes are upregulated or downregulated, or when the total RNA content per cell changes. Despite the presence of global expression shifts in a number of contexts, few methods exist that can provide accurate normalization and estimate linear models under this context without spike-in controls. Here, we present \textbf{GLORB} (\textbf{G}\textbf{L}\textbf{O}bal-shift \textbf{R}obust \textbf{B}ayesian model), a method for estimating generalized linear models under global upregulation. We develop two models that are able to recover differentially expressed genes and linear model coefficients with lower distortion of results. We show that our model's method of accounting for library size variance is consistent with DESeq2's median of ratios, and edgeR's trimmed mean of M-values under conditions when a minority of genes are upregulated and outperforms them under circumstances when most genes are either increased or decreased between groups. Finally, because our method does not rely on calculating geometric means for each gene it is able to work in datasets with much higher sparsity.

In competing risks settings, covariate effects and group comparisons are usually assessed one event at a time - through log-rank or Cox tests on the cause-specific hazards, or Gray's test or Fine-Gray regression on a cumulative incidence function (CIF). This can obscure a clinically important quantity: the ratio between the event of interest and the competing event, since groups may differ little on the individual events yet differ sharply in their ratio. The generalized competing event (GCE) framework makes this ratio the object of inference; on the cause-specific scale the hazard ratio omega+(t) = lambda_1(t)/lambda_2(t) is estimated efficiently from a single stacked (Lunn-McNeil) model. We extend the framework to two scales that describe realized incidence. The subdistribution hazard ratio omega-tilde+(t) = lambda-tilde_1(t)/lambda-tilde_2(t) is estimated by a stacked, risk-set-weighted extension of the Lunn-McNeil construction; the cumulative-incidence ratio rho(t) = F_1(t)/F_2(t) - the odds that a subject's realized event by time t is the event of interest - by jackknife pseudo-observation regression of the Aalen-Johansen estimator. We relate the three contrasts: rho equals omega+ exactly under proportional cause-specific hazards, and equals omega-tilde+ only in the small-time limit under proportional subdistribution hazards, drifting toward 1 thereafter. The orthogonality that makes omega+ efficient is lost on both cumulative-incidence scales - omega tilde+ through overlapping weighted risk sets and shared censoring weights, rho through the shared all-cause survivor - so each carries a covariance term that must be handled and that bounds efficiency relative to the hazard-scale test. We derive the corresponding variances, study operating characteristics by simulation, illustrate on hypothetical prostate and head-and-neck cohorts, and provide an implementation in the gcemod R package.

Background. Hypermobile Ehlers-Danlos syndrome (hEDS), postural orthostatic tachycardia syndrome (POTS) and mast cell activation syndrome (MCAS) are reported to co-occur frequently. It is unclear how strongly, whether symptom profiles sharpen prediction of a second diagnosis given a first, and whether the published literature can support such inference at all. Methods. We pooled 22 published cohorts-aggregate prevalence data, no primary human-subjects data-using Bayesian hierarchical random-effects models on the logit scale, and propagated the resulting posteriors through naive and tempered symptom updating. We introduce a feasibility screen derived from the Frechet-Hoeffding bounds that tests whether separately pooled marginals can describe a single population, and we characterise the identifiability of latent class structure under disease-selected sampling. Results. Directed comorbidity is strongly asymmetric: {pi}POTS|hEDS = 46.6% (95% CrI [32.5,61.5]) against {pi}hEDS|POTS = 12.1% ([3.5,38.5]), a near-fourfold gap, with {pi}MCAS|POTS lowest at 3.9% ([0.7,21.6]). Prediction intervals exceed credible intervals throughout, indicating substantial between-cohort heterogeneity. The feasibility screen finds 26 of 102 testable cells (25.5%) incompatible with any joint distribution; critically, 21 of these fail the upper Frechet bound and are invisible to the one-sided screen that is the natural first implementation. Among cells surviving the screen, symptom evidence is informative in four of six directions-P(hEDS | POTS,S) rises from 12.1% to 49.7% on a four-symptom panel under tempered updating, and P(POTS | MCAS,S) from 49.5% to 82.1%-but inert in both hEDS-cohort directions. A pathway-dispersion contrast excludes zero in two of six directions, in opposite signs and by margins of 0.1-0.2 percentage points, consistent with chance at this number of comparisons. We show latent class structure is not identified from disease-selected aggregate data, and that the single cohort reporting trivariate structure (N = 8) yields an exactly balanced table (OR = 1.00, 95% CI [0.063, 15.99]). Conclusions. The pooled directional probabilities are usable as clinical priors, with intervals wide enough to preclude precision. Symptom-conditioned prediction is supported in some directions but not those most often invoked clinically, and every estimate rests on cohorts dominated by self-reported ascertainment. The principal methodological contribution is the two-sided feasibility screen: applied here it shows that a quarter of the testable literature cannot describe one coherent population, and that a one-sided implementation understates this sixfold. Keywords: hypermobile Ehlers-Danlos syndrome; postural orthostatic tachycardia syndrome; mast cell activation syndrome; comorbidity; Bayesian meta-analysis; random-effects model; Frechet bounds; identifiability; latent class analysis; collider bias

Selecting stochastic gene-expression models from single-cell counts requires balancing goodness of fit against unnecessary mechanistic complexity. The probability-generating-function-based Bayesian information criterion (PGF-BIC) combines covariance-weighted fitting in generating-function space with a complexity penalty, allowing candidate models to be compared without reconstructing their full count distributions. However, its conventional zero-threshold rule does not account for sampling uncertainty in the fitted score difference and may therefore favor overly complex models in finite samples. To address this limitation, we develop an uncertainty-aware PGF-BIC rule that selects the more complex model only when its score advantage exceeds a data-driven threshold. We use Cantelli's one-sided inequality to motivate a selection margin expressed in terms of a standard deviation. To determine this scale, we use influence functions to quantify sensitivity to small perturbations in the data distribution and obtain a first-order description of sampling fluctuations. The resulting variance estimate accounts for variability in both the empirical probability generating function and the estimated covariance weights, yielding a data-driven threshold for assessing the complex model's score advantage. A Poisson versus Bursty benchmark shows that the calibrated rule reduces incorrect selection of the more complex model. The calibration requires neither resampling nor additional optimization, incorporating sampling uncertainty into model selection while retaining the computational efficiency of PGF-BIC.

Personalized medicine aims to tailor treatments to individual patients, but its implementation is limited by scarce clinical resources and heterogeneous treatment effects. Electronic health records now offer longitudinal data that can support data-driven therapy selection. We focus on SGLT2 inhibitors, medications with broad metabolic and cardiovascular benefits, whose clinical impact varies significantly based on individual patient profiles. We propose a counterfactual Structural Causal Model (SCM) to estimate individual treatment effects (ITE) of SGLT2 inhibitors from observational data. The model assumes counterfactual stability and uses a Gumbel-Max sampling mechanism to capture stochastic treatment assignment while enabling differentiable inference. Optimal treatments are defined by maximizing the counterfactual value of future diagnostic outcomes. We evaluate the Counterfactual Gumbel-Max SCM using a doubly robust value estimator and show that, across diagnostic categories, it outperforms real-world prescriptions in predicted treatment value, highlighting subpopulations where SGLT2 inhibitors yield superior outcomes. By integrating causal inference with electronic health data, this framework provides individualized counterfactual reasoning about SGLT2 treatment effects and can support clinicians in identifying optimal therapies for type 2 diabetes and comorbid conditions.

Clinical decisions for determining optimal patient-specific interventions are complicated prediction tasks that rely on health care professionals' understanding of physiological mechanisms and their dynamics. These decisions are challenged by (a) observational data sparsity and (b) patient heterogeneity. Here, we focus on estimating and forecasting specific physiological properties--that are not explicitly present in clinical observations--to provide additional features using only data available bedside at the time of decision-making. Mechanistic models of physiological system(s), e.g., physiological ordinary differential equation (ODE) models, provide pathways to compensate for data sparsity by synchronizing the model with observations of an individual patient using data assimilation (DA). However, DA used in a standard computational workflow to estimate constant model parameters from presently-known data is less effective at optimizing state forecasts of the model governed by physiological processes that evolve before new observations are available. Stated simply, we cannot forecast the future evolution of the model because we cannot forecast model parameters. To support next-generation clinical decision support, we develop a new DA and machine learning (ML) hybrid pipeline to estimate and forecast individual future physiological processes by forecasting ODE model parameters. This pipeline overcomes model and DA workflow limitations by stacking a DA-estimated posterior empirical distribution of physiological parameters with longitudinal ML forecasting models. We work within the context of glycemic management in an ICU using EHR data to construct and test a use case. We use synthetic data and real-world clinical data to validate the integrated pipeline and quantify uncertainties.

Sample-specific molecular networks, which capture how an individual's gene regulatory structure may deviate from the population as a whole, are important tools for understanding heterogeneity in health and disease. However, most existing methods either do not accommodate uncertainty quantification or cannot handle missing data, non-Gaussian modalities, and longitudinal structure common in modern multi-omic studies. For example, copy number alterations in cancer genomic studies are non-Gaussian and often only partially observed, and their regulatory effects on gene expression may vary substantially across patients, variation that a single, population-averaged network cannot capture. To address these challenges, we propose PRISM (Personalized Relational Inference via Sample-specific Modeling), an empirical Bayes framework for estimating sample-specific covariance matrices from cross-sectional and longitudinal multi-omic data. PRISM models each individual sample's covariance matrix as drawn from an inverse-Wishart prior whose parameters are estimated from the data and allowed to vary across subpopulations or evolve over time, yielding a closed-form posterior and edge-level uncertainty quantification, ensuring scalability to high-dimensional omics data. In simulation experiments, PRISM achieves point-estimate accuracy comparable to or better than existing methods, substantially improved uncertainty calibration under non-Gaussian marginals, and lower computational cost, while maintaining robust coverage under moderate missingness. We apply PRISM to a yeast cell-cycle time course dataset, recovering time-varying biologically meaningful regulatory relationships independently documented in literature, and to paired copy number and gene expression data from ovarian cancer patients, identifying copy-number-expression interactions associated with survival, including TFs HNF4G and PAX8 which have independent evidence of clinical relevance in this cancer.

BackgroundGaussian process models underlie many spatial transcriptomics tools but typically assume stationary covariance. While typically ignored, non-stationarity of spatial covariance in gene expression may correspond to tissue heterogeneity or cell aggregates. ResultsAcross 13 Visium datasets, we use approximate Bayes factors from R-INLA to compare stationary and non-stationary Matern covariance functions. Evidence for covariance non-stationarity appears in 3% to 50% of genes across tissue samples. We further characterize the power and false discovery rate of the Bayesian analysis of non-stationarity. We find that gene sets associated with immune, cytokine, and other effector functions are enriched among genes favoring non-stationary spatial covariance. ConclusionsCovariance stationarity is not a benign technical simplification in spatial transcriptomics; it is frequently violated, the violation is biologically structured, and it changes the definition and classification of spatially varying genes.

Recent studies have reached conflicting conclusions about the statistical significance of lesion network mapping (LNM), especially regarding the impact of regional node strength on lesion-associated network detection. Here, we present a statistical framework that clarifies the origin of these apparently conflicting findings. Based on the simplified formulation of LNM introduced by van den Heuvel et al. (2026), we propose alternative, permutation-based null models corresponding to the sensitivity and specificity tests used in standard LNM analysis. We derive analytical expressions for both the proposed null models and the node-strength-constrained approach recently introduced by Zalesky and Cash (2026), thereby providing a computationally efficient alternative to permutation-based significance testing. Using synthetic lesion and connectivity matrices, as well as clinical datasets, we compare the outcome of the proposed null models with the standard LNM analysis and demonstrate how the choice of null models influences statistical inference and the resulting lesion network maps. Our framework shows that the apparent disagreements in the recent LNM literature can be understood as a consequence of different statistical null models rather than to conflicting conclusions about LNM itself.

Population stratification is a major source of inflated false positive rates in genome wide association studies. However, relatively few studies have examined its impact on gene-gene interaction detection, despite the importance of epistasis for understanding the genetic architecture of complex traits. In this study, we identify scenarios under which population stratification can inflate the interaction test statistics. Through analytical derivations and simulation studies, we show that this inflation is not adequately controlled by including principal components as covariates in the regression model. We then propose an alternative approach that effectively controls the inflation of false-positive rates for interaction test statistics due to population stratification by using single nucleotide polymorphism-by-population structure interaction as an additional covariate term in the regression model.

Estimating population-level dependence between brain regions is challenging when the number of regions greatly exceeds the number of individuals. We introduce an information-borrowing generalized Bayesian method for high-dimensional covariance estimation from region-level brain measurements. A divide-and-conquer parameterization separates marginal variances from correlation calibrations: an empirical \emph{pilot} correlation matrix--by default, obtained by standardizing a sample covariance matrix (SCM)--provides a reference structure that is adaptively calibrated through region-specific parameters shared across pairwise correlations, reducing the number of free parameters from $\mathcal{O}(d^2)$ to $\mathcal{O}(d)$ ($d$ is the number of regions) while guaranteeing a positive-definite covariance through the inclusion of a ridge term. Horseshoe priors on the calibration parameters enable selective borrowing and shrinkage of pilot information. Under suitable conditions on pilot accuracy, we establish theoretical guarantees for covariance estimation while retaining scalability in ultra-high-dimensional settings via a low-rank likelihood representation and a Woodbury-accelerated Hamiltonian Monte Carlo algorithm. Simulations showed lower estimation error than the SCM, bagging and iteratively refined principal orthogonal complement thresholding (POETRY). Applications to a semi-synthetic cortical-thickness and ADHD resting-state fMRI data revealed significant group differences in the default-mode--visual network and somatomotor network--limbic network blocks after Benjamini--Hochberg correction.