Interval estimation of a proportion estimated from testing of pooled samples has been studied by a variety of researchers, who have examined both exact and asymptotic methods. Recent work in point estimation has seen the use of Firth's correction to maximum likelihood estimation to reduce bias effectively. We consider the Firth-corrected score statistic, using either expected or observed information, as the first derivative function of a penalized likelihood and develop score-based confidence intervals wholly within this framework. We evaluate their performance, comparing them by information type and to the existing, recommended asymptotic method of Gart. The methods are illustrated using data on West Nile virus infection in field-collected mosquitoes and on yellow fever virus infection in mosquitoes reported in Walter et al. The penalized likelihood approach using expected information is found to unify previously recommended point and interval estimates under one inferential framework. Detailed evaluation of coverage properties of the intervals over a range of pooling designs show improved performance for the intervals using observed information and skewness-correction to the score. We derive simple, interpretable expressions for the score and skewness-corrected score statistics, and give a quadratic formula for the skewness-corrected score interval for the case that all pools are the same size, which reduces to a skewness-correction for the standard Wilson interval in the standard binomial case.

We consider the optimal design problem for identifying effective dose combinations within drug combination studies where the effect of the combination of two drugs is investigated. Drug combination studies are becoming increasingly important as they investigate potential interaction effects rather than the individual impacts of the drugs. In this situation, identifying effective dose combinations that yield a prespecified effect is of special interest. If nonlinear surface models are used to describe the dose combination-response relationship, these effective dose combinations, also called isoboles, result in specific contour lines of the fitted response model. Consequently, accurately estimating these effective dose combinations is crucial. We propose a novel design criterion that targets the precise estimation of these effective dose combinations. In particular, an optimal design minimizes the width of the confidence band of the contour lines of interest. Optimal design theory is developed for this problem, including equivalence theorems and efficiency bounds. The performance of the optimal design is illustrated in different examples modeling dose combination data by various nonlinear surface models. It is demonstrated that the proposed optimal design for identifying effective dose combinations yields a more precise estimation of the effective dose combinations than ray or factorial designs, which are commonly used in practice. This particularly holds true for a case study motivated by data from an oncological dose combination study.

The Cox proportional hazards model is often used to analyze data from randomized controlled trials (RCTs) with time-to-event outcomes. Random survival forest (RSF) is a machine-learning algorithm known for its high predictive performance. We conduct a comprehensive neutral comparison study to compare the performance of Cox regression and RSF in various simulation scenarios based on two reference datasets from RCTs. The motivation is to identify settings in which one method is preferable over the other when comparing different aspects of performance using measures according to the TRIPOD (Transparent Reporting of a multivariable prediction model for Individual Prognosis or Diagnosis) recommendations. Our results show that conclusions solely based on the C index, a performance measure that has been predominantly used in previous studies comparing predictive accuracy of the Cox-PH and RSF model based on real-world observational time-to-event data and that has been criticized by methodologists, may not be generalizable to other aspects of predictive performance. We found that measures of overall performance may generally give more reasonable results, and that the standard log-rank splitting rule used for the RSF may be outperformed by alternative splitting rules, in particular in nonproportional hazards settings. In our simulations, the performance of the RSF suffers less in data with treatment-covariate interactions compared to data where these are absent. The performance of the Cox-PH model is affected by the violation of the proportional hazards assumption.

In oncology, clinical trials are a cornerstone of evaluating new treatments. However, traditional designs face significant challenges, particularly when assessing multiple treatment options. The emergence of multi-arm multi-stage (MAMS) designs, such as the drop-the-losers (DtL) approach, offers innovative solutions by combining multiple hypotheses within a single trial. This work evaluates the DtL approach. We extend the design to binary and survival endpoints. The statistical performance (Type I error control, statistical power, and biases) of the DtL design was assessed using a simulation study. Results demonstrated that the DtL design effectively balances statistical rigor and efficiency. The design strongly controls Type I error while ensuring high power in detecting drug effects. Scenarios with ineffective treatments highlighted the advantage of eliminating suboptimal options early. One limitation identified is that long-term survival endpoints may not be mature enough to support early treatment selection. Early decision-making is a key aspect of adaptive designs to support futility analysis or early efficacy analysis. It is critical to define properly the decision thresholds for such early analyses. Updating the endpoint of interest over time also aligns with clinical practices, starting with ORR, transitioning to benefit-risk scores or progression-free survival (PFS), and concluding with overall survival (OS) at the final analysis. Such an approach requires handling of correlations between drug effects across these endpoints. This work provides a comprehensive framework for implementing DtL design, demonstrating its potential to accelerate treatment evaluation in oncology.

Row-column designs play an important role in applications where two orthogonal sources of error need to be controlled for by blocking. Field or greenhouse experiments, in which experimental units are arranged as a rectangular array of experimental units, are a prominent example. In plant breeding, the amount of seed available for the treatments to be tested may be so limited that only one experimental unit per treatment can be accommodated. In such settings, augmented designs become an interesting option, where a small set of treatments, for which sufficient seed is available, is replicated across the rectangular layout so that row and column effects, as well as the error variance, can be estimated. Here, we consider the use of an auxiliary design, also known as a contraction, to generate an augmented row-column design. We make use of the fact that the efficiency factors of the contraction and the associated augmented design are closely interlinked. A major advantage of this approach is that an efficient contraction can be found by computer search at much higher computational speed than is required for direct search for an efficient augmented design. Two examples are used to illustrate the proposed method. Furthermore, we contrast the usage of our approach when the array dimensions are fixed, as is the case with microplates, to settings with more flexibility regarding the number of rows and columns of the layout, as in greenhouse and field trials.

Evaluating the change in gene expression is a common goal in many research areas, such as in toxicological studies, which are particularly important in pre-clinical research. In practice, the analysis is often based on multiple t-tests evaluated at the observed time points of the experiment, which limits the accuracy of determining the precise time at which the gene changes in expression. If a parametric approach is chosen, the analysis is often restricted to identifying the onset of an effect, but not its length. In this paper, we propose a parametric method to identify the time frame during which the gene expression significantly changes. This is achieved by fitting a parametric model and constructing a confidence band for its first derivative. The confidence band is derived by a two-step bootstrap approach. It is summarized in terms of a hypothesis test, such that rejecting the null hypothesis means detecting a significant change in gene expression. Furthermore, a method for calculating confidence intervals for time points of interest (e.g., the beginning of significant change) is developed. We demonstrate the validity of our approach through a simulation study and present a variety of different applications to mouse gene expression data from a study investigating the effect of a Western diet on the progression of non-alcoholic fatty liver disease.

Modern biomedical studies increasingly collect hybrid data, consisting of functional observations (e.g., curves or images) and multiple scalar (vector-valued) clinical variables. Integrating these modalities in an unsupervised learning framework can improve patient subgroup identification and interpretation, yet most existing clustering approaches handle only a single data type. We introduce a clustering framework for hybrid data combining multivariate functional and vector outcomes. The method first applies hybrid principal component analysis to capture joint mean structures and modes of variation across modalities, then iteratively reassigns subjects using a hybrid distance metric based on cluster-specific Karhunen-Loéve expansions. This approach accommodates multiple functions of varying dimensions, integrates contributions from functional and vector components in mean and covariance structures, and avoids parametric distributional assumptions. Simulation studies show that the proposed method outperforms competing approaches when subgroup information, in terms of mean and/or variance differences, is either distributed across modalities or concentrated in a single modality. We illustrate the method using renal radionuclide imaging data, including baseline and diuretic renogram curves and pharmacokinetic variables from patients with suspected kidney obstruction. The method identifies clinically meaningful subgroups consistent with expert assessment, demonstrating its potential to support data-driven decision-making in multimodal biomedical studies.

A central focus in survival analysis is examining how covariates affect survival time. These covariate effects are often found to be either time-varying, heterogeneous-such as being specific to patients, treatments, or subgroups-or exhibit both characteristics simultaneously. While the standard model, the Cox proportional hazards model, allows neither time-varying nor heterogeneous effects, several extensions to the Cox model as well as alternative modeling frameworks have been introduced. However, no unified framework for incorporating heterogeneously time-varying effects of covariates has been proposed. Such effects occur when a covariate affects survival not only in a heterogeneous and time-varying manner, but when the time-variation is also heterogeneous. We propose to model such effects by introducing heterogeneously time-varying coefficients to piecewise exponential additive mixed models. We deploy functional random effects, also known as factor smooths, to model such coefficients as the interaction effect of heterogeneity and time-variation. Our approach allows for non-linear time-effects due to being based on penalized splines and uses an efficient random effects basis to model the heterogeneity. Using a penalized basis prevents overfitting in case of absence of such effects. In addition, the penalization mostly solves the problem of choosing the number of intervals which is usually present in unregularized piecewise exponential approaches. We demonstrate the superiority of our approach in comparison to competitors by means of a simulation study. Finally, the practical application and relevance are outlined by presenting a brain tumor case study.

In stepped-wedge clinical trials the patients are randomized into separate groups. Each group transitions from no treatment to treatment at a different time period. The designs are useful when limited resources or geographical constraints make it impossible to treat all patients at the same time. In applications of the design to individuals, it is typical that there is a single treatment and that equal numbers of patients are randomized to each sequence. Results from the methods of optimal experimental design indicate that this equal allocation is not optimal. Building on an information-theoretic framework for this problem, we optimize participant allocation to maximize the trial's information yield. We formulate the problem as a semidefinite programming optimization and extend it to incorporate: (i) differential attrition rates between treatment and control groups, (ii) budget constraints where treatment costs increase over time, (iii) fairness constraints, and (iv) multiple treatments with different switching policies. While the first three challenges are addressed by introducing additional constraints, the systematic treatment of the last represents a novel contribution.

Researchers in biomedical research often analyze data that are subject to clustering. Development and validation of risk prediction models generally assumes independence of observations. For survival outcomes, the Cox proportional hazards (PH) regression model is commonly used to estimate an individual's risk at fixed time horizons. The stratified Cox PH and the shared gamma frailty Cox PH regression models are two common approaches to account for the presence of clustering in the data. The relative accuracy of the predictions of these two approaches has not been examined. We conducted a set of Monte Carlo simulations to assess the impact of the number of clusters, the size of the clusters, and the within-cluster correlation in outcomes on the accuracy of the conditional predictions developed using the stratified and the shared gamma frailty Cox PH regression model. We compared the accuracy of the predictions in terms of discrimination, calibration, and overall performance metrics. We found that the stratified and the shared gamma frailty model had similar performance, especially for larger cluster size and higher number of clusters. For small cluster size, we observed slightly better discrimination and overall performance for the stratified model and better calibration for the shared gamma frailty model at shorter prediction horizons. The utility of the stratified Cox PH model for risk prediction is limited, especially for high within-cluster correlation and when clusters are small, and at longer prediction horizons. Our results were accompanied with two applications using open-source data on myelodysplastic syndrome and bladder cancer.

In observational studies, propensity score estimation is crucial for estimating the average treatment effect (ATE). However, covariate imbalance can introduce estimation bias, and including unnecessary covariates can also negatively affect the bias and statistical efficiency of propensity score estimation. To address this issue, this paper proposes an OALIPS estimation method for covariate balancing with causal variable selection. Through a two-step framework of screening followed by estimation, the method first precisely identifies core covariates using a comprehensive propensity score objective function with an outcome-adaptive penalty term. Subsequently, propensity score estimation is performed in a reduced-dimensional space based on a covariate balancing approach, effectively avoiding the shrinkage bias problem in traditional regularized estimation. We prove the consistency of the method's variable selection, the asymptotic normality of the parameter estimates, and the consistency of the ATE estimator based on these estimates. Simulation studies show that the proposed method outperforms conventional methods, accurately identifies confounders and predictors, and remains robust under conditions of covariate imbalance and model misspecification. Subsequently, we applied this method to right heart catheterization (RHC) data, verifying its applicability in handling complex clinical data. The results indicate that, after effectively correcting for severe baseline bias, RHC significantly increases the length of hospital stay for surviving patients.

Clinical trials using a hybrid control, which integrates a randomized control with external control data, may be one solution to facilitate clinical development where traditional randomized controlled trials are challenging. Despite its attractive features, systematic differences between controls can introduce bias in treatment effect estimation and inflate Type I error. Although propensity score methods may be used to address systematic differences from measured covariate imbalance, potential differences from unmeasured or unknown factors may still arise despite careful consideration. In such cases, dynamic borrowing methods have been proposed to account for potential differences between randomized and external control data and discount the contribution of external control data when needed. Conventional methods, however, often rely on Bayesian approaches, requiring proper specification of the likelihood. This is particularly challenging for survival analysis using proportional hazards model due to specification of the baseline hazard function. To address these challenges, we propose to utilize the weighted partial likelihood score equation where external control patients are weighted by the inverse probability of the propensity score and an additional discounting weight, adjusting the contribution of external control data according to its similarity to randomized control data. A new variance estimator based on stacked estimating equations is proposed to incorporate the uncertainty in estimating discounting weights. Operating characteristics of the proposed method are studied via extensive simulation. The proposed method yields reduced bias in treatment effect estimation and Type I error while improving statistical power in either scenarios where measured or unmeasured confounders exist.

Accurately estimating the parameters of a continuous distribution from dichotomized or aggregated data is a common problem in biomedical and environmental research. Many studies report only the proportion of subjects exceeding a threshold, without releasing individual-level measurements. To address this limitation, we develop a hierarchical binomial-probit modeling framework to reconstruct the parameters of an underlying normal distribution from threshold-based data. The framework considers two principal settings. In the fixed-mean model, all studies are assumed to share a common mean and variance, and the parameters μ and σ are estimated using a maximum-likelihood estimator (MLE) and a generalized linear model (GLM) approximation. In the random-mean model, each study has its own mean μ i drawn from a population distribution N (μ 0 , τ 2) with a common within-study variance σ 2 ; parameters μ 0 , σ , and τ are estimated using MLE, a generalized linear mixed model (GLMM) approximation, and a fully Bayesian Markov chain Monte Carlo (MCMC) method. Extensive simulations varying the number of studies, sample size, and heterogeneity ratio r = τ 2 / (σ 2 + τ 2) evaluate estimator bias, variance, mean squared error, and coverage probability. Results show that MLE performs efficiently under well-identified conditions, whereas GLMM and Bayesian estimators are more robust with small samples or strong heterogeneity. The proposed framework provides a unified and practical approach for inferring latent distributions from aggregated or privacy-restricted data, with applications in clinical trial design, biomarker analysis, environmental monitoring, and quality control.

Recently, clustered bivariate survival data have been extensively studied using different modeling approaches, such as frailty models and copula models. These data can take several forms, including bivariate censored data, semicompeting risks data, and competing risks data. Traditionally, each type has been analyzed using a separate model. In this paper, we propose a unified joint frailty modeling approach that is capable of handling the three different types of clustered bivariate survival data within a single model-based likelihood framework. Here, the unknown baseline hazards in the joint frailty models are modeled based on a cubic M-spline basis function that does not require a specific parametric form. Inference for the model parameters is performed via the hierarchical likelihood (h-likelihood) method, which avoids the intractable integration over frailty required in marginal likelihood approaches and effectively captures heterogeneity across clusters. The performance of the proposed approach is evaluated through simulation studies, which demonstrate that the estimated regression coefficients appear reasonable for the three types of clustered bivariate survival data. The proposed method is further illustrated using three real-world data sets.