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In this paper, we propose a Bayesian design framework for a biosimilars clinical program that entails conducting concurrent trials in multiple therapeutic indications to establish equivalent efficacy for a proposed biologic compared to a reference biologic in each indication to support approval of the proposed biologic as a biosimilar. Our method facilitates information borrowing across indications through the use of a multivariate normal correlated parameter prior (CPP), which is constructed from easily interpretable hyperparameters that represent direct statements about the equivalence hypotheses to be tested. The CPP accommodates different endpoints and data types across indications (eg, binary and continuous) and can, therefore, be used in a wide context of models without having to modify the data (eg, rescaling) to provide reasonable information-borrowing properties. We illustrate how one can evaluate the design using Bayesian versions of the type I error rate and power with the objective of determining the sample size required for each indication such that the design has high power to demonstrate equivalent efficacy in each indication, reasonably high power to demonstrate equivalent efficacy simultaneously in all indications (ie, globally), and reasonable type I error control from a Bayesian perspective. We illustrate the method with several examples, including designing biosimilars trials for follicular lymphoma and rheumatoid arthritis using binary and continuous endpoints, respectively., (© 2019 The International Biometric Society.)

A challenge arising in cancer immunotherapy trial design is the presence of a delayed treatment effect wherein the proportional hazard assumption no longer holds true. As a result, a traditional survival trial design based on the standard log-rank test, which ignores the delayed treatment effect, will lead to substantial loss of statistical power. Recently, a piecewise weighted log-rank test is proposed to incorporate the delayed treatment effect into consideration of the trial design. However, because the sample size formula was derived under a sequence of local alternative hypotheses, it results in an underestimated sample size when the hazard ratio is relatively small for a balanced trial design and an inaccurate sample size estimation for an unbalanced design. In this article, we derived a new sample size formula under a fixed alternative hypothesis for the delayed treatment effect model. Simulation results show that the new formula provides accurate sample size estimation for both balanced and unbalanced designs., (© 2019 John Wiley & Sons, Ltd.)

The win ratio has been studied methodologically and applied in data analysis and in designing clinical trials. Researchers have pointed out that the results depend on follow-up time and censoring time, which are sometimes used interchangeably. In this article, we distinguish between follow-up time and censoring time, show theoretically the impact of censoring on the win ratio, and illustrate the impact of follow-up time. We then point out that, if the treatment has long-term benefit from a more important but less frequent endpoint (eg, death), the win ratio can show that benefit by following patients longer, avoiding masking by more frequent but less important outcomes, which occurs in conventional time-to-first-event analyses. For the situation of nonproportional hazards, we demonstrate that the win ratio can be a good alternative to methods such as landmark survival rate, restricted mean survival time, and weighted log-rank tests., (© 2019 John Wiley & Sons, Ltd.)

Interim analyses are routinely used to monitor accumulating data in clinical trials. When the objective of the interim analysis is to stop the trial if the trial is deemed futile, it must ideally be conducted as early as possible. In trials where the clinical endpoint of interest is only observed after a long follow-up, many enrolled patients may therefore have no information on the primary endpoint available at the time of the interim analysis. To facilitate earlier decision-making, one may incorporate early response data that are predictive for the primary endpoint (eg, an assessment of the primary endpoint at an earlier time) in the interim analysis. Most attention so far has been given to the development of interim test statistics that include such short-term endpoints, but not to decision procedures. Existing tests moreover perform poorly when the information is scarce, eg, due to rare events, when the cohort of patients with observed primary endpoint data is small, or when the short-term endpoint is a strong but imperfect predictor. In view of this, we develop an interim decision procedure based on the conditional power approach that utilizes the short-term and long-term binary endpoints in a framework that is expected to provide reliable inferences, even when the primary endpoint is only available for a few patients, and has the added advantage that it allows the use of historical information. The operational characteristics of the proposed procedure are evaluated for the phase III clinical trial that motivated this approach, using simulation studies., (© 2019 John Wiley & Sons, Ltd.)

Background: The rationale for the use of composite time-to-event endpoints is to increase the number of expected events and thereby the power by combining several event types of clinical interest. The all-cause hazard ratio is the standard effect measure for composite endpoints where the all-cause hazard function is given as the sum of the event-specific hazards. However, the effect of the individual components might differ, in magnitude or even in direction, which leads to interpretation difficulties. Moreover, the individual event types often are of different clinical relevance which further complicates interpretation. Our working group recently proposed a new weighted effect measure for composite endpoints called the 'weighted all-cause hazard ratio'. By imposing relevance weights for the components, the interpretation of the composite effect becomes more 'natural'. Although the weighted all-cause hazard ratio seems an elegant solution to overcome interpretation problems, the originally published approach has several shortcomings: First, the proposed point estimator requires pre-specification of a parametric survival model. Second, no closed formula for a corresponding test statistic was provided. Instead, a permutation test was proposed. Third, no clear guidance for the choice of the relevance weights was provided. In this work, we will overcome these problems., Methods: Within this work a new non-parametric estimator and a related closed formula test statistic are presented. Performance of the new estimator and test is compared to the original ones by a Monte-Carlo simulation study., Results: The original parametric estimator is sensible to miss-specifications of the survival model. The new non-parametric estimator turns out to be very robust even if the required assumptions are not met. The new test shows considerably better power properties than the permutation test, is computationally much less expensive but might not preserve type one error in all situations. A scheme for choosing the relevance weights in the planning stage is provided., Conclusion: We recommend to use the non-parametric estimator along with the new test to assess the weighted all-cause hazard ratio. Concrete guidance for the choice of the relevance weights is now available. Thus, applying the weighted all-cause hazard ratio in clinical applications is both - feasible and recommended.

Adaptive trial methodology for multiarmed trials and enrichment designs has been extensively discussed in the past. A general principle to construct test procedures that control the family-wise Type I error rate in the strong sense is based on combination tests within a closed test. Using survival data, a problem arises when using information of patients for adaptive decision making, which are under risk at interim. With the currently available testing procedures, either no testing of hypotheses in interim analyses is possible or there are restrictions on the interim data that can be used in the adaptation decisions as, essentially, only the interim test statistics of the primary endpoint may be used. We propose a general adaptive testing procedure, covering multiarmed and enrichment designs, which does not have these restrictions. An important application are clinical trials, where short-term surrogate endpoints are used as basis for trial adaptations, and we illustrate how such trials can be designed. We propose statistical models to assess the impact of effect sizes, the correlation structure between the short-term and the primary endpoint, the sample size, the timing of interim analyses, and the selection rule on the operating characteristics., (© 2019 John Wiley & Sons, Ltd.)

Background: Proportional hazards (PH) is an assumption often made by researchers, despite evidence of nonproportionality in a significant proportion of clinical trials. In the presence of non-PH, the interpretation of hazard ratios, medians, and landmark survival as summary measures of treatment effect can become problematic. Several recent studies have recommended restricted mean survival time (RMST) as an alternative metric for survival analysis, particularly where non-PH may apply., Objectives: To determine the current approaches of health technology assessment (HTA) agencies to value assessment in the presence of non-PH, and the extent to which RMST is accepted as an alternative measure of treatment benefit., Methods: Methodological guidelines published by 10 HTA agencies were reviewed to establish recommended approaches for presenting survival benefit from clinical trials. Published HTA reports for 23 oncology agents approved by the US Food and Drug Administration and the European Medicines Agency since 2014 were reviewed to determine how guidelines are implemented in practice and identify instances where the PH assumption was tested and RMST analyses reported., Results: Testing for non-PH is not widely incorporated into HTA except by the UK National Institute for Health and Care Excellence. RMST is used infrequently but has been used in a number of countries, particularly by agencies that focus on cost effectiveness., Conclusions: HTA agencies vary in their approaches to non-PH. Most do not routinely check the PH assumption. RMST has played a role in assessing clinical benefit within HTA, although not consistently within countries (across drugs) or across countries (for the same drug)., (Copyright © 2019 ISPOR–The Professional Society for Health Economics and Outcomes Research. Published by Elsevier Inc. All rights reserved.)

Background: In proportionate or adaptive interventions, the dose or intensity can be adjusted based on individual need at predefined decision stages during the delivery of the intervention. The development of such interventions may require an evaluation of the effectiveness of the individual stages in addition to the whole intervention. However, evaluating individual stages of an intervention has various challenges, particularly the statistical design and analysis. This review aimed to identify the use of trials of proportionate interventions and how they are being designed and analysed in current practice., Methods: We searched MEDLINE, Web of Science and PsycINFO for articles published between 2010 and 2015 inclusive. We considered trials of proportionate interventions in all fields of research. For each trial, its aims, design and analysis were extracted. The data synthesis was conducted using summary statistics and a narrative format., Results: Our review identified 44 proportionate intervention trials, comprising 28 trial results, 13 protocols and three secondary analyses. These were mostly described as stepped care (n=37) and mainly focussed on mental health research (n=30). The other studies were aimed at finding an optimal adaptive treatment strategy (n=7) in a variety of therapeutic areas. Further terminology used included adaptive intervention, staged intervention, sequentially multiple assignment trial or a two-phase design. The median number of decision stages in the interventions was two and only one study explicitly evaluated the effect of the individual stages., Conclusions: Trials of proportionate staged interventions are being used predominantly within the mental health field. However, few studies consider the different stages of the interventions, either at the design or the analysis phase, and how they may interact with one another. There is a need for further guidance on the design, analyses and reporting across trials of proportionate interventions., Trial Registration: Prospero, CRD42016033781. Registered on 2 February 2016.

While current guidelines generally recommend single endpoints for primary analyses of confirmatory clinical trials, it is recognized that certain settings require inference on multiple endpoints for comprehensive conclusions on treatment effects. Furthermore, combining treatment effect estimates from several outcome measures can increase the statistical power of tests. Such an efficient use of resources is of special relevance for trials in small populations. This paper reviews approaches based on a combination of test statistics or measurements across endpoints as well as multiple testing procedures that allow for confirmatory conclusions on individual endpoints. We especially focus on feasibility in trials with small sample sizes and do not solely rely on asymptotic considerations. A systematic literature search in the Scopus database, supplemented by a manual search, was performed to identify research papers on analysis methods for multiple endpoints with relevance to small populations. The identified methods were grouped into approaches that combine endpoints into a single measure to increase the power of statistical tests and methods to investigate differential treatment effects in several individual endpoints by multiple testing.

Multi-arm multi-stage designs, in which multiple active treatments are compared to a control and accumulated information from interim data are used to add or remove arms from the trial, may reduce development costs and shorten the drug development timeline. As such, this adaptive update is a natural complement to Bayesian methodology in which the prior clinical belief is sequentially updated using the observed probability of success. Simulation is often required for planning clinical trials to accommodate the complexity of the design and to optimize key design characteristics. This paper addresses two key limiting factors in simulations, namely the computational burden and the time needed to obtain results. We first introduce a generic process for simulating Bayesian multi-arm multi-stage designs with binary endpoints. Then, to address the computational burden and time, we optimize the method for calculating the posterior probability and posterior predictive probability of success.

In clinical trials, selection of appropriate study endpoints is critical for an accurate and reliable evaluation of safety and effectiveness of a test treatment under investigation. In practice, however, there are usually multiple endpoints available for measurement of disease status and/or therapeutic effect of the test treatment under study. For example, in cancer clinical trials, overall survival, response rate, and/or time to disease progression are usually considered as primary clinical endpoints for evaluation of safety and effectiveness of the test treatment under investigation. Once the study endpoints have been selected, sample size required for achieving a desired power is then determined. It, however, should be noted that different study endpoints may result in different sample sizes. In practice, it is usually not clear which study endpoint can best inform the disease status and measure the treatment effect. Moreover, different study endpoints may not translate one another although they may be highly correlated one another. In this article, we intend to develop an innovative endpoint namely therapeutic index based on a utility function to combine and utilize information collected from all study endpoints. Statistical properties and performances of the proposed therapeutic index are evaluated theoretically. A numerical example concerning a cancer clinical trial is given to illustrate the use of the proposed therapeutic index.

Recently, new draft guidelines on multiplicity issues in clinical trials have been issued by European Medicine Agency (EMA) and Food and Drug Administration (FDA), respectively. Multiplicity is an issue in clinical trials, if the probability of a false-positive decision is increased by insufficiently accounting for testing multiple hypotheses. We outline the regulatory principles related to multiplicity issues in confirmatory clinical trials intended to support a marketing authorization application in the EU, describe the reasons for an increasing complexity regarding multiple hypotheses testing and discuss the specific multiplicity issues emerging within the regulatory context and being relevant for drug approval.

Background/aims: A potential use of biomarkers is to assist in prognostic enrichment of clinical trials, where only patients at relatively higher risk for an outcome of interest are eligible for the trial. We investigated methods for evaluating biomarkers for prognostic enrichment., Methods: We identified five key considerations when considering a biomarker and a screening threshold for prognostic enrichment: (1) clinical trial sample size, (2) calendar time to enroll the trial, (3) total patient screening costs and the total per-patient trial costs, (4) generalizability of trial results, and (5) ethical evaluation of trial eligibility criteria. Items (1)-(3) are amenable to quantitative analysis. We developed the Biomarker Prognostic Enrichment Tool for evaluating biomarkers for prognostic enrichment at varying levels of screening stringency., Results: We demonstrate that both modestly prognostic and strongly prognostic biomarkers can improve trial metrics using Biomarker Prognostic Enrichment Tool. Biomarker Prognostic Enrichment Tool is available as a webtool at http://prognosticenrichment.com and as a package for the R statistical computing platform., Conclusion: In some clinical settings, even biomarkers with modest prognostic performance can be useful for prognostic enrichment. In addition to the quantitative analysis provided by Biomarker Prognostic Enrichment Tool, investigators must consider the generalizability of trial results and evaluate the ethics of trial eligibility criteria.

Objective: To identify the occurrence and determinants of protocol-publication discrepancies in clinical drug trials., Study Design and Setting: All published clinical drug trials reviewed by the Dutch institutional review boards in 2007 were analyzed. Discrepancies between trial protocols and publications were measured among key reporting aspects. We evaluated the association of trial characteristics with discrepancies in primary endpoints by calculating the risk ratio (RR) and 95% confidence interval (CI)., Results: Of the 334 published trials, 32 (9.6%) had a protocol/publication discrepancy in the primary endpoints. Among the subgroup of randomized controlled trials (RCTs; N = 204), 12 (5.9%) had a discrepancy in the primary endpoint. Investigator-initiated trials with and without industry (co-) funding were associated with having discrepancies in the primary endpoints compared with industry-sponsored trials (RR 3.7; 95% CI 1.4-9.9 and RR 4.4; 95% CI 2.0-9.5, respectively). Furthermore, other than phase 1-4 trials (vs. phase 1; RR 4.6; 95% CI 1.1-19.3), multicenter trials were also conducted outside the European Union (vs. single center; RR 0.2; 95% CI 0.1-0.6), not prospectively registered trials (RR 3.3; 95% CI 1.5-7.5), non-RCTs (vs. superiority RCT; RR 2.4; 95% CI 1.2-4.8) and, among the RCTs, crossover compared with a parallel group design (RR 3.7; 95% CI 1.1-12.3) were significantly associated with having discrepancies in the primary endpoints., Conclusions: Improvement in completeness of reporting is still needed, especially among investigator-initiated trials and non-RCTs. To eliminate undisclosed discrepancies, trial protocols should be available in the public domain at the same time when the trial is published., (Copyright © 2017 Elsevier Inc. All rights reserved.)

To analyze prioritized outcomes, Buyse (2010) and Pocock et al. (2012) proposed the win loss approach. In this paper, we first study the relationship between the win loss approach and the traditional survival analysis on the time to the first event. We then propose the weighted win loss statistics to improve the efficiency of the unweighted methods. A closed-form variance estimator of the weighted win loss statistics is derived to facilitate hypothesis testing and study design. We also calculated the contribution index to better interpret the results of the weighted win loss approach. Simulation studies and real data analysis demonstrated the characteristics of the proposed statistics. Copyright © 2017 John Wiley & Sons, Ltd., (Copyright © 2017 John Wiley & Sons, Ltd.)

Clinical research should ultimately improve patient care. For this to be possible, trials must evaluate outcomes that genuinely reflect real-world settings and concerns. However, many trials continue to measure and report outcomes that fall short of this clear requirement. We highlight problems with trial outcomes that make evidence difficult or impossible to interpret and that undermine the translation of research into practice and policy. These complex issues include the use of surrogate, composite and subjective endpoints; a failure to take account of patients' perspectives when designing research outcomes; publication and other outcome reporting biases, including the under-reporting of adverse events; the reporting of relative measures at the expense of more informative absolute outcomes; misleading reporting; multiplicity of outcomes; and a lack of core outcome sets. Trial outcomes can be developed with patients in mind, however, and can be reported completely, transparently and competently. Clinicians, patients, researchers and those who pay for health services are entitled to demand reliable evidence demonstrating whether interventions improve patient-relevant clinical outcomes.

For about a decade, early clinical development in oncology is facing new challenges. This is due to two main reasons. The first one is linked to the developed molecular targeted agents (MTA) themselves for which the maximum tolerated dose (MTD) is no longer the only dose of interest. The second reason is related to the fact that costs and attrition rates are huge. When selecting a dose, evidence of early activity signal becomes required for future engagements. This implies the need to handle both toxicity and activity endpoints in the analysis and also in the dose escalation design of early-phase trials. We propose a model-based design taking into account both safety and activity for dose escalation. The proposed model involves a bivariate Gaussian latent variable depending on a monotonic toxicity curve and a quadratic activity curve. This model is fitted under the Bayesian framework that allows the incorporation of prior information. The predictive distributions of dose-response curves are used to lead the dose recommendation. Uncertainty in the dose-response relationship is taken into account to calculate the probability of being an over-toxic or a target dose. The proposed design is compared to two other widely used methods.

Nowadays, two main frameworks for the evaluation of surrogate endpoints, based on causal-inference and meta-analysis, dominate the scene. Earlier work showed that the metrics of surrogacy introduced in both paradigms are related, although in a complex way that is difficult to study analytically. In the present work, this relationship is further examined using simulations and the analysis of a case study. The results indicate that the extent to which both paradigms lead to similar conclusions regarding the validity of the surrogate, depends on a complex interplay between multiple factors like the ratio of the between and within trial variability and the unidentifiable correlations between the potential outcomes. All the analyses were carried out using the newly developed R package Surrogate, which is freely available via CRAN., (Copyright © 2015 John Wiley & Sons, Ltd.)

'Multistage testing with adaptive designs' was the title of an article by Peter Bauer that appeared 1989 in the German journal Biometrie und Informatik in Medizin und Biologie. The journal does not exist anymore but the methodology found widespread interest in the scientific community over the past 25 years. The use of such multistage adaptive designs raised many controversial discussions from the beginning on, especially after the publication by Bauer and Köhne 1994 in Biometrics: Broad enthusiasm about potential applications of such designs faced critical positions regarding their statistical efficiency. Despite, or possibly because of, this controversy, the methodology and its areas of applications grew steadily over the years, with significant contributions from statisticians working in academia, industry and agencies around the world. In the meantime, such type of adaptive designs have become the subject of two major regulatory guidance documents in the US and Europe and the field is still evolving. Developments are particularly noteworthy in the most important applications of adaptive designs, including sample size reassessment, treatment selection procedures, and population enrichment designs. In this article, we summarize the developments over the past 25 years from different perspectives. We provide a historical overview of the early days, review the key methodological concepts and summarize regulatory and industry perspectives on such designs. Then, we illustrate the application of adaptive designs with three case studies, including unblinded sample size reassessment, adaptive treatment selection, and adaptive endpoint selection. We also discuss the availability of software for evaluating and performing such designs. We conclude with a critical review of how expectations from the beginning were fulfilled, and - if not - discuss potential reasons why this did not happen., (© 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)

In this paper, we propose a design that uses a short-term endpoint for accelerated approval at interim analysis and a long-term endpoint for full approval at final analysis with sample size adaptation based on the long-term endpoint. Two sample size adaptation rules are compared: an adaptation rule to maintain the conditional power at a prespecified level and a step function type adaptation rule to better address the bias issue. Three testing procedures are proposed: alpha splitting between the two endpoints; alpha exhaustive between the endpoints; and alpha exhaustive with improved critical value based on correlation. Family-wise error rate is proved to be strongly controlled for the two endpoints, sample size adaptation, and two analysis time points with the proposed designs. We show that using alpha exhaustive designs greatly improve the power when both endpoints are effective, and the power difference between the two adaptation rules is minimal. The proposed design can be extended to more general settings., (Copyright © 2015 John Wiley & Sons, Ltd.)

Background: The assessment of treatment success in clinical trials when multiple (repeated) doses (courses) are involved is quite common, for example, in the case of infertility treatment with assisted reproductive technology (ART), and medical abortion using misoprostol alone or in combination with mifepristone. Under these or similar circumstances, most researchers assess success using binomial proportions after a certain number of consecutive doses, and some have used survival analysis. In this paper we discuss the main problems in using binomial proportions to summarize (the overall) efficacy after two or more consecutive doses of the relevant treatment, particularly for the case of misoprostol in medical abortion studies. We later discuss why the survival analysis is best suited under these circumstances, and illustrate this by using simulated data., Methods: The formulas required for the binomial proportion and survival analysis (without and with competing risks) approaches are summarized and analytically compared. Additionally, numerical results are computed and compared between the two approaches, for several theoretical scenarios., Results: The main conceptual limitations of the binomial proportion approach are identified and discussed, caused mainly by the presence of censoring and competing risks, and it is demonstrated how survival analysis can solve these problems. In general, the binomial proportion approach tends to underestimate the "real" success rate, and tends to overestimate the corresponding standard error., Conclusions: Depending on the rates of censored observations or competing events between repeated doses of the treatment, the bias of the binomial proportion approach as compared to the survival analysis approaches varies; however, the use of the binomial approach is unjustified as the survival analysis options are well known and available in multiple statistical packages. Our conclusions also apply to other situations where success is estimated after multiple (repeated) doses (courses) of the treatment.

In oncology clinical trials, progression-free survival (PFS), generally defined as the time from randomization until disease progression or death, has been a key endpoint to support licensing approval. In the U.S. Food and Drug Administration guidance for industry, May 2007, concerning the PFS as the primary or co-primary clinical trial endpoint, it is recommended to have tumor assessments verified by an independent review committee blinded to study treatments, especially in open-label studies. It is considered reassuring about the lack of reader-evaluation bias if treatment effect estimates from the investigators' and independent review committees' evaluations agree. The agreement between these evaluations may vary for subjects with short or long PFS, while there exist no such statistical quantities that can completely account for this temporal pattern of agreements. Therefore, in this paper, we propose a new method to assess temporal agreement between two time-to-event endpoints, while the two event times are assumed to have a positive probability of being identical. This method measures agreement in terms of the two event times being identical at a given time or both being greater than a given time. Overall scores of agreement over a period of time are also proposed. We propose a maximum likelihood estimation to infer the proposed agreement measures using empirical data, accounting for different censoring mechanisms, including reader's censoring (event from one reader dependently censored by event from the other reader). The proposed method is demonstrated to perform well in small samples via extensive simulation studies and is illustrated through a head and neck cancer trial., (Copyright © 2014 John Wiley & Sons, Ltd.)

Evaluation of surrogate end points using patient-level data from multiple trials is the gold standard, where multi-trial copula models are used to quantify both patient-level and trial-level surrogacy. While limited consideration has been given in the literature to copula choice (e.g., Clayton), no prior consideration has been given to direction of implementation (via survival vs. distribution functions). We demonstrate that even with the "correct" copula family, directional misspecification leads to biased estimates of patient-level and trial-level surrogacy. We illustrate with a simulation study and a reanalysis of disease-free survival as a surrogate for overall survival in early stage colon cancer.

In a clinical trial where several doses are compared to a control, a multi-stage design that combines both the selection of the best dose and the confirmation of this selected dose is desirable. An example is the two-stage drop-the-losers or pick-the-winner design, where inferior doses are dropped after interim analysis. Selection of target dose(s) can be based on ranking of observed effects, hypothesis testing with adjustment for multiplicity, or other criteria at interim stages. A number of methods have been proposed and have made significant gains in trial efficiency. However, many of these designs started off with all doses with equal allocation and did not consider prioritizing the doses using existing dose-response information. We propose an adaptive staggered dose procedure that allows explicit prioritization of doses and applies error spending scheme that favors doses with assumed better responses. This design starts off with only a subset of the doses and adaptively adds new doses depending on interim results. Using simulation, we have shown that this design performs better in terms of increased statistical power than the drop-the-losers design given strong prior information of dose response.

The use of two or more primary correlated endpoints is becoming increasingly common. A mandatory approach when analyzing data from such clinical trials is to control the family-wise error rate (FWER). In this context, we provide formulas for computation of sample size and for data analysis. Two approaches are discussed: an individual method based on a union-intersection procedure and a global procedure, based on a multivariate model that can take into account adjustment variables. These methods are illustrated with simulation studies and applications. An R package known as rPowerSampleSize is also available.

It has been widely recognized that interim analyses of accumulating data in a clinical trial can inflate type I error. Different methods, from group sequential boundaries to flexible alpha spending functions, have been developed to control the overall type I error at prespecified level. These methods mainly apply to testing the same endpoint in multiple interim analyses. In this article, we consider a group sequential design with preplanned endpoint switching after unblinded interim analyses. We extend the alpha spending function method to group sequential stopping boundaries when the parameters can be different between interim, or between interim and final analyses.

In phase III cancer clinical trials, overall survival is commonly used as the definitive endpoint. In phase II clinical trials, however, more immediate endpoints such as incidence of complete or partial response within 1 or 2 months or progression-free survival (PFS) are generally used. Because of the limited ability to detect change in overall survival with response, the inherent variability of PFS and the long wait for progression to be observed, more informative and immediate alternatives to overall survival are desirable in exploratory phase II trials. In this paper, we show how comparative trials can be designed and analysed using change in tumour size as the primary endpoint. The test developed is based on the framework of score statistics and will formally incorporate the information of whether patients survive until the time at which change in tumour size is assessed. Using an example in non-small cell lung cancer, we show that the sample size requirements for a trial based on change in tumour size are favourable compared with alternative randomized trials and demonstrate that these conclusions are robust to our assumptions., (Copyright © 2012 John Wiley & Sons, Ltd.)

In experimental settings, one or more groups of subjects receive a treatment and they are compared to a group of subjects that receives a standard treatment or no treatment at all. These compared groups might have an equal number of subjects or some of the groups might have more participants relative to the other groups. Moreover, subjects in these groups can be followed over a short or a long period. To conduct experiments in a sufficient way, researchers should find a good design in the planning phase of the trial. The optimal design for experimental studies on event occurrence with discrete-time survival endpoints where two treatment groups are followed over time, is an optimal combination of the number of time periods, the total number of participants in the trial and the proportion of subjects in the experimental group. It is easy to find the best design for such studies using the PODSE program., (Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.)

We discuss sample size determination for clinical trials evaluating the joint effects of an intervention on two potentially correlated co-primary time-to-event endpoints. For illustration, we consider the most common case, a comparison of two randomized groups, and use typical copula families to model the bivariate endpoints. A correlation structure of the bivariate logrank statistic is specified to account for the correlation among the endpoints, although the between-group comparison is performed using the univariate logrank statistic. We propose methods to calculate the required sample size to compare the two groups and evaluate the performance of the methods and the behavior of required sample sizes via simulation.

In early stages of drug development, there is often uncertainty about the most promising among a set of different treatments. To ensure the best use of resources in such situations, it is important to decide which, if any, of the treatments should be taken forward for further testing. In later development, it has been shown that evaluating more than one dose increases the chance of success substantially. In this work, we discuss how multi-arm multi-stage trials can be designed such that all promising treatments are kept in the study at the interim analyses. We first investigate the impact of deviating from the planned design and show how confidence intervals can be constructed before we consider the impact of important covariates. We show that under orthogonality, the inclusion of covariates has no effect on familywise error rate control in the strong sense. We further show that the derived methodology can be used to investigate non-normal endpoints., (Copyright © 2012 John Wiley & Sons, Ltd.)

We propose a group sequential Holm procedure when there are multiple primary endpoints. This method addresses multiplicities arising from multiple primary endpoints and from multiple analyses in a group sequential design. It has been shown to be a closed testing procedure and preserves the familywise error rate in the strong sense. When multiple endpoints are the only concern without an interim analysis, the method simplifies to the weighted Holm procedure. The proposed method is more powerful than the parallel group sequential method and avoids the need to anticipate the testing order as in the fixed sequence testing scheme., (Copyright © 2012 John Wiley & Sons, Ltd.)

This paper introduces a new class of multiple testing procedures for addressing multiplicity problems arising in clinical trials with multiple objectives grouped into families. The families may correspond to equally important sets of objectives (co-primary endpoints) or ordered sets of objectives (primary and secondary endpoints). The procedures, termed superchain procedures, serve as an extension of several classes of other multiple testing procedures, including chain procedures and parallel gatekeeping procedures. Superchain procedures exhibit several desirable features, including flexible decision rules that can be tailored to a broad class of win criteria in confirmatory clinical trials. Additionally, superchain procedures enable the trial's sponsor to efficiently incorporate available distributional information to improve overall power. Finally, superchain procedures rely on straightforward testing algorithms, which facilitates their development. We illustrate the new methodology by using clinical trial examples with two and three families of objectives., (Copyright © 2012 John Wiley & Sons, Ltd.)

In clinical trials, interim analyses are often performed before the completion of the trial. The intention is to possibly terminate the trial early or adjust the sample size. The time of conducting an interim analysis affects the probability of the early termination and the number of subjects enrolled until the interim analysis. This influences the expected total number of subjects. In this study, we examine the optimal time for conducting interim analyses with a view to minimizing the expected total sample size. It is found that regardless of the effect size, the optimal time of one interim analysis for the early termination is approximately two-thirds of the planned observations for the O'Brien-Fleming type of spending function and approximately half of the planned observations for the Pocock type when the subject enrollment is halted for the interim analysis. When the subject enrollment is continuous throughout the trial, the optimal time for the interim analysis varies according to the follow-up duration. We also consider the time for one interim analysis including the sample size adjustment in terms of minimizing the expected total sample size.

To confirm results obtained from local evaluation at investigational centers, many oncology studies utilize blinded independent central review (BICR) to make assessments of the primary endpoint, progression-free survival (PFS). The comparison of data often leads to large discordances between these observations, casting doubt on the reliability of the estimated treatment effects from these trials. Here we propose new statistics to measure discordance and evaluate their utility to detect bias in the local evaluation of progression relative to the standard measures of discordance. A new observational error model is proposed that can be used to describe the discordance in patient assessments between multiple readers.

Consistency of treatment effects across different regions in multiregional clinical trials (MRCTs) has been an important question for the regulatory authorities. Many consistency definitions are proposed in literature. One of the definitions of consistency is expressed as qualitative consistency, whereas inconsistency is defined as qualitative treatment by region interaction. This article focuses on the qualitative consistency and extends Gail-Simon and Sasabuchi's one-sided multivariate likelihood ratio tests. Simulations are used to evaluate operating characteristics of these qualitative consistency assessment approaches. For a given number of regions, the guideline for setting significance level, and consistency cut-off are explored.

A clinical trial might involve more than one clinically important endpoint, each of which can characterize the treatment effect of the experimental drug under investigation. Underlying the concept of using such endpoints interchangeably to establish an efficacy claim, or pooling different endpoints to constitute a composite endpoint, is the assumption that findings from such endpoints are consistent with each other. While such an assumption about consistency of efficacy findings appears to be intuitive, it is seldom considered in the design and analysis literature of clinical trials with multiple endpoints. Failure to account for consistency of efficacy findings of two candidate endpoints to establish efficacy, at the design stage, has led to difficulties in interpreting study findings. This article presents a flexible testing strategy for accommodating findings of an alternative to the designated primary endpoint (or a subgroup) to support an efficacy claim. The method is built on the following two premises: (i) Efficacy findings of the designated primary endpoint, although nonsignificant, need to be supportive of those of the alternative endpoint, and (ii) the significance level allocated for testing the second endpoint is determined adaptively based on the magnitude of the p-value for the designated primary endpoint. The method takes into account the hierarchical ordering of the hypotheses tested and the correlation between the test statistics for the two endpoints to increase the chance of a positive trial. We discuss control of the type I error rate for the proposed test strategy and compare its power with that of other methods. In addition, we consider its application to two clinical trials.

In a study designed to establish the safety of a marketed drug, interim analyses performed to detect harm can protect trial participants and the wider public before the final analysis occurs. Monitoring for harm within a safety study is different from monitoring for benefit, so techniques commonly used in an efficacy study of an experimental drug may not apply. We propose potentially more suitable techniques in this setting, including a novel spending function and conditional power. These techniques have reasonable operating characteristics in a simulation. The appropriate technique to implement will depend on circumstances of specific to the individual safety study.

The statistical inference concerning the difference between two independent binominal proportions is often discussed in medical and statistical literature. However, such discussions are often based on the frequentist viewpoint rather than the Bayesian viewpoint. In this article, we propose an index θ =P(π(1, post ) > π(2, post )), where π(1, post ) and π(2, post ) denote binominal proportions following posterior density. We provide approximate and exact expressions for θ by using the beta prior. We also present the results of actual clinical trials to show the utility of θ. Our findings suggest that θ can potentially provide useful information in a clinical trial.

We propose an approach to analyze survival time in a crossover clinical trial by performing a primary ranking on whether events occur and a secondary ranking on event times. This hierarchical ranking method is meant to reflect the idea that the goal of therapy is to prevent a clinical event and, failing that, to delay the occurrence of the event, hopefully for a substantial amount of time. We compare our approach with other methods including one method proposed by Feingold and Gillespie, a recommended procedure. The power is similar in many settings, but the hierarchical ranking can have substantially greater power under certain censoring patterns and also under a cure model, or models where treatment induces a substantial delay in some fraction of patients. We additionally feel that the hierarchical ranking method should be more clinically relevant in many settings. The method can also be applied to continuous outcomes censored by a limit of detection, such as HIV viremia., (Copyright © 2011 John Wiley & Sons, Ltd.)

In this article, we address some of the statistical issues associated with the next generation of oncology clinical trials. Specifically, we focus on two critical aspects of oncologic clinical trials: study endpoints and study design. In our discussion of study endpoints, we provide an overview of endpoints relevant to each phase of clinical trials (phases I, II, and III) and discuss some of the trends in selecting endpoints in recent years. For phase I designs, the traditional assumption that increasing dose will always lead to increasing efficacy, appropriate for cytotoxic agents, is not applicable to novel therapeutics such as in colorectal carcinoma. We emphasize the role of surrogate endpoints in modern clinical trials. In our discussion of study design, we are particularly interested in the essential role of randomization, and discuss recently developed randomized phase II designs. We consider the role biomarkers play in the design of clinical trials and introduce study designs for biomarker evaluations. Finally, we briefly discuss the application of adaptive designs in clinical trials., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Background: Overall survival (OS) is the gold standard for the demonstration of a clinical benefit in cancer trials. Replacement of OS by a surrogate endpoint allows to reduce trial duration. To date, few surrogate endpoints have been validated in digestive oncology. The aim of this study was to draw up an ordered list of potential surrogate endpoints for OS in digestive cancer trials, by way of a survey among clinicians and methodologists. Secondary objective was to obtain their opinion on surrogacy and quality of life (QoL)., Methods: In 2007 and 2008, self administered sequential questionnaires were sent to a panel of French clinicians and methodologists involved in the conduct of cancer clinical trials. In the first questionnaire, panellists were asked to choose the most important characteristics defining a surrogate among six proposals, to give advantages and drawbacks of the surrogates, and to answer questions about their validation and use. Then they had to suggest potential surrogate endpoints for OS in each of the following tumour sites: oesophagus, stomach, liver, pancreas, biliary tract, lymphoma, colon, rectum, and anus. They finally gave their opinion on QoL as surrogate endpoint. In the second questionnaire, they had to classify the previously proposed candidate surrogates from the most (position #1) to the least relevant in their opinion.Frequency at which the endpoints were chosen as first, second or third most relevant surrogates was calculated and served as final ranking., Results: Response rate was 30% (24/80) in the first round and 20% (16/80) in the second one. Participants highlighted key points concerning surrogacy. In particular, they reminded that a surrogate endpoint is expected to predict clinical benefit in a well-defined therapeutic situation. Half of them thought it was not relevant to study QoL as surrogate for OS.DFS, in the neoadjuvant settings or early stages, and PFS, in the non operable or metastatic settings, were ranked first, with a frequency of more than 69% in 20 out of 22 settings. PFS was proposed in association with QoL in metastatic primary liver and stomach cancers (both 81%). This composite endpoint was ranked second in metastatic oesophageal (69%), colorectal (56%) and anal (56%) cancers, whereas QoL alone was also suggested in most metastatic situations.Other endpoints frequently suggested were R0 resection in the neoadjuvant settings (oesophagus (69%), stomach (56%), pancreas (75%) and biliary tract (63%)) and response. An unexpected endpoint was metastatic PFS in non operable oesophageal (31%) and pancreatic (44%) cancers. Quality and results of surgical procedures like sphincter preservation were also cited as eligible surrogate endpoints in rectal (19%) and anal (50% in case of localized disease) cancers. Except for alpha-FP kinetic in hepatocellular carcinoma (13%) and CA19-9 decline (6%) in pancreas, few endpoints based on biological or tumour markers were proposed., Conclusion: The overall results should help prioritise the endpoints to be statistically evaluated as surrogate for OS, so that trialists and clinicians can rely on endpoints that ensure relevant clinical benefit to the patient.

In clinical trials, several endpoints (EPs) are often evaluated to compare treatments in some therapeutic area. Suppose that there are two EPs in a clinical trial. We propose a new set of composite hypotheses for continuous variables, taking the relative clinical importance of the EPs into account. The main hypotheses were formulated to show that a treatment is so superior to the control treatment, which is not necessarily a placebo, in one EP, that the possible non-inferiority of the treatment by at most a certain value in the other EP can be compensated sufficiently, taking the clinical point of view into account. The maximum non-inferiority margin of one EP might not be a biologically unimportant difference in exchange for much superiority of the other EP. This formulation leads to a new composite EP and a very simple test statistic. The intersection-union principle was employed to derive the proposed test.

Often a treatment is assessed by co-primary endpoints so that a comprehensive picture of the treatment effect can be obtained. Co-primary endpoints can be different medical assessments angled at different aspects of a disease, therefore, are used collectively to strengthen evidence for the treatment effect. It is common sense that if a treatment is ineffective, the chance to show that the treatment is effective in all co-primary endpoints should be small. Therefore, it may not be necessary to require all the co-primary endpoints to be statistically significant at the 1-sided 0.025 level to control the error rate of wrongly approving an ineffective treatment. Rather it is reasonable to allow certain variation for the p -values within a range close to 0.025. In this paper, statistical methods are developed to derive decision rules to evaluate co-primary endpoints collectively. The decision rules control the error rate of wrongly accepting an ineffective treatment at the level of 0.025 for a study and the error rate at a slightly higher level for a treatment that works for all the co-primary endpoints except perhaps one. The decision rules also control the error rates for individual endpoints. Potential applications in clinical trials are presented., (2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)