The Annals of Applied Statistics

Multimodal Gaussian process factor analysis provides a flexible framework for dimensionality reduction in temporally or spatially resolved omics data. Existing approaches, however, typically rely on pre-specified Gaussian process kernel families and do not explicitly separate each latent factor into a component capturing gradual, smooth variation and a complementary component capturing fine-scale, non-smooth variation. Here, we present MOFTy, a Bayesian multimodal factor analysis framework based on numerical information field theory (NIFTy) that replaces fixed kernel families with the flexible correlated field model in NIFTy and enables explicit additive component separation within each latent factor with quantified uncertainty. NIFTy has been successfully applied to high-resolution Bayesian imaging in astrophysics and facilitates scalable, curvature-aware variational inference for efficient posterior approximations. We validate MOFTy on simulated data; applications to published multi-omics data demonstrate that MOFTy disentangles latent spatial structures by separating smooth gradients from localized fine-scale heterogeneity in human glioblastoma and recovers cross-modal patterns in a mouse gastrulation dataset.

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.

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.

Diffusion within the cytoplasm is fundamental to numerous biological processes. Fluorescence recovery after photobleaching (FRAP) is one of the most common method for quantifying molecular diffusivity in living cells using standard laser scanning confocal microscopy (LSCM). However, accurately measuring fast cytoplasmic diffusion (typically >10 m^2/s) is challenging due to rapid recovery kinetics, weak signal-to-noise ratios, post-bleach signal artifacts, and spatial restrictions affecting normalization. While individual challenges have been addressed in specific contexts, a simple and robust framework to quantify cytoplasmic diffusivity remains elusive. Here, we present a FRAP methodology specifically designed to overcome these obstacles. By utilizing the Gaussian function -- the impulse response (ImpRes) of the diffusion equation in an infinite medium -- our approach leverages the full spatiotemporal dataset through a single-equation three-parameter fitting procedure, thus releasing restrictions to small regions of interest and arbitrary initial time-points. The methodology was validated on three datasets of increasing complexity: in silico simulated recovery profiles, in vitro data from FITC-dextran in glycerol solution, and live-cell imaging of free cytoplasmic GFP. Systematic comparison with existing models demonstrates that the ImpRes approach significantly reduces sensitivity to noise and imperfect fluorescence normalization, while remaining robust against short-term biases, such as transient probe photo-activation. Given its robustness under realistic experimental conditions and its ease of implementation, the proposed FRAP methodology provides a reliable tool for quantitative cytoplasmic analysis.

Accurate normalization is essential for differential expression analysis of RNA-sequencing data. Popular normalization methods such as the median-of-ratios and trimmed mean of M-values do not leverage information from the experimental design. This may be inefficient in experiments with large-scale systematic expression changes or complex designs. Here, we introduce design-informed size factor estimation (disize), a normalization method that uses information from the experimental design to improve accuracy. disize uses a modified generalized linear mixed model to robustly distinguish between biological signal and sample-specific size factors. We also propose a mechanistically justified data-generating process for RNA-sequencing counts that is derived from previous models of transcription and sequencing. Through simulations based on this data-generating process and validating on true RNA-seq data, we show that disize recovers size factors more accurately than existing methods, particularly in challenging scenarios with low gene expression and a high proportion of differentially expressed genes; this in turn improves downstream analysis. disize provides a robust and accurate approach to normalization, highlighting the significant benefits of integrating experimental design information directly into normalization for transcriptomic datasets. Author summaryIn transcriptomic analysis, normalization adjusts for technical biases arising from library preparation and sequencing. Methods implemented in widely used packages like DESeq2 and edgeR ignore information in the experimental design during normalization. Incorporating information from the experimental design into a normalization method has the potential to yield more accurate results. To do this, we developed a new method, design-informed size factor estimation (disize), that uses a statistical model to jointly account for the biological signal defined by the design and the sample-specific batch effect. By separating the biological variation into its components, disize can more robustly estimate the batch effect. To validate our approach, we constructed a flexible simulation framework relying on a mechanistically justified data-generating process for RNA-seq data. Our benchmarks on both simulated and true RNA-seq data show that disize recovers the true size factors more accurately than existing methods, particularly in challenging scenarios with low counts or a high proportion of differentially expressed genes. This improved normalization yields more reliable downstream results in differential expression analysis.

Maternal healthcare prediction systems often suffer from algorithmic biases due to socio-economic disparities and imbalanced datasets, limiting their effectiveness for equitable healthcare policymaking. This paper introduces MaternaAI, a fairness-aware and explainable learning framework designed to enhance maternal healthcare predictions in Kerala, India. The framework focuses on three critical health indicators:(1) Tetanus Toxoid (TT) booster uptake,(2) immunization coverage rates, and (3) the percentage of pregnant women completing four or more Antenatal Care (ANC) visits. To address fairness, we propose Adaptive Equity Score Optimization (AESO), a novel optimization algorithm that dynamically integrates fairness constraints into model training. AESO is model-agnostic and adapts group equity weights in response to real-time disparities. We integrate SHAP, LIME, and feature permutation techniques for explainability, enabling transparent global and local interpretation. Empirical results demonstrate that MaternaAI significantly improves fairness metrics and model accuracy across diverse machine learning and deep learning models, offering interpretable and equitable decision support for public health stakeholders.

Selecting stochastic gene-expression models from single-cell counts requires accurate parameter inference and efficient model selection. Likelihood methods in count space can be costly when full stationary count distributions are unavailable, whereas approximate methods may lose accuracy. Probability generating functions (PGFs) offer a compact analytical alternative, but existing PGF workflows are generally not likelihood based and therefore rely on computationally intensive cross-validation. We develop a likelihood-based PGF framework for both tasks. Correlated empirical PGF values are used to construct a Gaussian quasi-likelihood for parameter inference and PGF-based Bayesian information criterion (BIC) for model selection. We show that the empirical PGF is exactly unbiased and that the parameter estimator is consistent, converges at the inverse-square-root sample-size rate, and is first-order asymptotically unbiased. For large samples and a uniquely preferred model, PGF-BIC selects the same model as leave-one-out cross-validation in PGF space.

The dynamics of gene regulatory networks are governed by intrinsic noise, stemming from the random nature of biochemical reactions, and by extrinsic noise, arising from fluctuations in cellular components and environmental conditions. Together, these sources can compromise the reliability of predictive computational models if not properly accounted for, and capturing both effects within a single framework remains a non-trivial task in computational biology. In this work, we propose an uncertainty quantification framework that addresses these two contributions jointly: intrinsic stochasticity is described through a partial integro-differential equation (PIDE) for the protein probability density function, whereas extrinsic noise is represented as parametric uncertainty in the kinetic parameters. The propagation of the uncertainty is carried out via an intrusive polynomial chaos expansion (PCE), in which the PCE coefficients are obtained from a stochastic Galerkin projection of the PIDE, yielding a coupled deterministic system that is solved with standard numerical methods. We illustrate the approach on a positive autoregulatory gene network with one and two uncertain kinetic parameters. The proposed approach accurately reproduces the mean, variance, and full protein probability density function, including the bimodal distributions, at a substantially lower computational cost.

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.

Within the studies of stochastic gene expression, apart from the variability of copy number of gene products, the problems of threshold crossing of those products are biologically important as they often lead to terminal cellular events. Here, we study the threshold crossing problem of the messenger ribonucleic acid (mRNA) and present an exact probability distribution of first passage times in Laplace space. The function furnishes moments of any order and also predicts the characteristic time of the exponential tail of the distribution, which we match against Gillespie simulations. We find that all the measures of relative fluctuations of the threshold crossing times show U-shapes within this simple model of mRNA, as was found earlier in more mathematically involved models of threshold crossing time statistics of proteins. Furthermore, we extend the exact formula to include the phenomenon of DNA duplication and the corresponding doubling of transcription rate. As expected, the distribution varies considerably depending on the onset of the duplication stage within the cell cycle.

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.

Scaling laws help determine the optimal data size for training large models but are established in domains where the target is deterministic. Physiological signals are different: heartbeat sequences are stochastic, so part of the error is irreducible even with large amounts of data. Metrics such as MAE do not account for non-deterministic behavior, and therefore assessing scaling requires evaluating distributional calibration (measuring how well predicted probability densities capture true conditional characteristics). We formulate a scaling law metric(n) = E + A n- and evaluate it with five metrics: accuracy (MAE, RMSE), distributional calibration (KS distance, goodness-of-fit), and training objective (negative log loss) using a neural temporal point process trained on a cohort of four-ECG datasets. The law fits all five metrics. While point accuracy is near saturation at n = 183, KS distance and goodness-of-fit improve by 6% and 12% respectively when extrapolated to 10,000 subjects, showing that scaling decisions in stochastic domains must be guided by distributional calibration rather than point accuracy.

Bayesian borrowing of external information can improve trial efficiency, particularly in pediatric and rare disease settings where patient populations are limited, but may introduce bias and inflate the Type~I error rate when the trial differs from external studies. Recent U.S. Food and Drug Administration (FDA) draft Bayesian guidance emphasizes careful evaluation of external information, prior specification, and assessment of operating characteristics. This paper compares three meta-analytic-predictive (MAP)-based methods for Bayesian borrowing: the MAP prior, robust MAP (RMAP) prior, and self-adapting mixture (SAM) prior. An adaptive platform trial design in Rett syndrome is used as a case study. Simulation studies evaluate frequentist operating characteristics under varying prior--data conflict, between-study heterogeneity, treatment effects, and clinically significant differences (CSDs) for the SAM prior. The MAP prior achieved the greatest efficiency when external and current data were compatible but exhibited the largest bias under substantial prior--data conflict. The RMAP priors improved robustness through fixed robust-component weights, whereas the SAM prior adaptively adjusted borrowing and was less sensitive to prior--data conflict while retaining efficiency gains when the data were compatible. Although the CSD influenced the degree of adaptive borrowing, as reflected by effective sample size, it had only a modest impact on frequentist operating characteristics. Sensitivity analyses using a skeptical robust component yielded similar qualitative conclusions, while accentuating the differences between the MAP and RMAP priors. These findings provide guidance for evaluating and selecting MAP-based borrowing strategies before trial implementation, particularly in rare disease settings, consistent with current FDA recommendations.

To disentangle complex fiber configurations that remain challenging for diffusion MRI tractography, insights might be gained from microscopy tractography. Indeed, by precisely following small white matter (WM) fascicles invisible at the resolution of diffusion MRI, microscopy tractography can help explain how fiber populations are organized at the finest scales. Serial optical coherence tomography (S-OCT) is an imaging modality relying on the intrinsic contrast of a sample. When applied to brain tissues, the S-OCT contrast is primarily driven by the myelin reflectivity. Due to its high resolution, on the order of microns, and its 3D nature, S-OCT offers promise for studying WM connections at the microscale. However, while other microscopy imaging modalities have been shown to enable tractography, whether the reflectivity contrast from S-OCT supports the reconstruction of long-range WM fascicles at the microscale remains unknown. Furthermore, there is a gap in the literature regarding how an ideal microscopy tractography algorithm should behave with respect to the choice of tractography algorithm, tracking maps definition and microscale orientation distribution functions (ODF) estimation. In this work, we describe a tailored approach to reconstruct WM fascicles at the microscale from S-OCT acquisitions. We improve microscale orientation distribution functions (ODF) estimation by implementing a sliding-window formulation allowing the estimation of ODF at S-OCT resolution, and use apodized Dirac delta functions for reducing unwanted interference. We validate our approach on a simulated microscopy-like FiberCup dataset, and show that using multiscale Frangi filters for estimating ODF outperforms structure tensor analysis. We also show that particle filtering tractography with anatomical constraints enables targetted, region-to-region tractography, and outperforms standard deterministic or probabilistic tracking approaches. We further demonstrate our method on a whole mouse brain S-OCT reconstruction at 10 m by reconstructing the thalamocortical white-matter projections. Overall, our results show that S-OCT tractography recovers fine white matter fascicles visible at the microscale, and that these connections are supported by viral tracing experiments from the Allen Mouse Brain Connectivity Atlas. Moreover, this work shows the first ODF estimation and fully-3D probabilistic particle filtering tractography of the mouse brain from S-OCT reconstructions at 10 m isotropic resolution.

In vitro fertilization (IVF) laboratories equipped with timelapse incubators generate vast quantities of sequential embryo images, yet the absence of standardized, annotated databases impedes the development of reproducible computational tools for embryo assessment. Here we describe the construction of a standardized time-lapse imaging database comprising 631 normally fertilized zygotes from 218 treatment cycles, integrating timelapse image sequences, patient clinical records, and embryo developmental outcomes. We further present a gradient boosting decision tree (GBDT) ensemble framework that integrates zygote morphokinetic parameters-continuous time-series features extracted via a validated CNN-based segmentation algorithm (US Patent US11210494B2)-with conventional embryo assessment grades (categorical features per the Istanbul consensus). The fusion framework employs equal-weight initialization followed by iterative residual-decreasing training to optimally combine heterogeneous feature types. Ablation analysis demonstrated that the integrated model achieved an AUC of 0.78, significantly outperforming morphokinetics-only (AUC 0.71) and conventional-only (AUC 0.65) models, confirming the complementary value of the two data modalities. The database and fusion framework provide a reproducible foundation for embryo development assessment and are generalizable to other multimodal data integration tasks in reproductive medicine.

Standard polygenic risk scores (PRSs) are constructed based on additive genome-wide association study (GWAS) summary statistics. Nonlinear machine learning methods have been increasingly applied to construct PRSs directly from individual-level data, with the aim of improving predictive performance over standard PRSs through their ability to model non-additive genetic effects. However, their superiority across studies has been inconsistent, and the conditions under which they provide meaningful improvements remain unclear. We combined theoretical analysis, simulations and a real-world application to investigate when two widely used nonlinear machine learning methods, random forest and XGBoost, outperform standard PRSs. Theoretical analysis showed that standard PRSs can implicitly capture part of the genetic variance attributable to nonadditive genetic effects through their contributions to marginal SNP effects, thereby losing less information than commonly assumed. Although nonlinear models have a higher theoretical potential, their greater flexibility incurs a bias-variance trade-off that can limit predictive gains at finite sample sizes. Simulations showed that XGBoost outperformed the standard PRS only when the genetic architecture involves a sufficiently large proportion of interaction genetic variance concentrated across relatively few interaction effects and large training samples were available. Random forest consistently underperformed the standard PRS. In an application to ischemic heart disease prediction using UK Biobank data, XGBoost showed no meaningful improvement in predictive performance over the standard PRS, whereas random forest again performed worse. Together, these findings suggest that nonlinear machine learning do not uniformly outperform standard PRSs; rather, their relative performance depends jointly on genetic architecture and training sample size. Our study helps to reconcile the inconsistent results reported across previous studies and provides a framework for identifying settings in which more complex PRS models are likely to be beneficial.

Accurate prediction of individual medical outcomes is essential for optimizing treatment allocation amid rising costs, coverage denials, and limited clinical resources. Traditional predictive models, including regression and neural networks, rely on average effects and cannot tailor predictions to the specific circumstances of individual cases. We present relevance-based prediction (RBP), a model-free method that predicts outcomes as weighted averages of observed cases, with weights determined by a rigorously defined measure of relevance. Unlike model-based methods that rely on fixed calibrated parameters, RBP revisits the original data for each prediction and customizes both the cases and variables used. Applied to opioid treatment, RBP provides case-specific insights unavailable from conventional models, including how each prior case informs a prediction, how each variable affects its reliability and value, and how reliable the prediction is before it is made. These individualized insights may prevent misleading average-based decisions and reduce harmful or suboptimal treatment.

A differential-expression scan reports the genes with the largest moderated t-statistics, so controlling the family-wise error rate means controlling the null distribution of the maximum statistic over genes. Under gene correlation this is widely believed to require permutation, because correlation changes the effective multiplicity and corrupts the empirical-Bayes variance prior behind the moderated t-statistic. We decompose that liberality by an error-budget ablation and show that, within the simulated model class, it reduces principally to an inflation of the empirical-Bayes prior degrees of freedom: substituting the true prior returns the family-wise error to the independent-gene small-sample baseline, so dependence imposes no separate barrier once the prior is correct. Correlation deflates the cross-gene spread of the log sample variances; because the prior degrees of freedom decreases in that spread, the prior is over-estimated and the moderated maximum turns liberal. Dividing the observed spread by one minus the mean squared gene correlation, estimated by a tuning-free spectral U-statistic with an unbiased trace target, reverses the mechanism and holds the family-wise error near the baseline at retained power without permutation. An observable instability index flags when severe co-expression should defer to permutation.

A dental AI system and a dentist reading the same radiographs form a paired comparison. Published comparative studies often report the two arms separately against a reference standard, leaving the joint pattern of correctness between them unavailable for secondary paired inference. We show what that omission costs. The accuracy difference remains exactly identified; its sampling variance does not, so the report contains the estimate and not its uncertainty. On a study of 282 units, two published accuracies are consistent with 38 distinct joint tables whose confidence intervals differ in width by a factor of 2.5. The consequence is a three-zone decision map rather than a single threshold: differences at or below 1.06 points are non-significant under every compatible table, differences at or above 6.03 points are significant under every compatible table, and in between the published numbers cannot decide. We then show the omission is repairable at negligible cost. One additional integer, the number of units both arms classify correctly, identifies the joint table exactly and restores standard paired inference. For a panel of readers the pairwise dependences must arise from one joint distribution, a constraint that binds once three readers are present; publishing each reader's joint-correct count against a single reference reader cannot widen and may tighten every pairwise bound, and in a 7-arm experiment reduced them by a median of 37% even for pairs excluding that reference. Where the integer was never published we give DentalPair-Cert, an interval with finite-sample coverage uniformly over every admissible within-unit AI-dentist dependence under the independent-sampling-unit model, certified in both the nuisance maximization and the inversion. Across 4,200,000 simulated comparisons an independence analysis falls to 74.5% coverage with 12.2% type-I error; in a purposive sample of 9 recent comparative studies, 1 reported a paired test on discordant units.

High-dimensional population balance equations (PBEs) provide a natural framework for modeling heterogeneous cell populations, but their direct numerical solution becomes computationally prohibitive when the internal state space contains many molecular variables. We propose a hybrid mechanistic-machine learning framework for reducing and simulating PBEs defined over high-dimensional intracellular coordinates. The cell population is described by a number density n(x, t), where x [isin] [R]N represents gene and protein states associated with macrophage activation. A dynamics-preserving autoencoder maps this state space to a low-dimensional latent coordinate z [isin] [R]d, with d << N, while retaining key qualitative features of the underlying gene regulatory network, including attractor structure and multistability. Mechanistic information from the original regulatory dynamics is used to construct interpretable drift and diffusion terms for the reduced latent-space PBE. The reduced PBE is solved using a stochastic Lagrangian particle representation, in which particles evolve according to stochastic differential equations (SDEs) corresponding to the latent drift and diffusion fields. The resulting latent-space solution is subsequently decoded and propagated back into the original state space to recover physically interpretable cellular dynamics. We demonstrate the framework on macrophage polarization under cytokine-dependent regulation, including gene knockout perturbations. Overall, the proposed framework provides a computationally tractable and mechanistically interpretable route for integrating single-cell genomic data with population balance models of cell-state dynamics.