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Randomized controlled trials commonly employ multiple endpoints to collectively assess the intended effects of the new intervention on multiple aspects of the disease. Focusing on the estimation of the global win probability (WinP), defined as the (weighted) mean of the WinPs across the endpoints that a treated participant would have a better outcome than a control participant, we propose a closed-form sample size formula incorporating pre-specified precision and assurance, with precision denoted by the lower limit of confidence interval and assurance denoted by the probability of achieving that lower limit. We make use of the equivalence of the WinP and the area under the receiver operating characteristic curve (AUC) and adapt a formula originally developed for the difference between two AUCs to handle the global WinP. Unequal variances between treatment groups are allowed. Simulation results suggest that the method performs very well. We illustrate the proposed formula using a Parkinson's disease clinical trial design example.

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BACKGROUND: The conduct of rare disease clinical trials is still hampered by methodological problems. The number of patients suffering from a rare condition is variable, but may be very small and unfortunately statistical problems for small and finite populations have received less consideration. This paper describes the outline of the iSTORE project, its ambitions, and its methodological approaches. METHODS: In very small populations, methodological challenges exacerbate. iSTORE's ambition is to develop a comprehensive perspective on natural history course modelling through multiple endpoint methodologies, subgroup similarity identification, and improving level of evidence. RESULTS: The methodological approaches cover methods for sound scientific modeling of natural history course data, showing similarity between subgroups, defining, and analyzing multiple endpoints and quantifying the level of evidence in multiple endpoint trials that are often hampered by bias. CONCLUSION: Through its expected results, iSTORE will contribute to the rare diseases research field by providing an approach to better inform about and thus being able to plan a clinical trial. The methodological derivations can be synchronized and transferability will be outlined.

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In contemporary exploratory phase of oncology drug development, there has been an increasing interest in evaluating investigational drug or drug combination in multiple tumor indications in a single basket trial to expedite drug development. There has been extensive research on more efficiently borrowing information across tumor indications in early phase drug development including Bayesian hierarchical modeling and the pruning-and-pooling methods. Despite the fact that the Go/No-Go decision for subsequent Phase 2 or Phase 3 trial initiation is almost always a multi-facet consideration, the statistical literature of basket trial design and analysis has largely been limited to a single binary endpoint. In this paper we explore the application of considering clinical priorities of multiple endpoints based on matched win ratio to the basket trial design and analysis. The control arm data will be simulated for each tumor indication based on the corresponding null assumptions that could be heterogeneous across tumor indications. The matched win ratio matching on the tumor indication can be performed for individual tumor indication, pooled data, or the pooled data after pruning depending on whether an individual evaluation or a simple pooling or a pruning-and-pooling method is used. We conduct the simulation studies to evaluate the performance of proposed win ratio-based framework and the results suggest the proposed framework could provide desirable operating characteristics.

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We discuss three issues. In the first part, we discuss the criteria emphasized by Maurer, Bretz, and Xun, warning that it modifies the per comparison error rate that does not address the concerns raised by multiple testing. In the second part, we strengthen the optimality results developed in the paper, based on our recent results. In the third part, we highlight the potentially important role that the use of weights may have in practice and discuss the difficulties in assigning weights that convey the importance in the gain and loss functions, especially as it pertains to multiple endpoints.

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This paper builds on the recently proposed prediction test for muliple endpoints. The prediction test combines information across multiple endpoints while accounting for the correlation between them. The test performs well with small samples relative to the number of endpoints of interest and is flexible in the hypotheses across the individual endpoints that can be combined. The prediction test addresses a global hypothesis that is of particular interest in early-stage studies and can be used as justification for continuing on to a larger trial. However, the prediction test has several limitations which we seek to address. First, the prediction test is overly conservative when both the effect sizes across all endpoints and the number of endpoints are small. By using a parametric bootstrap to estimate the null distribution, we show that the test achieves the nominal error rate in this situation and increases the power of the test. Second, we provide a framework to allow for predictions of a difference on one or more endpoints. Finally, we extend the test with a composite null hypothesis that allows for different null hypothesized predictive abilities across the endpoints which can be especially useful if the study contains both familiar and novel endpoints. We use an example from a physical activity trial to illustrate these extensions.

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We propose a method to construct simultaneous confidence intervals for a parameter vector from inverting a series of randomization tests (RT). The randomization tests are facilitated by an efficient multivariate Robbins-Monro procedure that takes the correlation information of all components into account. The estimation method does not require any distributional assumption of the population other than the existence of the second moments. The resulting simultaneous confidence intervals are not necessarily symmetric about the point estimate of the parameter vector but possess the property of equal tails in all dimensions. In particular, we present the constructing the mean vector of one population and the difference between two mean vectors of two populations. Extensive simulation is conducted to show numerical comparison with four methods. We illustrate the application of the proposed method to test bioequivalence with multiple endpoints on some real data.

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Competing risks data are commonly encountered in randomized clinical trials or observational studies. Ignoring competing risks in survival analysis leads to biased risk estimates and improper conclusions. Often, one of the competing events is of primary interest and the rest competing events are handled as nuisances. These approaches can be inadequate when multiple competing events have important clinical interpretations and thus of equal interest. For example, in COVID-19 in-patient treatment trials, the outcomes of COVID-19 related hospitalization are either death or discharge from hospital, which have completely different clinical implications and are of equal interest, especially during the pandemic. In this paper we develop nonparametric estimation and simultaneous inferential methods for multiple cumulative incidence functions (CIFs) and corresponding restricted mean times. Based on Monte Carlo simulations and a data analysis of COVID-19 in-patient treatment clinical trial, we demonstrate that the proposed method provides global insights of the treatment effects across multiple endpoints.

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Joint models for recurrent event and terminating event data are increasingly used for the analysis of clinical trials. However, few methods have been proposed for designing clinical trials using these models. In this article, we develop a Bayesian clinical trial design methodology focused on evaluating the effect of an investigational product (IP) on both recurrent event and terminating event processes considered as multiple primary endpoints, using a multifrailty joint model. Dependence between the recurrent and terminating event processes is accounted for using a shared frailty. Inferences for the multiple primary outcomes are based on posterior model probabilities corresponding to mutually exclusive hypotheses regarding the benefit of IP with respect to the recurrent and terminating event processes. We propose an approach for sample size determination to ensure the trial design has a high power and a well-controlled type I error rate, with both operating characteristics defined from a Bayesian perspective. We also consider a generalization of the proposed parametric model that uses a nonparametric mixture of Dirichlet processes to model the frailty distributions and compare its performance to the proposed approach. We demonstrate the methodology by designing a colorectal cancer clinical trial with a goal of demonstrating that the IP causes a favorable effect on at least one of the two outcomes but no harm on either.

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A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal procedures become more complex. In this paper, we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the procedures. This leads us to an explicit optimization problem with objective and constraints that describe its specific desiderata. We present a complete solution for deriving optimal procedures for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal procedures that are identical to existing procedures, such as Hommel's procedure or the procedure of Bittman et al. (2009), while for other cases it yields completely novel and more powerful procedures than existing ones. We demonstrate the nature of our novel procedures and their improved power extensively in a simulation and on the APEX study (Cohen et al., 2016).

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BACKGROUND: In randomized controlled trials, multiple time-to-event endpoints are commonly used to determine treatment effects. However, choosing an appropriate method to address multiple endpoints, according to different purposes of clinical practice, is a challenge for researchers. METHODS: We applied single endpoint, composite endpoint and win ratio analysis to chronic myeloid leukemia (CML) data to illustrate the distinctions with different multiple endpoints, including relapse, recovery and death after transplantation. RESULTS: Regarding relapse and death, the hazard ratio in single endpoint analysis (HRs ) were 1.281 (95% CI: 1.061-1.546) and hazard ratio in composite endpoint analysis (HRc ) were 1.286 (95% CI: 1.112-1.486) and 1/WR (win ratio) was 1.292 (95% CI: 1.115-1.497) indicated a similar negative effect for non-prophylaxis patients. However, when considering recovery and death, the corresponding HRs = 1.280 (95% CI: 1.056-1.552) may not be enough to describe the effect on death with nonproportional hazards (p < 0.05), and for the composite endpoint analysis, the HRc = 0.828 (95% CI: 0.740-0.926) cannot quantify and interpret the clinical effect on the composite endpoint with the combination of recovery and death, while the 1/WR = 1.351 (95% CI: 1.207-1.513) showed an unfavourable effect for non-prophylaxis patients CONCLUSIONS: When dealing with multiple endpoints, single endpoints, researchers may choose single endpoints, composite endpoints and WR analysis due to different clinical applications and purposes. However, both single and composite endpoint analyses are hazard-based measures, and thus, the proportional hazards assumption should be considered. Moreover, composite endpoint analysis should be applied for endpoints with similar clinical meanings but not opposing implications. Win ratio analysis can be considered for different clinical importance of multiple endpoints, but the meaning of 'winner' needs to be specified for desired or undesired endpoints.

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Tumor mutation burden (TMB) is a recognized stratification biomarker for immunotherapy. Nevertheless, the general TMB-high threshold is unstandardized due to severe clinical controversies, with the underlying cause being inconsistency between multiple assessment criteria and imprecision of the TMB value. The existing methods for determining TMB thresholds all consider only a single dimension of clinical benefit and ignore the interference of the TMB error. Our research aims to determine the TMB threshold optimally based on multifaceted clinical efficacies accounting for measurement errors. We report a multi-endpoint joint model as a generalized method for inferring the TMB thresholds, facilitating consistent statistical inference using an iterative numerical estimation procedure considering mis-specified covariates. The model optimizes the division by combining objective response rate and time-to-event outcomes, which may be interrelated due to some shared traits. We augment previous works by enabling subject-specific random effects to govern the communication among distinct endpoints. Our simulations show that the proposed model has advantages over the standard model in terms of precision and stability in parameter estimation and threshold determination. To validate the feasibility of the proposed thresholds, we pool a cohort of 73 patients with non-small-cell lung cancer and 64 patients with nasopharyngeal carcinoma who underwent anti-PD-(L)1 treatment, as well as validation cohorts of 943 patients. Analyses revealed that our approach could grant clinicians a holistic efficacy assessment, culminating in a robust determination of the TMB screening threshold for superior patients. Our methodology has the potential to yield innovative insights into therapeutic selection and support precision immuno-oncology.

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In oncology drug development, indication selection and optimal dose identification are the primary objectives for the early phase of clinical trials and could significantly impact the probability of success. Master protocols, e.g., basket trial, umbrella trial, and platform trial, have become popular in practice considering the connection of trial designs with multiple indications and treatment candidates. They also enable the optimization of operational resources and maximize the capability of data-driven decision-making. However, most of the available designs are developed with the efficacy endpoint only for treatment effect estimation and testing, without consideration of the safety end point. Thus, it often lacks a comprehensive quantitative framework to allow optimal treatment selection, which could put future development at risk. We propose an optimal Bayesian platform trial design with multiple end points (PMED) to characterize the overall benefit-risk profile. The design is further extended to allow treatment and indication selection within and across arms, with continuous monitoring on multiple interim analyses for futility. In addition, we propose dynamic borrowing across arms to increase the efficiency and accuracy of estimation given the level of similarity across arms. A hierarchical hypothesis structure is utilized to achieve optimal indication and treatment combination selection by controlling family-wise error. Through simulation studies, we show that PMED is a robust design under the studied scenarios with superb power and controlled family-wise error rate.

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The graphical approach by Bretz et al. is a convenient tool to construct, visualize and perform multiple test procedures that are tailored to structured families of hypotheses while controlling the familywise error rate. A critical step is to update the transition weights following a pre-specified algorithm. In their original publication, however, the authors did not provide a detailed rationale for the update formula. This paper closes the gap and provides three alternative arguments for the update of the transition weights of the graphical approach. It is a legacy of the first author, based on an unpublished technical report from 2014, and after his untimely death reconstructed by the other two authors as a tribute to Willi Maurer's collaboration with Andy Grieve and contributions to biostatistics over many years.

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We propose a class of two-sample statistics for testing the equality of proportions and the equality of survival functions. We build our proposal on a weighted combination of a score test for the difference in proportions and a weighted Kaplan-Meier statistic-based test for the difference of survival functions. The proposed statistics are fully non-parametric and do not rely on the proportional hazards assumption for the survival outcome. We present the asymptotic distribution of these statistics, propose a variance estimator, and show their asymptotic properties under fixed and local alternatives. We discuss different choices of weights including those that control the relative relevance of each outcome and emphasize the type of difference to be detected in the survival outcome. We evaluate the performance of these statistics with small sample sizes through a simulation study and illustrate their use with a randomized phase III cancer vaccine trial. We have implemented the proposed statistics in the R package SurvBin, available on GitHub (https://github.com/MartaBofillRoig/SurvBin).

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For semi-competing risks data involving a non-terminal event and a terminal event we derive the asymptotic distributions of the event-specific win ratios under proportional hazards (PH) assumptions for the relevant cause-specific hazard functions of the non-terminal and terminal event, respectively. The win ratios converge to the respective hazard ratios under the PH assumptions and therefore are censoring-free, whether or not the censoring distributions in the two treatment arms are the same. With the asymptotic bivariate normal distributions of the win ratios, confidence intervals and testing procedures are obtained. Through extensive simulation studies and data analysis, we identified proper transformations of the win ratios that yield good control of the type one error rate for various testing procedures while maintaining competitive power. The confidence intervals also have good coverage probabilities. Furthermore, a test for the PH assumptions and a test of equal hazard ratios are developed. The new procedures are illustrated in the clinical trial Aldosterone Antagonist Therapy for Adults With Heart Failure and Preserved Systolic Function, which evaluated the effects of spironolactone in patients with heart failure and a preserved left ventricular ejection fraction.

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In dose-response analysis, it is a challenge to choose appropriate linear or curvilinear shapes when considering multiple, differently scaled endpoints. It has been proposed to fit several marginal regression models that try sets of different transformations of the dose levels as explanatory variables for each endpoint. However, the multiple testing problem underlying this approach, involving correlated parameter estimates for the dose effect between and within endpoints, could only be adjusted heuristically. An asymptotic correction for multiple testing can be derived from the score functions of the marginal regression models. Based on a multivariate t-distribution, the correction provides a one-step adjustment of p-values that accounts for the correlation between estimates from different marginal models. The advantages of the proposed methodology are demonstrated through three example datasets, involving generalized linear models with differently scaled endpoints, differing covariates, and a mixed effect model and through simulation results. The methodology is implemented in an R package.

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Adaptive designs are gaining popularity in early phase clinical trials because they enable investigators to change the course of a study in response to accumulating data. We propose a novel design to simultaneously monitor several endpoints. These include efficacy, futility, toxicity and other outcomes in early phase, single-arm studies. We construct a recursive relationship to compute the exact probabilities of stopping for any combination of endpoints without the need for simulation, given pre-specified decision rules. The proposed design is flexible in the number and timing of interim analyses. A R Shiny app with user-friendly web interface has been created to facilitate the implementation of the proposed design.

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We introduce an improved Bonferroni method for testing two primary endpoints in clinical trial settings using a new data-adaptive critical value that explicitly incorporates the sample correlation coefficient. Our methodology is developed for the usual Student's t-test statistics for testing the means under normal distributional setting with unknown population correlation and variances. Specifically, we construct a confidence interval for the unknown population correlation and show that the estimated type-1 error rate of the Bonferroni method with the population correlation being estimated by its lower confidence limit can be bounded from above less conservatively than using the traditional Bonferroni upper bound. We also compare the new procedure with other procedures commonly used for the multiple testing problem addressed in this paper.

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Polychlorinated naphthalenes (PCNs) are widely distributed in the aquatic environment and can be transmitted through the food chain, which can amplify their toxic effects on human. To inhibit their transmission in the trophic level, this study aimed to predict the joint toxicity mechanism of polychlorinated naphthalenes (PCNs) to the key organisms and control scheme of its toxicity in the aquatic food chain (green algae-Daphnia magna-fish). The toxic effect grade and mode of action (MoA) of PCNs on the food chain were first predicted to guide the establishment of toxic mechanism model. QSAR models were constructed to quantify the mechanism of aquatic toxicity due to PCNs. The results showed the PCN compounds studied were highly toxic at all the trophic levels of the aquatic food chain. The binding ability of PCNs to the aquatic organisms was the main factor causing the toxicity of PCNs in the food chain, followed by electronic parameters EHOMO and ELUMO. Moreover, the binding ability between PCNs and food chain receptors was related to the molecular hydrophobicity, the hydrophobicity can be changed by adjusting the ability of PCNs to be adsorbed by sediment and their chlorine substituents, while the effect of PCNs electronic parameters (EHOMO and ELUMO) can be adjusted by their solvation effect. In addition, the macro-control scheme of PCN-based aquatic toxicity mechanism was established, and the molecular dynamics (MD) simulation confirmed its effectiveness and accessibility. The MD simulation showed the inhibition effect of nutrition-grade toxicity in the food chain was significant when the external stimulation conditions of solvation, anaerobic dechlorination and molecular adsorption were improved, with the decrease range of 66.26-263.16%, 198.93-323.98% and 189.24-549.48%, respectively. This work reveals new insights into the mechanism of PCNs joint toxicity to aquatic ecosystem food chain and develop appropriate strategies for its ecological risk management.

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Current in vitro genotoxicity tests can produce misleading positive results, indicating an inability to effectively predict a compound's subsequent carcinogenic potential in vivo. Such oversensitivity can incur unnecessary in vivo tests to further investigate positive in vitro results, supporting the need to improve in vitro tests to better inform risk assessment. It is increasingly acknowledged that more informative in vitro tests using multiple endpoints may support the correct identification of carcinogenic potential. The present study, therefore, employed a holistic, multiple-endpoint approach using low doses of selected carcinogens and non-carcinogens (0.001-770 µM) to assess whether these chemicals caused perturbations in molecular and cellular endpoints relating to the Hallmarks of Cancer. Endpoints included micronucleus induction, alterations in gene expression, cell cycle dynamics, cell morphology and bioenergetics in the human lymphoblastoid cell line TK6. Carcinogens ochratoxin A and oestradiol produced greater Integrated Signature of Carcinogenicity scores for the combined endpoints than the "misleading" in vitro positive compounds, quercetin, 2,4-dichlorophenol and quinacrine dihydrochloride and toxic non-carcinogens, caffeine, cycloheximide and phenformin HCl. This study provides compelling evidence that carcinogens can successfully be distinguished from non-carcinogens using a holistic in vitro test system. Avoidance of misleading in vitro outcomes could lead to the reduction and replacement of animals in carcinogenicity testing.

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