Background/Aims: Multi-arm multi-stage trials benefit patients by providing a flexible and versatile clinical trial design compared with standard randomized controlled trials. Multi-arm multi-stage trials can evaluate multiple interventions for a single disease, which avoids the need to run multiple trials. Multi-arm multi-stage trials incorporate decision-making at interim analysis, which enables the trial to stop early for futility or efficacy of a treatment. As a result, multi-arm multi-stage trials reach conclusions faster, requiring less time and resources. Despite their growing popularity, limited research has been done to examine how decision-making methods used in Bayesian multi-arm multi-stage trials impact the efficiency of the trial.Methods: This study examines how decision-making strategies influence the efficiency of Bayesian multi-arm multi-stage trials, including approaches for setting thresholds to declare superiority or futility and evaluating multiple treatments simultaneously. We apply the Nelder-Mead optimization algorithm to determine the decision thresholds that maximize statistical power while maintaining family-wise type I error rate below 5%. We conduct a simulation study to compare the conventional method to evaluate multiple treatments in a Bayesian multi-arm multi-stage trial to three alternatives. At each interim analysis, posterior probabilities are derived from a Normal-Gamma conjugate model, and trial decisions are made by comparing decision criteria derived from the posterior probabilities to the optimized decision thresholds. Simulation scenarios vary by treatment effect size and number of treatment arms to assess the robustness of each decision-making strategy.Results: All treatment comparison methods achieve similar power across simulation scenarios. However, the optimal decision thresholds vary substantially among methods. These thresholds are also lower than those currently used in Bayesian multi-arm multi-stage trials, which are often conservative and lead to reduced power. Thus, adjusting decision thresholds to the optimized values can improve trial efficiency.Conclusion: This study provides an exploration of alternative decision-making methods in Bayesian multi-arm multi-stage trials. Initial findings show that optimizing decision-making thresholds can improve the power of the trial without inflating the family-wise type I error rate, thus improving the efficiency of the trial. Further research should include the implementation of complex trial designs and non-normal outcomes to confirm that the results apply to adaptive platform trials.

BACKGROUND:Nirmatrelvir-ritonavir has been shown to reduce progression to severe illness from severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in unvaccinated high-risk outpatients. The effectiveness of nirmatrelvir-ritonavir in persons who have been vaccinated, infected naturally, or both is unclear. METHODS:In two open-label platform trials (PANORAMIC in the United Kingdom and CanTreatCOVID in Canada), we enrolled higher-risk adults (≥50 years of age or ≥18 years of age with coexisting conditions) in the community who tested positive for SARS-CoV-2 and had been unwell for 5 days or less. The participants were randomly assigned to receive usual care plus nirmatrelvir (300 mg)-ritonavir (100 mg) twice a day for 5 days or to receive usual care alone. The primary outcome was hospitalization or death from any cause within 28 days after randomization. RESULTS:From December 8, 2021, to September 30, 2024, a total of 3516 participants in the PANORAMIC trial and 716 participants in the CanTreatCOVID trial underwent randomization. In the PANORAMIC trial, 14 of 1698 participants (0.8%) in the nirmatrelvir-ritonavir group and 11 of 1673 participants (0.7%) in the usual-care group were hospitalized or died (adjusted odds ratio, 1.18; 95% Bayesian credible interval, 0.55 to 2.62; probability of superiority, 0.334). In the CanTreatCOVID trial, 2 of 343 participants (0.6%) in the nirmatrelvir-ritonavir group and 4 of 324 participants (1.2%) in the usual-care group were hospitalized or died (adjusted odds ratio, 0.48; 95% Bayesian credible interval, 0.08 to 2.23; probability of superiority, 0.830). In a substudy involving 634 participants, viral load was reduced by the end of treatment with nirmatrelvir-ritonavir. Serious adverse events with nirmatrelvir-ritonavir were reported in 9 participants in the PANORAMIC trial and in 4 participants in the CanTreatCOVID trial. CONCLUSIONS:In two open-label trials, nirmatrelvir-ritonavir did not reduce the incidence of hospitalization or death among vaccinated higher-risk participants with SARS-CoV-2 infection. (Funded by the National Institute for Health and Care Research, and others; PANORAMIC ISRCTN number, 2021-005748-31; CanTreatCOVID ClinicalTrials.gov number, NCT05614349.).

Reliable prognoses for progressive illnesses often require analysis of a series of medical images rather than a single snapshot. Classical joint models and many recent deep-learning approaches either discard censored observations, ignore temporal dependencies between adjacent scans or offer limited insight into the image regions that drive risk. We introduce SurLonMamba, a joint survival model that couples a computationally efficient selective state-space model for sequential image processing and survival prediction. Its vision encoder extracts spatial features from each image scan; the sequence encoder propagates these representations through time, capturing long-range progression patterns at linear computational complexity; and the survival module converts the resulting sequence summary into a hazard score trained by minimizing the negative log partial likelihood, thereby leveraging all censored data. The architecture naturally supports participant-level interpretation through occlusion sensitivity and survival risk prediction. Extensive simulations and experiments on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) cohort show that SurLonMamba exhibits strong predictive performance, while highlighting brain regions consistently linked to conversion to dementia.

We propose a basket trial design that addresses patient heterogeneity in treatment effect across subgroups and evaluates the effectiveness of treatments with a survival endpoint via Bayesian latent subgroup analysis. In basket trials, various cancer types are enrolled, yet the response to treatment can vary across these types. To accommodate this variability, our design assumes cancer types may belong to either a sensitive subgroup, responsive to treatment, or an insensitive subgroup, unresponsive to treatment. During interim analyses, Bayesian subgroup analysis is conducted to classify the cancer types into different clusters according to both the survival time and the longitudinal biomarker measurements of the patient. Finally, we make Bayesian inferences to decide whether to stop recruiting patients for each cluster early and assess whether the treatment is effective for each cluster according to the estimated median survival time. The simulation study shows that our proposed method performs better than the independent approach and the Bayesian Hierarchical Modeling (BHM) method in most of the scenarios, with higher power to detect treatment effects in sensitive cancer types while maintaining the desired type I error rate for insensitive types. This integrated approach holds promise for optimizing treatment efficacy across diverse cancer populations with varying characteristics.

Abstract Integrating longitudinal data with survival models is a prevalent strategy for dynamic survival risk prediction while accounting for subjects' longitudinally observed variables. However, existing methods primarily focus on scalar longitudinal data and seldom tackle the complexities associated with high‐dimensional longitudinal imaging data. This article introduces a new approach that effectively incorporates longitudinal medical images as features for dynamic risk prediction. This approach ensures interpretability, enhances computational efficiency, and performs robustly even with small datasets. Our method achieves high prediction accuracy, as validated through extensive simulation studies and a real‐world application to Alzheimer's disease data. To the best of our knowledge, this is the first attempt to use longitudinal medical images for predicting dynamic survival risk.

Background: Although the acute phase of the COVID–19 pandemic has passed, SARS–CoV–2 continues to cause outpatient morbidity. Antioxidant micronutrients support immune regulation and may offer a low–cost, scalable adjunctive treatment in early infection. Objective: To evaluate a pilot combination antioxidant therapy within CanTreatCOVID. Methods: This pilot sub–protocol enrolled non–hospitalized adults across five Canadian provinces (September 5th, 2024–March 31st, 2025) with mild–to–moderate SARS–CoV–2 infection within five days of symptom onset. Participants were randomized to usual care plus a 10–day antioxidant regimen (selenium 300 μg, zinc 40 mg, lycopene 45 mg, vitamin C 1.5 g) or usual care alone. Pilot objectives assessed feasibility, retention, adherence, and safety. The primary outcome was hospitalization or death within 28 days; exploratory outcomes included recovery and symptom measures by day 14. Results: Eighty–one participants were randomized (41 antioxidant; 40 usual care). Retention was high 85.4% antioxidant; 82.5% usual care), and 90.2% of antioxidant participants completed the intervention course. Adverse events were infrequent (9.8% vs 2.5%), with no serious adverse events reported. No deaths occurred in either group; no hospitalizations occurred in the antioxidant arm versus 2/40 (5%) in usual care. By day 14, recovery was reported in 32/40 (80.0%) participants receiving antioxidants versus 23/36 (63.9%) in usual care (OR 2.128; 95% CI 0.7474.871). Sustained alleviation of all symptoms occurred in 38/40 (95.0%) versus 29/36 (80.6%), respectively (OR 3.498; 95% CI 0.872 —10.017). Return to usual activity by day 14 occurred in 38/40 (95.0%) versus 30/36 (83.3%) (OR 3.113; 95% CI 0.762—9.022). Adjusted between–group differences in dietary intake were not statistically significant. Conclusions: Combination antioxidant therapy was feasible to deliver in a decentralized outpatient setting, with high adherence and tolerability. While the trial was not powered for definitive efficacy conclusions, consistent directional improvements across symptom outcomes support evaluation of this host-directed antioxidant strategy in larger trials. Keywords: Adaptive Platform Trial; Antioxidant Therapy; SARS–CoV–2 ; Outpatient Therapeutics; Micronutrient Supplementation Trial registration number: https://clinicaltrials.gov/study/ NCT05614349

Motivated by a recent trial using MRI scans to compare treatments for nasopharyngeal carcinoma, we recognize that imaging predictors can significantly improve treatment selection. However, such models are built retrospectively under equal randomization, not integrated in real time to inform adaptive treatment allocation. This article proposes a covariate-adjusted response-adaptive (CARA) randomization framework that prospectively incorporates imaging data. Using supervised functional principal component analysis (sFPCA), we extract features from patient images to enable adaptive randomization based on imaging covariates. By dynamically adjusting randomization probabilities to favour more effective treatments as data accumulate, our method aims to enhance patient outcomes within the trial, supporting an ethical trial design. Simulations show that CARA with imaging covariates allocates more patients to better treatments while maintaining good statistical power and accuracy.

Pursuing accurate observations and rational assumptions always drives advances in clinical trial design. In recent years, more trials have begun to collect multi-graded outcomes for more informative analyses. At the same time, assumptions other than the traditional monotonicity relationship have been considered in the dose-efficacy curve to be more realistic. Inspired by these two trends, we propose a phase I/II design that simultaneously considers multi-categorical toxicity and efficacy with multi-graded outcomes, measured as quasi-continuous probability based on prespecified weight matrices of clinical significance. Following keyboard design, our approach aims to screen out overly toxic doses by the toxicity probability intervals and adaptively makes dose escalation or de-escalation decisions by comparing the posterior distributions of dose desirability (utility) among the adjacent levels of the current dose. It helps to more accurately identify the OBD in a non-monotonically increasing dose-efficacy relationship. We also comprehensively present the safety, accuracy and reliability performance through numerical simulations in multiple scenarios and compare the results with several already available designs. The benchmarking results of multiple operating characteristics convincingly support that our design leads in overall performance while ensuring robustness.

Introduction SARS-CoV-2 is now endemic and expected to remain a health threat, with new variants continuing to emerge and the potential for vaccines to become less effective. While effective vaccines and natural immunity have significantly reduced hospitalisations and the need for critical care, outpatient treatment options remain limited, and real-world evidence on their clinical and cost-effectiveness is lacking. In this paper, we present the design of the Canadian Adaptive Platform Trial of Treatments for COVID in Community Settings (CanTreatCOVID). By evaluating multiple treatment options in a pragmatic adaptive platform trial, this study will generate high-quality, generalisable evidence to inform clinical guidelines and healthcare decision-making.Methods and analysis CanTreatCOVID is an open-label, individually randomised, multicentre, national adaptive platform trial designed to evaluate the clinical and cost-effectiveness of therapeutics for non-hospitalised SARS-CoV-2 patients across Canada. Eligible participants must present with symptomatic SARS-CoV-2 infection, confirmed by PCR or rapid antigen testing (RAT), within 5 days of symptom onset. The trial targets two groups that are expected to be at higher risk of more severe disease: (1) individuals aged 50 years and older and (2) those aged 18–49 years with one or more comorbidities. CanTreatCOVID uses numerous approaches to recruit participants to the study, including a multifaceted public communication strategy and outreach through primary care, outpatient clinics and emergency departments. Participants are randomised to receive either usual care, including supportive and symptom-based management, or an investigational therapeutic selected by the Canadian COVID-19 Outpatient Therapeutics Committee. The first therapeutic arm evaluates nirmatrelvir/ritonavir (Paxlovid), administered two times per day for 5 days. The second therapeutic arm investigates a combination antioxidant therapy (selenium 300 µg, zinc 40 mg, lycopene 45 mg and vitamin C 1.5 g), administered for 10 days. The primary outcome is all-cause hospitalisation or death within 28 days of randomisation.Ethics and dissemination The CanTreatCOVID master protocol and subprotocols have been approved by Health Canada and local research ethics boards in the participating provinces across Canada. The results of the study will be disseminated to policy-makers, presented at conferences and published in peer-reviewed journals to ensure that findings are accessible to the broader scientific and medical communities. This study was approved by the Unity Health Toronto Research Ethics Board (#22-179) and Clinical Trials Ontario (Project ID 4133).Trial registration number NCT05614349

Alzheimer's disease (AD) is a progressive neurodegenerative disorder that leads to memory loss, cognitive decline, and behavioral changes, without a known cure. Neuroimages are often collected alongside the covariates at baseline to forecast the prognosis of the patients. Identifying regions of interest within the neuroimages associated with disease progression is thus of significant clinical importance. One major complication in such analysis is that the domain of the brain area in neuroimages is irregular. Another complication is that the time to AD is interval-censored, as the event can only be observed between two revisit time points. To address these complications, we propose to model the imaging predictors via bivariate splines over triangulation and incorporate the imaging predictors in a flexible class of semiparametric transformation models. The regions of interest can then be identified by maximizing a penalized likelihood. A computationally efficient expectation-maximization algorithm is devised for parameter estimation. An extensive simulation study is conducted to evaluate the finite-sample performance of the proposed method. An illustration with the AD Neuroimaging Initiative dataset is provided.

Structural magnetic resonance imaging (MRI) is one of the primary predictors of Alzheimer's disease risk, enabling the identification of patients with similar risk profiles for precision medicine treatment. Motivated by the need for flexible modeling in AD research, we propose a latent-class model that addresses the heterogeneity within study populations. This model allows for varying relationships between covariates and survival outcomes, accommodating the dynamics of AD progression. The imaging predictors are characterized by bivariate splines over triangulation to accommodate the irregular domain of the brain images. We develop a generalized expectation-maximization (EM) algorithm that combines the computational methods for logistic regression and penalized proportional hazards models to implement the proposed approach. We demonstrate the advantages of the proposed method through extensive simulation studies and provide an application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, which helps to reveal different subtypes or stages of the disease process in Alzheimer's Disease.

The generalized linear model (GLM) is a popular modeling choice for pricing non-life insurance policies. However, high-cardinality categorical insurance data presents significant challenges for these GLM rate-making models. Additionally, insurance regulators often require rating territories, which are clusters of insurance policies' geographic locations for setting insurance rates, to meet certain standards. For instance, (1) the credibility standard ensures that the number of policies in a territory is large enough to be credible and representative, (2) the contiguity standard requires the locations in each territory to be geographically adjacent to promote a logical and practical spatial grouping, and (3) the cardinality standard specifies an acceptable range for the number of territories in a geographic area. To address these challenges, this article proposes a nested GLM framework for non-life insurance rate-making applications. In this framework, neural network models with categorical embedding layers are constructed to model the residual deviance from simple GLMs, using high-cardinality categorical variables as input. Low-dimensionly features extracted from the neural network model effectively translate categorical variables into meaningful numerical representations, capturing their effects on the initial model's residuals. The features corresponding to the location-related variable are further converted into a contiguous territory rating variable via spatially constrained clustering models. By incorporating outcomes from these models, the nested GLM not only satisfies regulatory requirements but also enhances the model's predictive power, while maintaining the interpretability from the (generalized) linear form. The construction of a nested Poisson GLM is presented in this article. Its performance is demonstrated using a real-life Brazil auto insurance data to model claim frequency.

Sample size determination in Bayesian randomized phase II trial design often relies on computationally intensive search methods, presenting challenges in terms of feasibility and efficiency. We propose a novel approach that greatly reduces the computing time of sample size calculations for Bayesian trial designs. Our approach innovatively connects group sequential design with Bayesian trial design and leverages the proportional relationship between sample size and the squared drift parameter. This results in a faster algorithm. By employing regression analysis, our method can accurately pinpoint the required sample size with significantly reduced computational burden. Through theoretical justification and extensive numerical evaluations, we validate our approach and illustrate its efficiency across a wide range of common trial scenarios, including binary endpoint with Beta-Binomial model, normal endpoint, binary/ordinal endpoint under Bayesian generalized linear model, and survival endpoints under Bayesian piecewise exponential models. To facilitate the use of our methods, we create an R package named "BayesSize" on GitHub.

Functional data analysis (FDA) is a rapidly growing field in modern statistics that provides powerful tools for analyzing data observed as curves, surfaces, or more general functions. Unlike traditional multivariate methods, FDA explicitly accounts for the smooth and continuous nature of functional data, enabling more accurate modeling and interpretation. Traditional FDA methods, such as functional principal component analysis, functional regression, and functional classification, rely on linear assumptions and basis function expansions, which can limit their effectiveness when applied to nonlinear, high-dimensional, or irregularly sampled data. Recent advances in neural networks provide promising alternatives to these traditional approaches. Deep learning methods offer several key advantages: They naturally capture nonlinear relationships, scale to high-dimensional data without explicit dimension reduction, learn task-specific representations directly from raw observations, and handle sparse or irregular sampling without requiring imputation. This article reviews recent methodological developments in FDA, with a focus on the integration of deep learning techniques. Through this comparative review, we highlight the strengths and limitations of classical and modern approaches, providing practical guidance and future directions.

Survival analysis utilizing multiple longitudinal medical images plays a pivotal role in the early detection and prognosis of diseases by providing insight beyond single-image evaluations. However, current methodologies often inadequately utilize censored data, overlook correlations among longitudinal images measured over multiple time points, and lack interpretability. We introduce SurLonFormer, a novel Transformer-based neural network that integrates longitudinal medical imaging with structured data for survival prediction. Our architecture comprises three key components: a Vision Encoder for extracting spatial features, a Sequence Encoder for aggregating temporal information, and a Survival Encoder based on the Cox proportional hazards model. This framework effectively incorporates censored data, addresses scalability issues, and enhances interpretability through occlusion sensitivity analysis and dynamic survival prediction. Extensive simulations and a real-world application in Alzheimer's disease analysis demonstrate that SurLonFormer achieves superior predictive performance and successfully identifies disease-related imaging biomarkers.

Penalized functional regression is a useful tool to estimate models for applications where the effect/coefficient function is assumed to be truncated. The truncated coefficient function occurs when the functional predictor does not influence the response after a certain cutoff point on the time domain. The R package PFLR offers an extensive suite of methods for advanced functional regression techniques with penalization. The package implements four distinct methods, each tailored to different models, effectively addressing a range of scenarios. This is demonstrated through simulations as well as an application to particulate matter emissions data. Generic S3 methods are also implemented for each model to help with summary, visualization and interpretation.

Brain imaging data is one of the primary predictors for assessing the risk of Alzheimer's disease (AD). This study aims to extract image-based features associated with the possibly right-censored time-to-event outcomes and to improve predictive performance. While the functional proportional hazards model is well-studied in the literature, these studies often do not consider the existence of patients who have a very low risk and are approximately insusceptible to AD. We introduce a functional mixture cure rate model that extends the proportional hazards model by allowing a proportion of event-free patients. We propose a novel supervised functional principal component analysis (sFPCA) method to extract image features associated with AD risk while accounting for the complexity arising from right censoring. The proposed method accommodates the irregular boundary issue inherent in brain images with bivariate splines over triangulations. We demonstrate the advantages of the proposed method through extensive simulation studies and provide an application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study.

Transportability analysis is a causal inference framework used to evaluate the external validity of studies by transporting treatment effects from a study sample to an external target population by adjusting for differences in the distributions of their effect modifiers. Most existing methods require individual patient-level data (IPD) for both the source and the target population, narrowing its applicability when only target aggregate-level data (AgD) are available. For survival analysis, accounting for censoring may be needed to reduce bias, yet AgD-based transportability methods in the presence of informative-censoring remain underexplored. Here, we propose a two-stage weighting framework named "Target Aggregate Data Adjustment" (TADA) that can simultaneously adjust for both censoring bias and distributional imbalances of effect modifiers. In our framework, the final weights are the product of the time-varying inverse probability of censoring weights and participation weights derived using the method of moments. We have conducted an extensive simulation study to evaluate TADA's performance. We have applied our methods to a real case study on the squamous non-small-cell lung cancer trial (NCT00981058). Our results indicate that TADA can effectively control the bias resulting from moderate censoring representative of most practical scenarios, and enhance the application and clinical interpretability of transportability analyses in settings with limited data availability.

We propose a function-on-function regression model that predicts a functional response by both a nonlinear dynamic effect of a functional predictor and a linear concurrent effect of another functional predictor. The nonlinear dynamic effect is characterized by taking an integral of a time-dependent two-dimensional smooth surface and the linear concurrent effect is modeled through a time-varying coefficient. The model structure combines the flexibility of nonlinear modeling with the interpretability of the linear concurrent effect. To approximate the two-dimensional surface, we use tensor product basis expansions, and for the time-varying coefficient in the concurrent effect, we employ B-spline expansions. The expansion parameters for each effect are estimated iteratively to account for the mutual dependencies between these two estimated effects. Each iteration of parameter estimation involves solving a penalized least squares problem. We establish the asymptotic properties of our estimator. The numerical performance of the proposed method is illustrated by simulation studies and two real data applications.