In biopharmaceutical studies, it is often of interest to compare the effects of two treatments (say, A and B), but data that contain a direct comparison are not available. However, there may be studies that compare them against another competitor (say, C). In this case, an indirect comparison of A versus B through C needs to be conducted. In this article, we consider the scenario where individual participant data (IPD) is available for the comparison of A versus C, but only aggregate-level data (AgD), for example, from a publication, is available for the comparison of B versus C. For such analysis, multilevel network meta-regression (ML-NMR) is advantageous since it can combine evidence from multiple trials with either IPD or AgD and can compare the treatments of interest in any target population. Most of the existing ML-NMR studies have focused on binary and continuous outcomes, while, relatively, research on censored survival outcomes remains limited with perhaps only one study modeling the marginal likelihood for AgD. Here, we aim to extend ML-NMR for time-to-event outcomes. We consider multiple popular parametric survival models and develop Bayesian estimation approaches built on mean and median survival. Extensive simulations show satisfactory performance. We further consider a case study on early-stage non-small cell lung cancer (NSCLC) overall survival. Emulation analyses of the Surveillance, Epidemiology, and End Results (SEER)-Medicare data are conducted. It is found that limited resection (LR) with adjuvant chemotherapy (ACT) prolongs survival compared to LR or lobectomy without ACT.
Non-inferiority trials play a central role in clinical research by demonstrating that an experimental treatment is not unacceptably worse than an established reference treatment when superiority is unlikely, but the new treatment offers other advantages, such as reduced toxicity, easier administration, lower cost, or improved adherence. These trials are typically designed as active control studies, making historical data from previous clinical trials or real-world evidence readily available. A key challenge, however, is how to appropriately incorporate multiple heterogeneous historical datasets into the design and analysis of a non-inferiority trial, as each source may differ in relevance, quality, and similarity to the current study. Moreover, a conventional two-arm non-inferiority trial lacks a placebo or standard of care control, requiring the reference treatment effect to be justified using external evidence. When ethically and practically feasible, including a placebo arm allows assessment of assay sensitivity and provides internal validation of the reference treatment effect, thereby strengthening the credibility of the non-inferiority conclusion. In this article, we propose two novel Bayesian self-adapting priors, the Additive Self-Adapting Mixture (ASAM) prior and the Cumulative Self-Adapting Product (CSAP) prior, to incorporate information from multiple historical reference and placebo studies in three-arm non-inferiority trials. The ASAM prior constructs study-specific priors and combines them through an adaptively weighted mixture, whereas the CSAP prior uses a cumulative product formulation with adaptive study-specific weights. Both approaches dynamically borrow information by assigning greater weight to historical studies that are more compatible with the current trial while down-weighting less comparable studies, thereby mitigating the impact of between-study heterogeneity. Extensive simulation studies demonstrate that the proposed methods maintain appropriate control of the Type I error rate while achieving substantial gains in statistical power, providing a flexible and robust framework for Bayesian analysis of three-arm non-inferiority trials.
Generalized estimating equations (GEE) produce population-averaged estimates of treatment effects in marginal mean models for correlated count outcomes, when intra-cluster correlations are considered as nuisance parameters. For joint inference of marginal means and correlations, paired estimating equations have been proposed. With a small number of clusters, matrix-adjusted estimating equations (MAEE) were introduced to correct finite-sample bias in correlation parameter estimates. This article extends the GEE/MAEE method by adding a third estimating equation for the scale parameter (3EE/MAEE) and demonstrates its superior performance for correlated count outcomes. In simulations, 3EE/MAEE reduced bias of ICC estimates and better maintained the nominal coverage of confidence intervals compared to its uncorrected counterpart. The performance of different bias-corrected sandwich variance estimators as well as working negative binomial (NB) and Poisson models is also evaluated. The 3EE/MAEE method is applied to overdispersed correlated count outcomes from a real-world, stepped wedge cluster randomized trial.
The selection and use of quality measures in value-based payment rely on single-period methods that conflate sampling noise with genuine within-provider year-to-year execution variability, producing assessments that are unstable across years and dependent on patient volume. We introduce a Longitudinal Beta-Binomial model, which separates three sources of variability simultaneously and produces a year-invariant measure-level assessment τ and a volume-independent provider-specific assessment τ n . Applied to five years of data (program years 2021-2025) for 744 providers on two CMS mental health quality measures, the analysis yields a striking reversal: under the standard Beta-Binomial framework, FUH-30 appears far more discriminating than READM-30-IPF ( ρ ( j ) = 0 . 78 -0.87 vs 0.51-0.63 per year); separating execution variability from sampling noise reverses this conclusion ( τ = 0 . 621 [0.598, 0.642] for FUH-30 vs τ = 0 . 758 [0.730, 0.784] for READM-30-IPF, 95% posterior credible intervals), because FUH-30's year-to-year provider instability is three times larger than its sampling noise. The framework proposes three requirements simultaneously: discriminability ( τ can separate good from poor health-care providers and is year-invariant where ρ ( j ) swings substantially across years); fairness (both τ and τ n are independent of patient volume, removing the structural disadvantage faced by small and rural providers); and actionability ( τ n distinguishes consistently substandard from erratic providers, enabling targeted intervention and more honest measure adoption decisions).
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.
The relationship between contextual factors, including neighborhood characteristics, and adolescent alcohol use remains unclear, with studies finding either no effect or associations in either direction. The current study used data from a subset of a Czech longitudinal cohort (ELSPAC; analytic N = 1528) to examine how family socioeconomic status (SES), neighborhood advantage (administrative data), and perceived neighborhood disorder (subjective ratings) jointly influence alcohol use at age 15 (latent factor using three reports as indicators). Parental drinking, maternal monitoring, and peer alcohol use were considered as proximal mediators. The results from structural equation modeling showed that, contrary to social disorganization theory, perceived neighborhood disorder was associated with lower adolescent alcohol use (β = -0.10, p = .007), while neighborhood advantage was not significantly associated with either alcohol use or the proximal mediators. Family SES showed no direct association with alcohol use but was indirectly associated with more drinking through lower perceived neighborhood disorder, greater parental alcohol use, and greater maternal monitoring (total indirect β = 0.017, 95% CI [0.004, 0.036]). Peer alcohol use remained the strongest correlate of adolescent drinking (β = 0.33, p < .001). These findings are inconsistent with the social disorganization theory but are in line with many existing studies. Both higher SES and greater perceived neighborhood disorder predicted increased maternal monitoring, indicating two distinct pathways to supervision: one driven by resources, the other by environmental risk. These results highlight the value of modeling subjective neighborhood perceptions alongside family-level mediators for understanding adolescent alcohol use.
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.
Informal employment is an important social determinant of health, yet little is known about whether transitions into and out of informal employment are associated with health in similar ways. Using nationally representative panel data from the China Family Panel Studies from 2014 to 2020, this study examines whether transitions from formal to informal employment and from informal to formal employment are differently associated with self-rated health among non-agricultural workers in China. Asymmetric fixed-effects models show that transitioning from formal to informal employment is associated with a 0.078-point decline in self-rated health on a five-point scale, equivalent to approximately 0.07 standard deviations. The corresponding estimate for exit from informal employment is smaller and not statistically significant. Event-study analyses indicate that the entry-related health decline becomes apparent around the observed transition interval and is not preceded by differential health deterioration. The entry-related health decline amounts to approximately 0.16 standard deviations among workers over age 45 and 0.08 standard deviations among workers with a high school education or less, whereas the corresponding entry estimates are not statistically significant among younger and more-educated workers. These findings suggest that the direction of labor-market transition matters for health and highlight the importance of reducing avoidable movement into informal employment and extending social protection across employment forms.
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.
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.
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.
BACKGROUND:Accurate and timely prediction of critical events from longitudinal electronic health record (EHR) data is essential for precision medicine, particularly in complex chronic diseases with heterogeneous and evolving patient trajectories. Despite rapid growth in the number of statistical and machine learning methods, prediction remains challenging, especially for binary outcomes. Many valid approaches either lack transparency, ignore temporal dependence, or are difficult to dynamically update with new data, limiting clinical applicability. Existing dynamic prediction methods are designed primarily for continuous outcomes and do not directly extend to binary settings, which are common in clinical practice. METHODS:We use a Bayesian generalized linear mixed model approach to develop a cross-validated sequential prediction (CVSP) algorithm for estimating the conditional probability of a binary outcome given all available historical data. The prediction model integrates population-level fixed effects, lagged outcomes to capture shorter-term dependence, and patient-specific random intercepts to account for longer-term dependence due to unobserved heterogeneity. Predictions are cross-validated and generated sequentially at each visit with Monte Carlo integration, without refitting the model as new data accrue. Variable selection via bootstrap LASSO is incorporated to improve model parsimony and prediction validity. RESULTS:The framework is motivated by and applied to systemic sclerosis (SSc) patients with longitudinal assessments of proximal muscle weakness. The proposed method demonstrates superior discriminative performance (cross-validated AUC of 0.86) compared to standard regression and machine learning approaches, while also maintaining good calibration. The CVSP approach allows efficient individualized predictions that incorporate a patient's entire medical history. Variable selection reduces the number of predictors while preserving accuracy. CONCLUSION:This Bayesian CVSP framework provides a generalizable approach for individualized, visit-by-visit prediction of binary outcomes from longitudinal EHR data. By dynamically updating risk estimates without repeated refitting, it supports real-time clinical decision-making and advances precision medicine for chronic disease management.
Bivariate first-event outcomes arise in longitudinal biomedical studies when two clinically related events are assessed on a shared visit schedule. We propose a Bayesian local Gaussian-copula allocation model for bivariate discrete-time first-event data with baseline and time-dependent covariates. Two outcome-specific working discrete-time decrement models define interval-specific working decrement probabilities and thereby generate marginal survival coordinates on the common interval grid. Among subjects jointly at risk at the start of an interval, a Gaussian copula is used locally to allocate probability mass across four terminal outcomes: no event, event 1 only, event 2 only, and same-interval co-occurrence. The Gaussian copula accommodates negative local dependence, independence, and positive local dependence. We consider constant, unstructured interval-specific, and hierarchical shrinkage specifications for the dependence parameter, and compare them with frequentist and Bayesian odds-ratio benchmarks on the observed-probability scale. Because the native copula-model coefficients act on the working decrement scale, observed-scale covariate effects are summarized by Kullback-Leibler projection. In simulations, the Gaussian-copula models were competitive with odds-ratio benchmarks for observed-scale covariate-effect estimation; the hierarchical model provided a regularized alternative to unstructured interval-specific dependence. We illustrate the method using National Health and Aging Trends Study data on first onset of mobility help and self-care help. The application gave broadly similar observed-scale covariate-effect conclusions across the odds-ratio, constant Gaussian-copula, and hierarchical Gaussian-copula models.
It is well-known that results from adaptive multi-arm experiments with treatment selection are subject to the bias of the selection process. In this article, we consider designs with a binary outcome that begin with randomized parallel arms. After each of the preplanned interim looks at data, researchers proceed to the next stage with treatments selected according to predetermined rules. The experiment ends with the best arm, and the binomial parameter is estimated from all the observations accrued throughout the experiment in this arm. We present a comprehensive and unified Bayesian approach to the point and interval estimations, which uses a class of design-dependent priors obtained from the reference prior theory (Bernardo 1979). The approach is applicable regardless of the treatment selection rule, and is not affected by the inclusion of a control arm if the treatment selection is based on direct comparisons of the response rates relative to the control arm. The frequentist characteristics of the posterior estimators are studied and compared with alternative methods, where available. To this end, we introduce specific tools that facilitate the evaluation of estimation methods in binary data analysis. We also study the influence of the treatment selection rule and the effect of the prior correction on estimates through various examples. The approach is easy to implement in the experimental practice, and can be used in the interim analyses to help researchers in the treatment selection process.
In analyzing clustered data, random effects (RE) and fixed effects (FE) models are two primary approaches. The RE model assumes that the cluster-specific effects are random and uncorrelated with individual characteristics. If this assumption is violated, the RE approach can lead to biased estimates of the coefficients of individual covariates and cluster effects. In contrast, the FE approach, which models cluster effects as fixed effects, yields unbiased estimates even if the cluster effects are correlated with individual covariates. Numerous studies have compared the FE and RE approaches. However, the practical importance of the biases observed in RE-based methods remains unclear. Some studies have demonstrated significant biases in RE models when the assumption of no correlation is violated, whereas others have found these biases to be negligible. These differences may be due to variations in study design, with some evaluations focusing on settings that may not reflect realistic data scenarios. In this paper, we compare FE and RE models through theoretical evaluation, simulation studies, and real-data applications. Specifically, we derive an approximate formula to quantify the asymptotic bias in the RE model and verify its accuracy through simulations. These results help to explain the different conclusions reached in the existing literature. Our goal is not to propose a new estimator or a fundamentally new inferential framework, but to provide an analytical clarification and practical quantification of the bias incurred by the standard RE estimator under a specific, interpretable dependence model, and to clarify how this bias relates to fixed-effects and correlated random-effects/between-within specifications.
To avoid unnecessary resource expenditure resulting from the sample size overestimation in seamless phase II/III designs, multi-stage early stopping may be incorporated in the phase III component. However, existing estimation methods for seamless phase II/III designs are primarily developed for two-stage settings and do not directly accommodate designs with multi-stage early stopping in phase III. In this paper, we develop a Score-statistics-based framework for point and interval estimation in this specific class of designs. The framework provides a design-specific formulation of conditional bias adjustment, conditional median-unbiased estimation, and Rao-Blackwellization for seamless phase II/III designs with multi-stage early stopping. Conditional on the trial continuing to phase III, the proposed framework targets valid and efficient estimation of the treatment effect for the selected arm and is applicable to a range of common endpoint distributions. Within this framework, we formulate and evaluate several representative conditional estimation procedures: the multiple iterations-based conditional bias-adjusted estimator (CBAE-MI), the single iteration-based conditional bias-adjusted estimator (CBAE-SI), the conditional median unbiased estimators with the unselected treatment group effects be estimated by their maximum likelihood estimators (CMUE-MLE) or set as zero (CMUE-ZERO), and the Rao-Blackwellized (RB) estimator. In addition, to properly quantify uncertainty around the point estimates, we derive confidence intervals based on CMUE-MLE, CMUE-ZERO, and RB. Through simulation under various endpoint types and parameter configurations, we recommend employing RB for point estimation and confidence interval, as it demonstrates superior robustness and conservative coverage probability across treatment selection and trial design settings.
BACKGROUND:The human microbiome comprises the microorganisms that inhabit the various locales of the human body and plays a vital role in human health. The composition of a microbial population is often quantified through measures of species diversity, which summarize the number of species along with their relative abundances into a single value. In a finite microbiome sample, there will be species missing from the target population, which will affect the diversity estimates. METHODS:We employ a model based on the hierarchical Pitman-Yor (HPY) process to model the species abundance distributions over multiple populations. The model parameters are estimated using a Gibbs sampler. We also derive estimates of species diversity, conditional and unconditional on the observed data, as a function of the HPY parameters. Finally, we derive a general formula for the Hill numbers in the HPY context. RESULTS:We show that the Gibbs sampler for the HPY model performs well in simulations. We also show that the conditional estimates of diversity from the HPY model improve over naïve estimates when species are missing. Similarly, the conditional HPY estimates tend to perform better than the naïve estimates especially when the number of individuals sampled from a population is small. Finally, we illustrate results of applying the HPY model in an infant gut microbiome dataset.
