We propose group-specific nonlinear mixed effects models for longitudinal data whose indexing time is right-aligned to specific events, modeled as the time preceding those events. These models are motivated by dementia cohort studies that examine nonlinear trajectories of longitudinal cognitive test scores in late life, with separate trajectories for individuals with and without dementia in the period leading up to death. The model framework includes three sub-models: one for group membership, which represents dementia status in our motivating data, one for time to the indexing events, and one for the longitudinal outcome. Group membership is modeled using logistic regression or random forest. Conditional on group memberships, time to indexing events is modeled using accelerated failure time (AFT) models. Given both group membership and time to the indexing event, longitudinal data are modeled using nonlinear mixed effects models. By modeling and integrating out the time to indexing events, individuals whose indexing events have not been observed can be incorporated into the models. Stochastic approximation expectation maximization (SAEM) algorithms are adopted to maximize the likelihood for parameter estimation. In addition to modeling group-specific longitudinal trajectories aligned to the index time, the proposed models can also be used to predict group memberships or improve the prediction of time to the indexing events. Simulation studies are conducted to evaluate finite sample performance. An application to data from a dementia study is used for illustration.

The goal of dose-finding oncology trials is to assess the safety of anti-cancer treatments across multiple doses and to recommend dose(s) for subsequent trials. As patients' outcomes accrue, trialists dynamically recommend new doses for further investigation during the trial. This adaptive decision-making lends itself to Bayesian learning, with Bayesian frameworks increasingly guiding dose recommendations in model-based dose-finding designs, including the Continual Reassessment Method (CRM). However, such approaches introduce increased complexity, not least when additional outcomes are incorporated within designs. Such trial designs require careful prior selection. Directly applying prior calibration methods developed for single outcome model-based trial designs to joint outcome trial designs may introduce unintended bias in dose recommendations, potentially limiting dose exploration and failing to accurately reflect trialists' a priori beliefs. We extend methodology to analytically calibrate priors for model-based joint outcome trial designs with divergence minimisation. Our method offers an analytical and computationally efficient technique. We demonstrate the flexibility of our calibration method relative to existing approaches in ensemble simulation scenarios, and show that calibrating priors in this way delivers improved accuracy and computational efficiency compared with traditional grid search methods. As Bayesian dose-finding trial designs continue to advance, research and guidance on the effective calibration of design parameters is essential to support uptake and ensure optimal performance in practice. This method provides an analytical and intuitive approach to prior calibration, highlighting the importance of rigorous prior calibration in improving model accuracy and dose selection for safer, more effective oncology treatments.

Acute lymphoblastic leukemia (ALL) is the most common childhood cancer, with survivors frequently experiencing long-term neurocognitive morbidities. Here, we utilize the TOTXVI clinical trial data to elucidate the mechanisms underlying treatment-related neurocognitive side effects in pediatric ALL patients by incorporating brain connectivity network data. To enable such analysis, we propose a high-dimensional mediation analysis method with a novel network mediation structural shrinkage (NMSS) prior, which is particularly suited for analyzing high-dimensional brain structural connectivity network data that serve as mediators. Our method is capable of addressing the structural dependencies of brain connectivity networks including sparsity, effective degrees of nodes, and modularity, yielding accurate estimates of the high-dimensional coefficients and mediation effects. We demonstrate the effectiveness and superiority of the proposed NMSS method through simulation studies and apply it to the TOTXVI data, revealing significant mediation effects of brain connectivity on visual processing speed directed by IT intensity. The findings shed light on the potential of targeted interventions to mitigate neurocognitive deficits in pediatric ALL survivors.

Bridging studies serve as an efficient approach to evaluate the applicability of findings from an original study to a new population. We propose a Bayesian adaptive design for bridging studies with time-to-event endpoints, aiming to assess the consistency of treatment effects with those observed in the original study. The design adopts a group sequential framework, using posterior probabilities at interim and final analyses to evaluate the evidence for consistency between the bridging and original studies. If strong evidence of consistency or inconsistency is observed, the trial may be stopped early to conserve sample size. Additionally, a sample size recalculation strategy based on Bayesian predictive probability is incorporated to enhance flexibility. Simulation studies demonstrate that, compared to a commonly used method, the proposed design offers favorable operating characteristics. It maintains control of the empirical type I error rate through prespecified calibration, accounting for interim analyses (IAs) and sample size adaptation, and yields substantial sample size savings when the treatment effect in the bridging study is either highly consistent or clearly inconsistent with that of the original study.

There is growing interest in a hybrid control design for treatment evaluation, where a randomized controlled trial is augmented with external control data from a previous trial or a real-world data source. The hybrid control design has the potential to improve efficiency but also carries the risk of introducing bias. The potential bias in a hybrid control study can be mitigated by adjusting for baseline covariates that are related to the control outcome. Existing methods that serve this purpose commonly assume that the internal and external control outcomes are exchangeable upon conditioning on a set of measured covariates. Possible violations of the exchangeability assumption can be addressed using a g-computation method with variable selection under a correctly specified outcome regression model. In this article, we point out that a particular version of this g-computation method is protected against misspecification of the outcome regression model. This observation leads to a model-robust g-computation method that is remarkably simple and easy to implement, consistent and asymptotically normal under minimal assumptions, and able to improve efficiency by exploiting similarities between the internal and external control groups. The method is evaluated in a simulation study and illustrated using real data from HIV treatment trials.

Missing data can pose fundamental challenges to statistical inference, with nonignorable missing or missing not at random (MNAR) presenting the most severe methodological difficulties. Despite substantial advances in MNAR inference methods, several limitations remain. These generally include interpretability issues, non-identifiability, unverifiable parametric assumptions, and reliance on external information for which clear practical guidance is often lacking-particularly in sensitivity and Bayesian methods. In this paper, motivated by a real-world COVID-19 dataset from the Centers for Disease Control and Prevention (CDC), we study an MNAR scenario in the presence of a shadow variable that may itself also be subject to MNAR. A shadow variable is associated with the primary variable that is MNAR, but is conditionally independent of that variable's missingness given the primary variable and other covariates. Under the pattern mixture model framework, we propose a nonparametric inference method that can leverage external data to explicitly address the identification and estimation problems in the primary data. The method requires inference only of an observed data density and an odds of missing function, with the latter forming the core of our approach. We further provide two multiple-imputation-based estimation strategies, enhancing transparency and interpretability. The proposed framework can accommodate both covariate MNAR and outcome MNAR settings, as well as different variable types, and extends the existing shadow variable paradigm for MNAR data by relaxing the common assumption that the shadow variable must be fully observed. We evaluate the proposed method through simulation studies and apply it to CDC COVID-19 surveillance data.

Externally controlled single-arm trials are increasingly popular because they do not require randomized controls, thereby substantially reducing financial costs; however, valid causal inference in this setting relies critically on transportability between the trial and external populations, an assumption that is untestable. Frequentist semiparametrically efficient estimators, such as the doubly robust estimator, are typically analyzed under first-order asymptotics and are designed to mitigate nuisance-estimation bias under correct specification; however, this framework does not account for structural bias arising under local transportability violations, where bias and stochastic fluctuation occur at the same parametric rate. We propose a reliable Bayesian framework for estimating the average treatment effect on the treated (ATT) that combines synthetic outcome construction with residualized power-prior borrowing. Flexible machine learning is first used to construct covariate-aligned synthetic controls, after which Bayesian inference on residualized outcomes allows external borrowing to modulate uncertainty without distorting covariate-driven heterogeneity. The posterior admits a heavy-tailed distribution-unlike classical Wald procedures-and the resulting estimator lies outside the class of regular asymptotically linear estimators, thereby revealing behavior beyond first-order semiparametric asymptotics. We establish a reliability-efficiency trade-off under local transportability violations. Simulations and a case study on schizophrenia trial design demonstrate the theoretical findings and practical utility.

Modeling of longitudinal cohort data typically involves complex temporal dependencies between multiple variables. There, the transformer architecture, which has been highly successful in language and vision applications, allows us to account for the fact that the most recently observed time points in an individual's history may not always be the most important for the immediate future. This is achieved by assigning attention weights to observations of an individual based on a transformation of their values. One reason why these ideas have not yet been fully leveraged for longitudinal cohort data is that typically, large datasets are required. Therefore, we present a simplified transformer architecture that retains the core attention mechanism while reducing the number of parameters to be estimated, to be more suitable for small datasets with few time points. Guided by a statistical perspective on transformers, we use an autoregressive model as a starting point and incorporate attention as a kernel-based operation with temporal decay, where aggregation of multiple transformer heads, that is, different candidate weighting schemes, is expressed as accumulating evidence on different types of underlying characteristics of individuals. This also enables a permutation-based statistical testing procedure for identifying contextual patterns. In simulation studies, including a controlled simulation on real clinical predictor data, the approach is shown to recover contextual dependencies even with a small number of individuals and time points. In an application to data from a resilience study, we identify temporal patterns in the dynamics of stress and mental health. This indicates that properly adapted transformers can not only achieve competitive predictive performance, but also uncover complex context dependencies in small data settings.

The US Food and Drug Administration's Project Optimus has initiated a paradigm shift in oncology drug development from "more is better" to "less is more." Methodological development for combination therapy trials remains limited due to their complex dose-combination space and the need to integrate multi-source data, including toxicity, clinical efficacy, and biological antitumor outcomes such as pharmacodynamic (PD) activity. We propose PROComb, a practical and robust design with randomization to optimize dose combinations, to address these challenges with minimal assumptions and to facilitate practical implementation. In the first stage, the complex dose-combination space is efficiently explored through the integration of multi-source data and the inherent relationships among different dose-outcomes. Patients are adaptively assigned to dose combinations to establish a therapeutic dose space (TDS), defined as the set of doses with acceptable toxicity and promising efficacy. A recommended Stage II dose set (RS2D) is constructed at the end of Stage I. In the second stage, patients are randomized to RS2D combinations for further monitoring, screening and identification of the optimal biologic dose combination (OBDC). Three PROComb versions are developed to mitigate potential between-stage drift. Simulation studies demonstrate that PROComb achieves favorable operating characteristics compared with conventional model-based and model-assisted designs.

A new Bayesian distribution-free medical survivor analysis is presented that strictly avoids using right-tail censored data. The Bayesian procedure is focused on two population parameters called ϕ f c and Ω E , which are separate metrics of a treatment difference between the two conditions. The ϕ f c parameter is the proportion of failures that are from the Control condition, and the Ω E parameter is a stochastic difference measure associated with longer survival time before a failure for the patients in the Experimental condition. Point and interval estimates along with a Bayes factor are provided for both parameters. Software is provided for implementing the Bayesian analysis. Monte Carlo simulations are also developed to study the interplay between the stop-testing time used in survival analysis with other variables such as effect size and sample size. The simulations also provide information that enable an approach to survival analysis where there is an early decision about the relative effectiveness of the treatments that is based on the Bayes factor value associated with the ϕ f c statistic. This decision can be made when there is a high proportion of right-tail censored data. In the limit of times so long that there are all failures-thus no right-tail censoring-the ϕ f c metric is not informative, but the Ω E metric is still a valid measure of the stochastic difference in failure times between the two conditions.

Multivariate endpoints are increasingly used in clinical studies on rare diseases, where sample sizes tend to be small and distributional assumptions are often violated. In such settings, commonly applied parametric multivariate methods, such as classical MANOVA approaches, may suffer from inflated type-I error or reduced statistical power. Therefore, a neutral simulation-based comparison of four methodologically different approaches for the analysis of multivariate outcomes in parallel group designs was conducted. The four approaches included the nonparametric R package npmv (using permutation and randomization resampling for small samples), a semiparametric MANOVA approach from the R package MANOVA.RM with both a Wald-type statistics (WTS) and a modified ANOVA-type statistics (MATS) using all available variants including also bootstrap approaches, a classical parametric MANOVA, and multiple univariate Mann-Whitney tests with Holm correction. The simulation framework was informed by empirical distributions derived from anonymized clinical data and clinical expert guidance. Two clinically realistic effect types were mainly evaluated: (i) percent-responder effects for wound size reduction and (ii) additional location shifts in pain and pruritus visual analog scales (VAS) scores. In addition, scenarios are examined in which classical assumptions such as multivariate normality and homogeneity of covariance matrices are violated. The sample sizes considered ranged from 12 to 360 subjects. Both balanced and unbalanced designs were evaluated, with the objective of illustrating potential limitations of methods when applied to small samples. Outcomes were assessed in terms of type-I error control and statistical power. Overall, npmv, the MATS using especially parametric bootstrap within the semiparametric MANOVA.RM package maintained reliable type-I error control, whereas the semiparametric MANOVA.RM approach with the WTS using its asymptotic approximation showed very liberal type-I error behavior to almost no type-I error control in small sample scenarios, and especially in unbalanced settings. Bootstrap approaches especially of the WTS substantially improved type-I error control compared with the asymptotic WTS. The nonparametric npmv approach achieved good power values, especially in small samples, as did the modified ATS approach using parametric bootstrap from the MANOVA.RM package, which achieved very similar results. The univariate Mann-Whitney U test with Holm correction tended to yield conservative results for small samples; however, despite the univariate nature of this approach, it achieved a high and comparable level of statistical power in many scenarios. Classical MANOVA also yielded good results in certain scenarios; however, it exhibited rather liberal type-I error rates, primarily in heteroscedastic scenarios and unbalanced designs, which can be explained by a violation of the assumption of homoscedastic covariance matrices. These results highlight the strengths and limitations of a multi-aspect analysis in parallel group designs especially for small sample settings, as common in rare diseases, and provide guidance for the analysis in rare disease research.

We develop a Bayesian Additive Regression Trees with Measurement Error (BART-ME) model for flexibly estimating exposure-response functions when multiple covariates are measured with classical error. Unlike existing approaches, BART-ME accommodates nonlinearities, interactions, correlated exposures, and correlated measurement errors, while exploiting replicate measurements to estimate the error variance-covariance structure. Posterior inference is obtained via a Metropolis-within-Gibbs algorithm, yielding estimates of exposure-response functions, variable importance, and measurement reliability. Simulation studies demonstrate that BART-ME reduces bias and improves coverage compared with Naïve BART analyses that ignore measurement error, even with sparse replication. In an application to first-trimester ultrasound data from the NICHD Fetal Growth Studies, BART-ME identified crown-rump length as the most reliable predictor of gestational age at delivery and revealed nonlinear patterns attenuated by Naïve methods. These results illustrate the potential of BART-ME as a general framework for correcting measurement error in complex exposure settings.

Generalized pairwise comparisons are increasingly being used in randomized clinical trials. This study evaluates how missing data strategies impact the operating characteristics of endpoints combining overall survival and a longitudinal outcome. A simulation study was conducted to evaluate the impact of censoring and missing longitudinal data on the Type I error, power, and bias of a hierarchical composite endpoint. Seven missing data strategies were identified from the literature, including assigning ties to missing patient pairs, comparing patients at their last common visit, and applying multiple imputation. Conditional longitudinal and survival data were generated based on the natural history of amyotrophic lateral sclerosis. Simulation scenarios varied in censoring rates, extent of missing longitudinal data, differential attrition between treatment arms, and the dependency of missingness on disease severity. All methods were unbiased and maintained nominal Type I error when censoring and missingness were balanced across treatment arms. Under imbalance, however, Type I error increased-reaching up to 0.378 for some strategies. The last common visit strategy was the only approach that consistently preserved nominal error rates (0.025 ± 0.002). Regarding statistical power, all methods exhibited a loss of precision and increased bias under the alternative hypothesis as missingness increased. Multiple imputation partially recovered power and reduced bias but inflated the Type I error rate in scenarios with differential attrition. As generalized pairwise comparisons are increasingly used in pivotal clinical trials-and therefore in regulatory contexts-our findings provide practical guidance for selecting a robust primary analysis strategy and minimizing bias arising from incomplete data.

Mediation analysis is a powerful tool for elucidating the causal mechanisms by which exposures influence outcomes through mediators. However, conventional approaches often yield biased estimates of mediation effects in scenarios involving high-dimensional exposures and high-dimensional mediators, alongside a small number of pervasive hidden confounders that simultaneously affect the exposures, mediators, and outcome or the exposures and outcome. To address these challenges, we propose a deconfounded-debiased method for estimation and inference in high-dimensional mediation analysis based on the difference-in-coefficients strategy. This approach effectively corrects biases arising from both pervasive hidden confounders and high-dimensionality without requiring prior knowledge of hidden confounders or a sparse precision matrix assumption. We establish the asymptotic normality of the proposed estimators for both direct and indirect effects, and develop hypothesis testing procedures that asymptotically achieve validity and power lower bounds. Simulation experiments demonstrate our method's superior finite-sample performance in both estimation and inference, especially in the presence of pervasive hidden confounding. We also apply the proposed method to real data from the Alzheimer's Disease Neuroimaging Initiative to identify serum metabolites that influence Alzheimer's disease progression through DNA methylation pathways.

It is common practice in randomized clinical trials with the standard survival outcome to follow patients until a prespecified number of events have been observed, a type of trial known as the event-driven trial. The event-driven design ensures that the target power for a specified Type I error rate is achieved to detect the target hazard ratio, regardless of the specification of other quantities. To understand the treatment effect for chronic conditions, the analysis of recurrent events has gained popularity in randomized controlled trials, particularly large-scale confirmatory trials. In the absence of within-subject correlation among multiple events, a similar event-driven design can be employed for recurrent event outcomes. On the other hand, in the presence of within-subject correlation, one needs to model the correlation among recurrent events in evaluating power and setting the sample size. However, information useful in modeling the within-subject correlation is limited at the design stage. Failing to properly account for correlation may lead to underpowered studies. We propose an event-driven type design for recurrent event outcomes. Our method ensures the target power for the target treatment effect, regardless of the specification of other quantities, by monitoring the robust variance under the marginal rates/means model in a blinded manner. We investigate the operating characteristics of the proposed monitoring procedure in simulation studies. The results of simulation studies showed that the proposed blinded monitoring procedure controlled the power well so that the test possessed the target power and did not lead to serious inflation of the Type I error rate. Furthermore, we illustrate the proposed method using a real clinical trial dataset.