Spatial regression effects may depend on covariates in disease-mapping models. For example, the association between infectious disease incidence and risk factors may vary according to climatic factors, such as time, season, and temperature. In this study, we aim to develop a spatial model that accounts simultaneously for the spatial and varying effects of covariates believed to modulate the spatial association. We employ a local linear estimation method to estimate covariate-dependent coefficients in a model for excess zero counts. The local linear estimator effectively smooths covariate-dependent coefficient estimation. Comprehensive simulation studies were conducted to evaluate the performance of the local linear estimators, and reported dengue cases in villages in Kaohsiung City from January 2014 to December 2015 are used to inform our proposed method for practical use in real-world applications.

Many rare diseases offer limited established treatment options, leading patients to switch therapies when new medications emerge. To analyze the impact of such treatment switches within the low sample size limitations of rare disease trials, it is important to use all available data sources. This, however, is complicated when the use of measurement instruments changes during the observation period, for example when instruments are adapted to specific age ranges. The resulting disjoint longitudinal data trajectories complicate the application of traditional modeling approaches like mixed-effects regression. We tackle this by mapping observations of each instrument to an aligned low-dimensional temporal trajectory, enabling longitudinal modeling across instruments. Specifically, we employ a set of variational autoencoder architectures to embed item values into a shared latent space for each time point. Temporal disease dynamics and treatment switch effects are then captured through a mixed-effects regression model applied to latent representations. To enable statistical inference, we present a novel statistical testing approach that accounts for the joint parameter estimation of mixed-effects regression and variational autoencoders. The methodology is applied to quantify the impact of treatment switches for patients with spinal muscular atrophy. Here, our approach aligns motor performance items from different measurement instruments for mixed-effects regression and maps estimated effects back to the observed item level to quantify the treatment switch effect. Our approach allows for model selection as well as for assessing effects of treatment switching. The results highlight the potential of modeling in joint latent representations for addressing small data challenges.

The win ratio (WR) has emerged as an increasingly used method for analyzing composite endpoints in randomized controlled trials (RCTs). Its growing popularity stems from its ability to accommodate a hierarchy of event types within a composite primary endpoint in an RCT. However, as a relatively new measure, the WR exhibits some surprising properties. Oakes and other authors have noted that for a given triplet of participants, there are realizations of event times and hierarchy of event types when "wins" form a loop. They term this property "intransitivity." In this paper, we report and study a different phenomenon, a violation of long-run transitivity of WRs, for example, when in the long run WR T A > T B > 1 , WR T B > T C > 1 and paradoxically WR T C > T A > 1 , where T A , T B , T C denote the time-to-event in trial arms A, B, and C (or placebo, standard of care and novel treatment, respectively). We refer to it as Efron-type "non-transitivity." Unlike Oakes-type intransitivity, Efron-type non-transitivity is an inherent property of the underlying random variables. As such, it cannot be resolved by a longer observation period or larger sample size. Lumley and Gillen showed that transitivity can be guaranteed only for univariate statistics (e.g., mean, median, etc.), whereas head-to-head comparisons can be non-transitive. WR and win proportion (WP) are head-to-head comparisons and may be non-transitive, in which case the best treatment cannot be determined. Therefore, the non-transitivity property challenges the utility of all head-to-head comparisons as efficacy measures in RCTs. In this paper, we explore the scope of this problem, focusing on identifying conditions that rule out non-transitivity for WR, WP, and hazard ratio (HR). We apply our findings to establish transitivity in two case studies using published RCTs. This work highlights an important phenomenon that must be recognized when the WR is used as an efficacy measure in randomized controlled trials.

Recent advances in Adaptive-Optics Confocal Scanning Laser Ophthalmoscopy (AO-cSLO) have enabled non-invasive, in-vivo imaging of retinal cell subsets, at near single-cell resolution. However, challenges such as spatial and temporal variability, limited observation windows, and segmentation errors hinder the effective use of this data for diagnosing neurodegenerative disorders like glaucoma. Common point pattern metrics used in this area, such as density and distance-based measures, are sensitive to noise and incomplete data, reducing their diagnostic utility. Fractal measures, with their scale-invariance and robustness to point pattern degradation, offer a promising alternative. In this study, we apply fractal analysis to RGC point pattern data sets from rodent glaucoma models and controls, comparing fractal dimension, lacunarity, and succolarity with traditional metrics. We find that lacunarity and succolarity provide more accurate and enable earlier detection of glaucoma than traditional metrics, demonstrating greater robustness to noisy and degraded data. These measures demonstrate significant potential for achieving an earlier and more reliable glaucoma diagnosis.

Epidemic models are invaluable tools to understand and implement strategies to control the spread of infectious diseases, as well as to inform public health policies and resource allocation. However, current modeling approaches have limitations that reduce their practical utility, such as the exclusion of human behavioral change in response to the epidemic or ignoring the presence of undetected infectious individuals in the population. These limitations became particularly evident during the COVID-19 pandemic, underscoring the need for more accurate and informative models. To address these challenges, we develop a novel Bayesian epidemic modeling framework to better capture the complexities of disease spread by incorporating behavioral responses and undetected infections. In particular, our framework makes three contributions: (1) leveraging additional data on hospitalizations and deaths in modeling the disease dynamics, (2) accounting for data uncertainty arising from the large presence of asymptomatic and undetected infections, and (3) allowing the population behavioral change to be dynamically influenced by multiple data sources (cases and deaths). We thoroughly investigate the properties of the proposed model via simulation, and illustrate its utility on COVID-19 data from Montréal and Miami.

In several biomedical contexts, the need for diagnostic analyses of data that is a set of directions in 2, 3, or higher dimensions arises, as for instance, when considering the relative movement of body parts like the limbs, or looking at anatomical orientations. Commonly used statistical tools, including graphical tools developed for data on the real line, or for dealing with multidimensional data taking values on Euclidean spaces, are quite inappropriate for analyzing such data, due to major differences in their underlying geometry. Taking clues from the Box-plot, which was introduced by Tukey [1977] for linear data, here we propose what we label a "Cloud-plot", which is a visualization tool and diagnostic framework for plotting data on 3-dimensional directions, which take values on the surface of a unit sphere, the 𝕊 2 . The analysis is based on "geodesic distances" between any 2 observations, which are the shortest paths between these two points on the surface of the sphere. Using these distances, we construct robust analogues of the spherical median and the quartiles. This is followed by a definition of the "Spherical Median Absolute Deviation" (S M A D). We use these quantities to define outliers, and the performance of the proposed method is evaluated through a comprehensive simulation study that compares true and false positive rates given by several existing discordancy tests. Our extensive results indicate that the approach based on our Cloud-plot provides a very successful and competitive performance for detecting outliers, and remains stable across a range of sample sizes and contamination settings. The cloud-plot is illustrated using two interesting medical applications viz. (i) the identification of structural biomarkers of glaucoma, and (ii) the analysis of functional joint instability in gait cyclograms. These examples demonstrate the potential of the Cloud-plots to detect directional anomalies that may not be captured otherwise by tools commonly used on Euclidean spaces.

The FDA initiated Project Optimus and issued guidance for dose optimization, recommending randomized parallel dose-response cohorts to generate additional data at promising dose levels and implying that different dosages may be needed for different indications. In addition to dose optimization, with recent advancements in precision medicine and cancer biology, the development of cancer treatments has shifted toward the search for agents targeted to specific molecular profiles that may appear in more than one type of cancer. The basket trials are clinical trial designs that enable the simultaneous assessment of a new treatment in multiple indications. Concerning the FDA's dose optimization perspective and the recent trend of basket trials in early-phase clinical trials, this paper proposes a dose-ranging basket trial design based on a Bayesian model-averaging approach considering efficacy and toxicity outcomes, where indications and dose levels define baskets. A key benefit of the proposed approach is that it explicitly accounts for the possible heterogeneity of response rates among baskets. Our simulation study shows that the proposed approach outperforms other methods, offering higher statistical power, better control of Type I error rates, precise optimal dose selection, and sample size savings in various scenarios with heterogeneous treatment effects between baskets.

The increasing prevalence of high-dimensional covariates presents a significant challenge to precision medicine. To overcome this, we propose a novel multi-stage optimal dynamic treatment regime method specifically designed for high-dimensional accelerated failure time models. Our approach, which aims to maximize individual survival time, employs backward induction with counterfactual survival times as the optimization objective at each stage. Parameter estimation leverages weighted counterfactual survival times to account for censoring, followed by the slope determination by analysis of residuals (SDAR) algorithm. Theoretical analysis guarantees exponential convergence with non-asymptotic error bounds under mild conditions. Simulation studies demonstrate a substantial improvement in survival time estimation, particularly under high censoring rates, compared to existing methods. We illustrate the practical utility of our method by applying it to a sepsis dataset, revealing clinically meaningful treatment recommendations.

Estimation of optimal individualized treatment rules (ITRs) tailored to patient characteristics is a crucial component of precision medicine. When such problems arise in multicenter randomized trials with known treatment assignment probabilities, the optimal ITR may vary across sites because of site-level heterogeneity, and directly pooling data across centers can lead to biased ITR estimation. Meanwhile, privacy constraints often prevent investigators from accessing individual-level data from all centers. We therefore propose Heterogeneous Distributed Learning (HD-learning) to estimate optimal site-specific ITRs using only summary-level data from each site in a single communication round. The method uses a distributed mixed-effects model to accommodate common fixed effects and site-specific random effects. We further develop Shrinkage HD-learning (SHD-learning) for moderate- or high-dimensional covariates. Under suitable conditions, we establish asymptotic properties of the proposed estimators. Simulations show that our methods are lossless relative to the corresponding pooled estimator and outperform methods that ignore heterogeneity. We illustrate the proposed methods using the acute upper respiratory tract infections (AURTIs) study and the opioid withdrawal study.

Mendelian randomization is currently mainly implemented through the use of genetic variants as instrumental variables to inestigate the causal effect of an exposure on an outcome of interest. Mendelian randomization studies are robust to confounding bias and reverse causation, but they remain susceptible to selection bias; for example, this can happen if the exposure or outcome are associated with selection into the study sample. Negative controls are sometimes used to detect biases (typically due to confounding) in observational studies. Here, we focus specifically on Mendelian randomization analyses and discuss under what conditions a variable can be used as a negative control outcome to detect selection mechanisms that could bias Mendelian randomization estimates. We show that the main requirement is that the negative control outcome relates to confounders of the exposure and outcome. Counter-intuitively, the effect of the negative control on selection is of secondary concern; for example, a variable that does not affect selection can be a valid negative control for an outcome that does. We also investigate under what conditions age and sex can be used as negative control outcomes in Mendelian randomization analyses. In a real-data application, we investigate the pairwise causal relationships between 19 traits, utilizing data from the UK Biobank. Treating biological sex and natural hair color as negative control outcomes, we identify selection bias in analyses involving commonly used traits such as alcohol consumption, body mass index and educational attainment.

Network meta-analysis (NMA) is widely used in healthcare decision-making, where estimates of the effect of multiple treatments on outcomes are required. For time-to-event outcomes such as survival or disease progression the most common approach is to model log hazard ratios; however, this relies on the proportional hazards assumption. Novel treatments such as immunotherapies are expected to display complex hazard functions that cannot be captured by standard parametric models, which results in non-proportional hazards when comparing treatments from different classes. As a result, alternative models such as fractional polynomials or restricted cubic splines are often used. These allow substantial flexibility on the shape of the baseline hazard, but require time-consuming model selection or are intractable for Bayesian analysis. We propose a flexible NMA model using M-splines on the baseline hazard, with a novel weighted random walk prior distribution that provides shrinkage to avoid overfitting and is invariant to the choice of knots and timescale. Non-proportional hazards are modeled either by stratifying by treatment or by introducing treatment effects on the spline coefficients, and covariates may be included on the log hazard rate and spline coefficients. Treatment and covariate effects on the spline coefficients are given random walk prior distributions to smoothly model departures from proportionality over time. The methods are implemented in the user-friendly R package multinma, which supports analyzes with aggregate data, individual participant data, or mixtures of both. We apply the methods to a NMA of progression-free survival with treatments for non-small cell lung cancer.

Health risk behaviors, including smoking, poor nutrition, alcohol misuse, and physical inactivity (SNAP), are leading contributors to chronic disease burden and healthcare costs worldwide. Their prevalence is shaped not only by individual demographic characteristics but also by contextual factors such as socioeconomic and occupational environments. We develop a Bayesian topic-informed dynamic mixture model to analyze SNAP behaviors using data from the Italian health and behavioral surveillance system PASSI. Free-text occupational descriptions are integrated through structural topic modeling to define latent occupational groups that inform the mixture weights of a multivariate ordered probit model. Covariate effects are allowed to vary across occupational clusters and evolve over time. To enhance interpretability and facilitate variable selection, we incorporate non-local spike-and-slab priors on regression coefficients. We further develop a tailored online learning strategy based on sequential Monte Carlo, enabling efficient updating of inference as new surveillance data become available. The proposed approach provides a flexible and interpretable framework for monitoring how occupational contexts modulate the impact of socio-demographic factors on multiple health risk behaviors over time, supporting targeted public health interventions. More broadly, the methodology is applicable to other longitudinal health surveillance and clinical settings where complex contextual information is available in textual form.

Evaluating diagnostic accuracy for multi-category outcomes remains a significant challenge, primarily due to computational limitations in existing performance metrics. The Polytomous Discrimination Index (PDI) has emerged as an order-agnostic solution suitable for nominal classifications. However, its broader adoption has been constrained by the lack of efficient implementation, especially for its variance estimation, which typically would require computationally intensive bootstrapping procedures. In this work, we address this limitation by proposing a novel asymptotic variance estimator for the PDI. Our method integrates classical U -statistic theory with recent advances in combinatorics, offering a scalable and theoretically grounded alternative. To assess the performance of the proposed approach, we conduct extensive simulation studies and observe remarkable gain in computing time. We further apply our method to a real-world brain image analysis where deep neural networks are used as a diagnostic tool. We can efficiently report the accuracy of the neural networks with different depth specifications.

Covariate-adaptive randomization (CAR) is increasingly used in clinical trials to balance baseline covariates, and its statistical properties have therefore attracted considerable attention in recent years. However, most existing studies overlook the issue of missing covariates, which is a common occurrence in practice. In this paper, we establish the theoretical properties of hypothesis testing for treatment and covariate effects when missing covariates are imputed using the single imputation method. The results indicate that the traditional test is conservative under certain conditions. However, this conservativeness can be corrected using an adjusted test, leading to higher statistical power. Furthermore, we extend our framework to the multiple imputation setting and compare its performance with single imputation through simulations. Our results provide a theoretical foundation for applying CAR procedures in the presence of missing covariates.

Frequent visits in cohort studies are important as they enable, among others, the assessment of disease progression and treatment effectiveness. In HIV studies, extended intervals between visits have been shown to be associated with adverse outcomes (e.g., antiretroviral therapy interruption). Prediction of the next visit time can be a useful tool in identifying those more prone to (temporarily) disengage from care. Since visit times are to a large extent individually driven, patient characteristics such as longitudinal markers history and past visit patterns have to be taken into account when dealing with the prediction of future visit times. The topic of dynamic prediction has been developed greatly, especially within the framework of joint models of longitudinal and survival data. While joint models have been extended to account for an informative visiting process, little attention has been given in the dynamic prediction of the next visit time. In this study we propose a model for the joint analysis of a longitudinal continuous marker and the visiting process. A gap time mechanism is employed for the visiting process, while a linear mixed model is used for the marker. The two submodels are linked via correlated normally distributed random effects. The resulting form of the marginal likelihood requires only uni-dimensional integration, irrespective of the dimension of the random effects in the longitudinal model, a property that holds with multiple continuous markers. The model is used to derive dynamic predictions for the time to the next visit, conditioning on patient's previous gap times and marker history. The performance of the proposed methodology is assessed through simulation. Finally, we apply the proposed model to data of people living with HIV from the Athens Multicenter AIDS Cohort Study.