Search

ABSTRACT In covariate‐adaptive or response‐adaptive randomization, the treatment assignment and outcome can be correlated. Under this situation, the re‐randomization test is a straightforward and attractive method to provide valid statistical inferences. In this paper, we investigate the number of repetitions in tests. This is motivated by a group sequential design in clinical trials, where the nominal significance bound can be very small at an interim analysis. Accordingly, re‐randomization tests lead to a very large number of required repetitions, which may be computationally intractable. To reduce the number of repetitions, we propose an adaptive procedure and compare it with multiple approaches under predefined criteria. Monte Carlo simulations are conducted to show the performance of different approaches in a limited sample size. We also suggest strategies to reduce total computation time and provide practical guidance in preparing, executing, and reporting before and after data are unblinded at an interim analysis, so one can complete the computation within a reasonable time frame. [ABSTRACT FROM AUTHOR]

Traditional two-arm randomized trial designs have played a pivotal role in establishing the efficacy of medical interventions. However, their efficiency is often compromised when confronted with multiple experimental treatments or limited resources. In response to these challenges, the multi-arm multi-stage designs have emerged, enabling the simultaneous evaluation of multiple treatments within a single trial. In such an approach, if an arm meets efficacy success criteria at an interim stage, the whole trial stops and the arm is selected for further study. However when multiple treatment arms are active, stopping the trial at the moment one arm achieves success diminishes the probability of selecting the best arm. To address this issue, we have developed a group sequential multi-arm multi-stage survival trial design with an arm-specific stopping rule. The proposed method controls the familywise type I error in a strong sense and selects the best promising treatment arm with a high probability. [ABSTRACT FROM AUTHOR]

Under current bioequivalence guidelines in Japan, it is mandatory to establish bioequivalence using a single pivotal study. Clinical trials with limited resources usually have a pre-defined maximum permissible number of participants. In this manuscript, we considered a trial design that would allow for bioequivalence evaluation at an interim analysis in which the total number of participants takes into account the resource constraints. Then, available options at the interim analysis are group sequential designs and adaptive designs, A comparison of the performance of the two methods under same maximum participant number has not been conducted thus far. So we examined which method should be used by conducting a simulation study. Since bioequivalence is expected to be achieved at the interim analysis, a study design using a Pocock-type alpha spending function is preferrable. Simulation results using a Pocock-type alpha spending function showed similar performance between group sequential and adaptive designs. Consequently, due to statistical and operational complexity, it is preferable to choose group sequential designs for bioequivalence study in Japan. [ABSTRACT FROM AUTHOR]

ABSTRACTBackground Traditional vaccine development, often a lengthy and costly process of three separated phases. However, the swift development of COVID-19 vaccines highlighted the critical importance of accelerating the approval of vaccines. This article showcases a seamless phase 2/3 trial design to expedite the development process, particularly for multi-valent vaccines.Research Design and Methods This study utilizes simulation to compare the performance of seamless phase 2/3 design with that of conventional trial design, specifically by re-envisioning a 9-valent HPV vaccine trial. Across three cases, several key performance metrics are evaluated: overall power, type I error rate, average sample size, trial duration, the percentage of early stop, and the accuracy of dose selection.Results On average, when the experimental vaccine was assumed to be effective, the seamless design that performed interim analyses based solely on efficacy saved 555.73 subjects, shortened trials by 10.29 months, and increased power by 3.70%. When the experimental vaccine was less effective than control, it saved an average of 887.73 subjects while maintaining the type I error rate below 0.025.Conclusion The seamless design proves to be a compelling strategy for vaccine development, given its versatility in early stopping, re-estimating sample sizes, and shortening trial durations.

Abstract Background Faced with the high cost and limited efficiency of classical randomized controlled trials, researchers are increasingly applying adaptive designs to speed up the development of new drugs. However, the application of adaptive design to drug randomized controlled trials (RCTs) and whether the reporting is adequate are unclear. Thus, this study aimed to summarize the epidemiological characteristics of the relevant trials and assess their reporting quality by the Adaptive designs CONSORT Extension (ACE) checklist. Methods We searched MEDLINE, EMBASE, Cochrane Central Register of Controlled Trials (CENTRAL) and ClinicalTrials.gov from inception to January 2020. We included drug RCTs that explicitly claimed to be adaptive trials or used any type of adaptative design. We extracted the epidemiological characteristics of included studies to summarize their adaptive design application. We assessed the reporting quality of the trials by Adaptive designs CONSORT Extension (ACE) checklist. Univariable and multivariable linear regression models were used to the association of four prespecified factors with the quality of reporting. Results Our survey included 108 adaptive trials. We found that adaptive design has been increasingly applied over the years, and was commonly used in phase II trials (n = 45, 41.7%). The primary reasons for using adaptive design were to speed the trial and facilitate decision-making (n = 24, 22.2%), maximize the benefit of participants (n = 21, 19.4%), and reduce the total sample size (n = 15, 13.9%). Group sequential design (n = 63, 58.3%) was the most frequently applied method, followed by adaptive randomization design (n = 26, 24.1%), and adaptive dose-finding design (n = 24, 22.2%). The proportion of adherence to the ACE checklist of 26 topics ranged from 7.4 to 99.1%, with eight topics being adequately reported (i.e., level of adherence ≥ 80%), and eight others being poorly reported (i.e., level of adherence ≤ 30%). In addition, among the seven items specific for adaptive trials, three were poorly reported: accessibility to statistical analysis plan (n = 8, 7.4%), measures for confidentiality (n = 14, 13.0%), and assessments of similarity between interim stages (n = 25, 23.1%). The mean score of the ACE checklist was 13.9 (standard deviation [SD], 3.5) out of 26. According to our multivariable regression analysis, later published trials (estimated β = 0.14, p

We investigate the familywise error rate (FWER) for time‐to‐event endpoints evaluated using a group sequential design with a hierarchical testing procedure for secondary endpoints. We show that, in this setup, the correlation between the log‐rank test statistics at interim and at end of study is not congruent with the canonical correlation derived for normal‐distributed endpoints. We show, both theoretically and by simulation, that the correlation also depends on the level of censoring, the hazard rates of the endpoints, and the hazard ratio. To optimize operating characteristics in this complex scenario, we propose a simulation‐based method to assess the FWER which, better than the alpha‐spending approach, can inform the choice of critical values for testing secondary endpoints. [ABSTRACT FROM AUTHOR]

Background: The Bayesian group sequential design has been applied widely in clinical studies, especially in Phase II and III studies. It allows early termination based on accumulating interim data. However, to date, there lacks development in its application to stepped-wedge cluster randomized trials, which are gaining popularity in pragmatic trials conducted by clinical and health care delivery researchers. Methods: We propose a Bayesian adaptive design approach for stepped-wedge cluster randomized trials, which makes adaptive decisions based on the predictive probability of declaring the intervention effective at the end of study given interim data. The Bayesian models and the algorithms for posterior inference and trial conduct are presented. Results: We present how to determine design parameters through extensive simulations to achieve desired operational characteristics. We further evaluate how various design factors, such as the number of steps, cluster size, random variability in cluster size, and correlation structures, impact trial properties, including power, type I error, and the probability of early stopping. An application example is presented. Conclusion: This study presents the incorporation of Bayesian adaptive strategies into stepped-wedge cluster randomized trials design. The proposed approach provides the flexibility to stop the trial early if substantial evidence of efficacy or futility is observed, improving the flexibility and efficiency of stepped-wedge cluster randomized trials. [ABSTRACT FROM AUTHOR]

ABSTRACT In clinical trials with time‐to‐event data, the evaluation of treatment efficacy can be a long and complex process, especially when considering long‐term primary endpoints. Using surrogate endpoints to correlate the primary endpoint has become a common practice to accelerate decision‐making. Moreover, the ethical need to minimize sample size and the practical need to optimize available resources have encouraged the scientific community to develop methodologies that leverage historical data. Relying on the general theory of group sequential design and using a Bayesian framework, the methodology described in this paper exploits a documented historical relationship between a clinical “final” endpoint and a surrogate endpoint to build an informative prior for the primary endpoint, using surrogate data from an early interim analysis of the clinical trial. The predictive probability of success of the trial is then used to define a futility‐stopping rule. The methodology demonstrates substantial enhancements in trial operating characteristics when there is a good agreement between current and historical data. Furthermore, incorporating a robust approach that combines the surrogate prior with a vague component mitigates the impact of the minor prior‐data conflicts while maintaining acceptable performance even in the presence of significant prior‐data conflicts. The proposed methodology was applied to design a Phase III clinical trial in metastatic colorectal cancer, with overall survival as the primary endpoint and progression‐free survival as the surrogate endpoint. [ABSTRACT FROM AUTHOR]

Multi-arm trials are increasingly of interest because for many diseases; there are multiple experimental treatments available for testing efficacy. Several novel multi-arm multi-stage (MAMS) clinical trial designs have been proposed. However, a major hurdle to adopting the group sequential MAMS routinely is the computational effort of obtaining stopping boundaries. For example, the method of Jaki and Magirr for time-to-event endpoint, implemented in R package MAMS, requires complicated computational efforts to obtain stopping boundaries. In this study, we develop a group sequential MAMS survival trial design based on the sequential conditional probability ratio test. The proposed method is an improvement of the Jaki and Magirr's method in the following three directions. First, the proposed method provides explicit solutions for both futility and efficacy boundaries to an arbitrary number of stages and arms. Thus, it avoids complicated computational efforts for the trial design. Second, the proposed method provides an accurate number of events for the fixed sample and group sequential designs. Third, the proposed method uses a new procedure for interim analysis which preserves the study power. [ABSTRACT FROM AUTHOR]

We consider several industry group sequential trials and associated issues over the last 30 years. Generally, group sequential design has provided a great deal of flexibility to overcome many challenges in a relatively straightforward way compared to more complex adaptive designs. Among the issues considered are the timing of and boundaries for interim and final analyses, dealing with multiple hypotheses created by dose groups, populations and endpoints. Tools for design and execution will also be discussed. [ABSTRACT FROM AUTHOR]

Background: Faced with the high cost and limited efficiency of classical randomized controlled trials, researchers are increasingly applying adaptive designs to speed up the development of new drugs. However, the application of adaptive design to drug randomized controlled trials (RCTs) and whether the reporting is adequate are unclear. Thus, this study aimed to summarize the epidemiological characteristics of the relevant trials and assess their reporting quality by the Adaptive designs CONSORT Extension (ACE) checklist. Methods: We searched MEDLINE, EMBASE, Cochrane Central Register of Controlled Trials (CENTRAL) and ClinicalTrials.gov from inception to January 2020. We included drug RCTs that explicitly claimed to be adaptive trials or used any type of adaptative design. We extracted the epidemiological characteristics of included studies to summarize their adaptive design application. We assessed the reporting quality of the trials by Adaptive designs CONSORT Extension (ACE) checklist. Univariable and multivariable linear regression models were used to the association of four prespecified factors with the quality of reporting. Results: Our survey included 108 adaptive trials. We found that adaptive design has been increasingly applied over the years, and was commonly used in phase II trials (n = 45, 41.7%). The primary reasons for using adaptive design were to speed the trial and facilitate decision-making (n = 24, 22.2%), maximize the benefit of participants (n = 21, 19.4%), and reduce the total sample size (n = 15, 13.9%). Group sequential design (n = 63, 58.3%) was the most frequently applied method, followed by adaptive randomization design (n = 26, 24.1%), and adaptive dose-finding design (n = 24, 22.2%). The proportion of adherence to the ACE checklist of 26 topics ranged from 7.4 to 99.1%, with eight topics being adequately reported (i.e., level of adherence ≥ 80%), and eight others being poorly reported (i.e., level of adherence ≤ 30%). In addition, among the seven items specific for adaptive trials, three were poorly reported: accessibility to statistical analysis plan (n = 8, 7.4%), measures for confidentiality (n = 14, 13.0%), and assessments of similarity between interim stages (n = 25, 23.1%). The mean score of the ACE checklist was 13.9 (standard deviation [SD], 3.5) out of 26. According to our multivariable regression analysis, later published trials (estimated β = 0.14, p < 0.01) and the multicenter trials (estimated β = 2.22, p < 0.01) were associated with better reporting. Conclusion: Adaptive design has shown an increasing use over the years, and was primarily applied to early phase drug trials. However, the reporting quality of adaptive trials is suboptimal, and substantial efforts are needed to improve the reporting. [ABSTRACT FROM AUTHOR]

Abstract Background Group sequential designs incorporating the option to stop for futility at the time point of an interim analysis can save time and resources. Thereby, the choice of the futility boundary importantly impacts the design’s resulting performance characteristics, including the power and probability to correctly or wrongly stop for futility. Several authors contributed to the topic of selecting good futility boundaries. For binary endpoints, Simon’s designs (Control Clin Trials 10:1–10, 1989) are commonly used two-stage designs for single-arm phase II studies incorporating futility stopping. However, Simon’s optimal design frequently yields an undesirably high probability of falsely declaring futility after the first stage, and in Simon’s minimax design often a high proportion of the planned sample size is already evaluated at the interim analysis leaving only limited benefit in case of an early stop. Methods This work focuses on the optimality criteria introduced by Schüler et al. (BMC Med Res Methodol 17:119, 2017) and extends their approach to binary endpoints in single-arm phase II studies. An algorithm for deriving optimized futility boundaries is introduced, and the performance of study designs implementing this concept of optimal futility boundaries is compared to the common Simon’s minimax and optimal designs, as well as modified versions of these designs by Kim et al. (Oncotarget 10:4255–61, 2019). Results The introduced optimized futility boundaries aim to maximize the probability of correctly stopping for futility in case of small or opposite effects while also setting constraints on the time point of the interim analysis, the power loss, and the probability of stopping the study wrongly, i.e. stopping the study even though the treatment effect shows promise. Overall, the operating characteristics, such as maximum sample size and expected sample size, are comparable to those of the classical and modified Simon’s designs and sometimes better. Unlike Simon’s designs, which have binding stopping rules, the optimized futility boundaries proposed here are not adjusted to exhaust the full targeted nominal significance level and are thus still valid for non-binding applications. Conclusions The choice of the futility boundary and the time point of the interim analysis have a major impact on the properties of the study design. Therefore, they should be thoroughly investigated at the planning stage. The introduced method of selecting optimal futility boundaries provides a more flexible alternative to Simon’s designs with non-binding stopping rules. The probability of wrongly stopping for futility is minimized and the optimized futility boundaries don’t exhibit the unfavorable properties of an undesirably high probability of falsely declaring futility or a high proportion of the planned sample evaluated at the interim time point.

Conditional power (CP) serves as a widely utilized approach for futility monitoring in group sequential designs. However, adopting the CP methods may lead to inadequate control of the type II error rate at the desired level. In this study, we introduce a flexible beta spending function tailored to regulate the type II error rate while employing CP based on a predetermined standardized effect size for futility monitoring (a so‐called CP‐beta spending function). This function delineates the expenditure of type II error rate across the entirety of the trial. Unlike other existing beta spending functions, the CP‐beta spending function seamlessly incorporates beta spending concept into the CP framework, facilitating precise stagewise control of the type II error rate during futility monitoring. In addition, the stopping boundaries derived from the CP‐beta spending function can be calculated via integration akin to other traditional beta spending function methods. Furthermore, the proposed CP‐beta spending function accommodates various thresholds on the CP‐scale at different stages of the trial, ensuring its adaptability across different information time scenarios. These attributes render the CP‐beta spending function competitive among other forms of beta spending functions, making it applicable to any trials in group sequential designs with straightforward implementation. Both simulation study and example from an acute ischemic stroke trial demonstrate that the proposed method accurately captures expected power, even when the initially determined sample size does not consider futility stopping, and exhibits a good performance in maintaining overall type I error rates for evident futility. [ABSTRACT FROM AUTHOR]

Background: Group sequential designs incorporating the option to stop for futility at the time point of an interim analysis can save time and resources. Thereby, the choice of the futility boundary importantly impacts the design's resulting performance characteristics, including the power and probability to correctly or wrongly stop for futility. Several authors contributed to the topic of selecting good futility boundaries. For binary endpoints, Simon's designs (Control Clin Trials 10:1–10, 1989) are commonly used two-stage designs for single-arm phase II studies incorporating futility stopping. However, Simon's optimal design frequently yields an undesirably high probability of falsely declaring futility after the first stage, and in Simon's minimax design often a high proportion of the planned sample size is already evaluated at the interim analysis leaving only limited benefit in case of an early stop. Methods: This work focuses on the optimality criteria introduced by Schüler et al. (BMC Med Res Methodol 17:119, 2017) and extends their approach to binary endpoints in single-arm phase II studies. An algorithm for deriving optimized futility boundaries is introduced, and the performance of study designs implementing this concept of optimal futility boundaries is compared to the common Simon's minimax and optimal designs, as well as modified versions of these designs by Kim et al. (Oncotarget 10:4255–61, 2019). Results: The introduced optimized futility boundaries aim to maximize the probability of correctly stopping for futility in case of small or opposite effects while also setting constraints on the time point of the interim analysis, the power loss, and the probability of stopping the study wrongly, i.e. stopping the study even though the treatment effect shows promise. Overall, the operating characteristics, such as maximum sample size and expected sample size, are comparable to those of the classical and modified Simon's designs and sometimes better. Unlike Simon's designs, which have binding stopping rules, the optimized futility boundaries proposed here are not adjusted to exhaust the full targeted nominal significance level and are thus still valid for non-binding applications. Conclusions: The choice of the futility boundary and the time point of the interim analysis have a major impact on the properties of the study design. Therefore, they should be thoroughly investigated at the planning stage. The introduced method of selecting optimal futility boundaries provides a more flexible alternative to Simon's designs with non-binding stopping rules. The probability of wrongly stopping for futility is minimized and the optimized futility boundaries don't exhibit the unfavorable properties of an undesirably high probability of falsely declaring futility or a high proportion of the planned sample evaluated at the interim time point. [ABSTRACT FROM AUTHOR]

Adaptive designs, such as group sequential designs (and the ones with additional adaptive features) or adaptive platform trials, have been quintessential efficient design strategies in trials of unmet medical needs, especially for generating evidence from global regions. Such designs allow interim decision making and making adjustment to study design when necessary, meanwhile maintaining study integrity and operating characteristics. However, driven by the heightened competitive landscape and the desire to bring effective treatment to patients faster, innovation in the already functional designs is still germane to further propel drug development to a more efficient path. One way to achieve this is by leveraging external real-world data (RWD) in the adaptive designs to support interim or final decision making. In this paper, we propose a novel framework of incorporating external RWD in adaptive design to improve interim and/or final analysis decision making. Within this framework, researchers can prespecify the decision process and choose the timing and amount of borrowing while maintaining objectivity and controlling of type I error. Simulation studies in various scenarios are provided to describe power, type I error, and other performance metrics for interim/final decision making. A case study in non-small cell lung cancer is used for illustration on proposed design framework. [ABSTRACT FROM AUTHOR]

AbstractGroup sequential tests have been effective tools in monitoring long term clinical trials. There have been several popular discrete sequential boundaries proposed for modeling interim analysis of clinical trials under the assumption of Brownian motion for the stochastic processes generated from test statistics. In this paper, we study five sequential boundaries under the fractional Brownian motion. The fractional Brownian includes the classic Brownian motion as a special case. We proposed a Bayesian method on how to estimate Hurst parameter, used simulated data to investigate the performance of boundary-based hypothesis-testing under either Bm or fBm assumption in both with and without “treatment effect” scenarios. [ABSTRACT FROM AUTHOR]

Cancer immunotherapy trials are frequently characterized by delayed treatment effects such that the proportional hazards assumption is violated and the log-rank test suffers a substantial loss of statistical power. To increase the efficacy of the trial design, a variety of weighted log-rank tests have been proposed for fixed sample and group sequential trial designs. However, in such a group sequential design, it is often not recommended for futility interim monitoring due to possible delayed treatment effect which could result a high false-negative rate. To resolve this problem, we propose a group sequential design using a piecewise weighted log-rank test which provides an event-driven approach based on number of events after the delayed time. That is, the interim looks will not be conducted until the planned number of events observed after the delay time. Thus, it avoids the possibility of false-negative rate due to the delayed treatment effect. Furthermore, with an event-driven approach, the proposed group sequential design is robust against the underlying survival, accrual and censoring distributions. The group sequential designs using Fleming-Harrington-($$\rho ,\gamma $$ ρ , γ) weighted log-rank test and a new weighted log-rank test are also discussed. [ABSTRACT FROM AUTHOR]

The 2-in-1 adaptive design (Chen et al. 2018) allows seamless expansion of an ongoing Phase 2 trial into a Phase 3 trial to expedite a drug development program. Under a mild assumption expected to generally hold in practice, as Slepian's lemma guarantees, the trial can be tested at the full alpha level with or without expansion, sacrificing no statistical power. The endpoint used for expansion decisions can be the same as or different from the primary endpoints, and there is no restriction on the expansion threshold. Due to its flexibility and robustness, it has drawn immediate attention from academic researchers and industry practitioners. The design has been substantially extended in the literature and successfully implemented in multiple trials. Group sequential methods are a cornerstone in trial monitoring. A preliminary investigation (Chen, Li, and Deng) suggests that it can be naturally incorporated into the 2-in-1 design without providing formal mathematical proof. In this article, we fill the gap by providing a sufficient condition that is expected to generally hold in practice to unlock the full potential of the 2-in-1 design and pave the way for its broader applications. In practice, the condition can be verified with trial data as needed using simulation studies per the FDA guideline on adaptive designs. We also discuss a special case that guarantees the validity without the need for any simulation checking. [ABSTRACT FROM AUTHOR]

Cancer immunotherapy trials are frequently characterized by a delayed treatment effect that violates the proportional hazards assumption. The log-rank test (LRT) suffers a substantial loss of statistical power under the nonproportional hazards model. Various group sequential designs using weighted LRTs (WLRTs) have been proposed under the fixed delayed treatment effect model. However, patients enrolled in immunotherapy trials are often heterogeneous, and the duration of the delayed treatment effect is a random variable. Therefore, we propose group sequential designs under the random delayed effect model using the random delayed distribution WLRT. The proposed group sequential designs are developed for monitoring the efficacy of the trial using the method of Lan-DeMets alpha-spending function with O’Brien-Fleming stopping boundaries or a gamma family alpha-spending function. The maximum sample size for the group sequential design is obtained by multiplying an inflation factor with the sample size for the fixed sample design. Simulations are conducted to study the operating characteristics of the proposed group sequential designs. The robustness of the proposed group sequential designs for misspecifying random delay time distribution and domain is studied via simulations. [ABSTRACT FROM AUTHOR]

Abstract Background Adaptive clinical trials are growing in popularity as they are more flexible, efficient and ethical than traditional fixed designs. However, notwithstanding their increased use in assessing treatments for COVID-19, their use in critical care trials remains limited. A better understanding of the relative benefits of various adaptive designs may increase their use and interpretation. Methods Using two large critical care trials (ADRENAL. ClinicalTrials.gov number, NCT01448109. Updated 12-12-2017; NICE-SUGAR. ClinicalTrials.gov number, NCT00220987. Updated 01-29-2009), we assessed the performance of three frequentist and two bayesian adaptive approaches. We retrospectively re-analysed the trials with one, two, four, and nine equally spaced interims. Using the original hypotheses, we conducted 10,000 simulations to derive error rates, probabilities of making an early correct and incorrect decision, expected sample size and treatment effect estimates under the null scenario (no treatment effect) and alternative scenario (a positive treatment effect). We used a logistic regression model with 90-day mortality as the outcome and the treatment arm as the covariate. The null hypothesis was tested using a two-sided significance level (α) at 0.05. Results Across all approaches, increasing the number of interims led to a decreased expected sample size. Under the null scenario, group sequential approaches provided good control of the type-I error rate; however, the type I error rate inflation was an issue for the Bayesian approaches. The Bayesian Predictive Probability and O’Brien-Fleming approaches showed the highest probability of correctly stopping the trials (around 95%). Under the alternative scenario, the Bayesian approaches showed the highest overall probability of correctly stopping the ADRENAL trial for efficacy (around 91%), whereas the Haybittle-Peto approach achieved the greatest power for the NICE-SUGAR trial. Treatment effect estimates became increasingly underestimated as the number of interims increased. Conclusions This study confirms the right adaptive design can reach the same conclusion as a fixed design with a much-reduced sample size. The efficiency gain associated with an increased number of interims is highly relevant to late-phase critical care trials with large sample sizes and short follow-up times. Systematically exploring adaptive methods at the trial design stage will aid the choice of the most appropriate method.

In vitro permeation tests (IVPT) offer accurate and cost‐effective development pathways for locally acting drugs, such as topical dermatological products. For assessment of bioequivalence, the FDA draft guidance on generic acyclovir 5% cream introduces a new experimental design, namely the single‐dose, multiple‐replicate per treatment group design, as IVPT pivotal study design. We examine the statistical properties of its hypothesis testing method—namely the mixed scaled average bioequivalence (MSABE). Meanwhile, some adaptive design features in clinical trials can help researchers make a decision earlier with fewer subjects or boost power, saving resources, while controlling the impact on family‐wise error rate. Therefore, we incorporate MSABE in an adaptive design combining the group sequential design and sample size re‐estimation. Simulation studies are conducted to study the passing rates of the proposed methods—both within and outside the average bioequivalence limits. We further consider modifications to the adaptive designs applied for IVPT BE trials, such as Bonferroni's adjustment and conditional power function. Finally, a case study with real data demonstrates the advantages of such adaptive methods. [ABSTRACT FROM AUTHOR]

Background: Adaptive clinical trials are growing in popularity as they are more flexible, efficient and ethical than traditional fixed designs. However, notwithstanding their increased use in assessing treatments for COVID-19, their use in critical care trials remains limited. A better understanding of the relative benefits of various adaptive designs may increase their use and interpretation. Methods: Using two large critical care trials (ADRENAL. ClinicalTrials.gov number, NCT01448109. Updated 12-12-2017; NICE-SUGAR. ClinicalTrials.gov number, NCT00220987. Updated 01-29-2009), we assessed the performance of three frequentist and two bayesian adaptive approaches. We retrospectively re-analysed the trials with one, two, four, and nine equally spaced interims. Using the original hypotheses, we conducted 10,000 simulations to derive error rates, probabilities of making an early correct and incorrect decision, expected sample size and treatment effect estimates under the null scenario (no treatment effect) and alternative scenario (a positive treatment effect). We used a logistic regression model with 90-day mortality as the outcome and the treatment arm as the covariate. The null hypothesis was tested using a two-sided significance level (α) at 0.05. Results: Across all approaches, increasing the number of interims led to a decreased expected sample size. Under the null scenario, group sequential approaches provided good control of the type-I error rate; however, the type I error rate inflation was an issue for the Bayesian approaches. The Bayesian Predictive Probability and O'Brien-Fleming approaches showed the highest probability of correctly stopping the trials (around 95%). Under the alternative scenario, the Bayesian approaches showed the highest overall probability of correctly stopping the ADRENAL trial for efficacy (around 91%), whereas the Haybittle-Peto approach achieved the greatest power for the NICE-SUGAR trial. Treatment effect estimates became increasingly underestimated as the number of interims increased. Conclusions: This study confirms the right adaptive design can reach the same conclusion as a fixed design with a much-reduced sample size. The efficiency gain associated with an increased number of interims is highly relevant to late-phase critical care trials with large sample sizes and short follow-up times. Systematically exploring adaptive methods at the trial design stage will aid the choice of the most appropriate method. [ABSTRACT FROM AUTHOR]

Traditional methods based on the assumption that the treatment distribution is a pure shift of the control distribution may not always hold. The possibility that an individual from the treatment group may not respond to the treatment motivates the use of a mixture distribution for the treatment group. This paper considers two test procedures based on the Wilcoxon rank-sum statistic for a group sequential design to detect the one-sided mixture alternative. Error spending functions are used for the allocation of error rates at each stage. The two tests are evaluated individually in determination of critical values and arm sizes and asymptotic multivariate normality is shown to hold for both. Upon comparison, the tests are presented to be asymptotically equivalent. Both test statistics maintain the Type I error rate even if F is misspecified in the design alternative. A more general definition of the treatment effect is used with the mixture distribution. Method of moments estimators and constrained k -means estimators for the treatment effect are evaluated. [ABSTRACT FROM AUTHOR]

A multi-armed trial based on ordinal outcomes is proposed that leverages a flexible non-proportional odds cumulative logit model and numerical utility scores for each outcome to determine treatment optimality. This trial design uses a Bayesian clustering prior on the treatment effects that encourages the pairwise null hypothesis of no differences between treatments. A group sequential design is proposed to determine which treatments are clinically different with an adaptive decision boundary that becomes more aggressive as the sample size or clinical significance grows, or the number of active treatments decreases. A simulation study is conducted for 3 and 5 treatment arms, which shows that the design has superior operating characteristics (family wise error rate, generalized power, average sample size) compared to utility designs that do not allow clustering, a frequentist proportional odds model, or a permutation test based on empirical mean utilities. [ABSTRACT FROM AUTHOR]

近年来，成组序贯设计因其可在期中分析时提前得出结论结束试验，具有更强的灵活性，已被广泛应用于临床试验中。本文将从背景、设计思路、与传统临床试验的比较、使用场景、案例解读、设计要点和报告规范等对该方法进行简单介绍。 Abstract: In recent years, the group sequential design has been widely used in clinical trials, because this design can draw conclusions in advance and end the trial during the interim analysis, which has greater flexibility. This article briefly introduced this design method from the following aspects of background, design procedure, comparison with traditional clinical trials, application scenarios, case analysis, the key points of design, and reporting standards.

A multi‐arm trial allows simultaneous comparison of multiple experimental treatments with a common control and provides a substantial efficiency advantage compared to the traditional randomized controlled trial. Many novel multi‐arm multi‐stage (MAMS) clinical trial designs have been proposed. However, a major hurdle to adopting the group sequential MAMS routinely is the computational effort of obtaining total sample size and sequential stopping boundaries. In this paper, we develop a group sequential MAMS trial design based on the sequential conditional probability ratio test. The proposed method provides analytical solutions for futility and efficacy boundaries to an arbitrary number of stages and arms. Thus, it avoids complicated computational effort for the methods proposed by Magirr et al. Simulation results showed that the proposed method has several advantages compared to the methods implemented in R package MAMS by Magirr et al. [ABSTRACT FROM AUTHOR]

For safety studies, two types of hypothesis testing are often considered: detecting a safety signal and ruling out a safety concern. Under the detecting framework, statistical non-significance is often confused with the conclusion that there is no safety concern. Such a conclusion, in the presence of low study power or large variability, is problematic. To overcome the interpretation issue with non-significant results from a detecting hypothesis, we propose a Two-Stage Decision-Making (TSDM) approach for safety studies. It is basically a ruling-out design allowing an interim analysis that applies both detecting and ruling-out criteria at the interim and final stages with a pre-specified alpha spending function. The proposed TSDM approach incorporates both detecting a safety signal and ruling out safety concerns into a single study design to increase the probability of making a definite decision. It is based on the ruling-out framework that utilizes both directions of the confidence interval to make a decision for ruling out unacceptable risk or detecting safety signal at each analysis stage. We assess the proposed TSDM approach by investigating properties such as operational type I error rate, overall study power based on analytical approximations, overall probability of making a decision, and required sample sizes. We conduct Monte Carlo simulations to evaluate such properties regarding various outcome types of confidence intervals and summarize the statistical interpretations and the implications on study design. [ABSTRACT FROM AUTHOR]

In late 2019, the U.S. FDA updated a new Guidance for Industry on Adaptive Designs for Clinical Trials of Drugs and Biologics. The guideline encourages developing and implementing innovative trial designs for future clinical trials. Group sequential, sample size re-estimation, and adaptive group sequential procedures have been very useful for improving the efficiency of conducting trials for decades. However, they face some challenges in operational aspects which limited their potentials. In this article, we introduce a procedure that addresses these issues. Our proposed procedure has the capability of providing anytime accessibility of the whole up-to-date data history. The procedure is largely built on the proven adaptive group sequential design theories and combined with advanced eClinical technologies in trial management to elevate the trial design and monitoring to a more dynamic level. The construct of a new trial monitoring screen is illustrated with real trial examples. The advantages of anytime accessibility of data and the monitoring a trial with the whole data history and trend are delineated. Data monitoring committees, sponsors and regulatory authorities are important stakeholders in the discussion of how future clinical trials should be monitored with respect to timing and frequency. [ABSTRACT FROM AUTHOR]

Group sequential design (GSD) has become a popular choice in recent clinical trials as it improves trial efficiency by providing options for early termination. The implementation of traditional tests for survival analysis (eg, the log‐rank test and the Cox proportional hazard (PH) model) in the GSD setting has been widely discussed. The PH assumption is required for conventional (sequential) design, it is, however, often violated in practice. As an alternative, some generalized tests have been proposed (eg, the Max‐Combo test) and their efficacies have been established. In this article, we explore the application of a more flexible, "first hitting time" based threshold regression (TR) model to GSD. TR assumes that subjects' health status is a latent (unobservable) process, and the clinical event of interest occurs when the latent health process hits a pre‐specified boundary. The simulation results supported our findings that, in most cases, this comparable new method can successfully control type I error while providing higher early stopping opportunities in the sequential design, even when non‐proportional hazard presents. [ABSTRACT FROM AUTHOR]

Randomized clinical trials in oncology typically utilize time‐to‐event endpoints such as progression‐free survival or overall survival as their primary efficacy endpoints, and the most commonly used statistical test to analyze these endpoints is the log‐rank test. The power of the log‐rank test depends on the behavior of the hazard ratio of the treatment arm to the control arm. Under the assumption of proportional hazards, the log‐rank test is asymptotically fully efficient. However, this proportionality assumption does not hold true if there is a delayed treatment effect. Cancer immunology has evolved over time and several cancer vaccines are available in the market for treating existing cancers. This includes sipuleucel‐T for metastatic hormone‐refractory prostate cancer, nivolumab for metastatic melanoma, and pembrolizumab for advanced nonsmall‐cell lung cancer. As cancer vaccines require some time to elicit an immune response, a delayed treatment effect is observed, resulting in a violation of the proportional hazards assumption. Thus, the traditional log‐rank test may not be optimal for testing immuno‐oncology drugs in randomized clinical trials. Moreover, the new immuno‐oncology compounds have been shown to be very effective in prolonging overall survival. Therefore, it is desirable to implement a group sequential design with the possibility of early stopping for overwhelming efficacy. In this paper, we investigate the max‐combo test, which utilizes the maximum of two weighted log‐rank statistics, as a robust alternative to the log‐rank test. The new test is implemented for two‐stage designs with possible early stopping at the interim analysis time point. Two classes of weights are investigated for the max‐combo test: the Fleming and Harrington (1981) Gρ,γ$G^{\rho , \gamma }$weights and the Magirr and Burman (2019) modest (τ∗)$ (\tau ^{*})$ weights. [ABSTRACT FROM AUTHOR]

Abstract Background In clinical trials with fixed study designs, statistical inference is only made when the trial is completed. In contrast, group sequential designs allow an early stopping of the trial at interim, either for efficacy when the treatment effect is significant or for futility when the treatment effect seems too small to justify a continuation of the trial. Efficacy stopping boundaries based on alpha spending functions have been widely discussed in the statistical literature, and there is also solid work on the choice of adequate futility stopping boundaries. Still, futility boundaries are often chosen with little or completely without theoretical justification, in particular in investigator initiated trails. Some authors contributed to fill this gap. In here, we rely on an idea of Schüler et al. (2017) who discuss optimality criteria for futility boundaries for the special case of trials with (multiple) time-to-event endpoints. Their concept can be adopted to define “optimal” futility boundaries (with respect to given performance indicators) for continuous endpoints. Methods We extend Schülers’ definition for “optimal” futility boundaries to the most common study situation of a single continuous primary endpoint compared between two groups. First, we introduce the analytic algorithm to derive these futility boundaries. Second, the new concept is applied to a real clinical trial example. Finally, the performance of a study design with an “optimal” futility boundary is compared to designs with arbitrarily chosen futility boundaries. Results The presented concept of deriving futility boundaries allows to control the probability of wrongly stopping for futility, that means stopping for futility even if the treatment effect is promizing. At the same time, the loss in power is also controlled by this approach. Moreover, “optimal” futility boundaries improve the probability of correctly stopping for futility under the null hypothesis of no difference between two groups. Conclusions The choice of futility boundaries should be thoroughly investigated at the planning stage. The sometimes met, arbitrary choice of futility boundaries can lead to a substantial negative impact on performance. Applying futility boundaries with predefined optimization criteria increases efficiency of group sequential designs. Other optimization criteria than proposed in here might be incorporated.

Non‐proportional hazards (NPH) have been observed in many immuno‐oncology clinical trials. Weighted log‐rank tests (WLRT) with suitable weights can be used to improve the power of detecting the difference between survival curves in the presence of NPH. However, it is not easy to choose a proper WLRT in practice. A versatile max‐combo test was proposed to achieve the balance of robustness and efficiency, and has received increasing attention recently. Survival trials often warrant interim analyses due to their high cost and long durations. The integration and implementation of max‐combo tests in interim analyses often require extensive simulation studies. In this report, we propose a simulation‐free approach for group sequential designs with the max‐combo test in survival trials. The simulation results support that the proposed method can successfully control the type I error rate and offer excellent accuracy and flexibility in estimating sample sizes, with light computation burden. Notably, our method displays strong robustness towards various model misspecifications and has been implemented in an R package. [ABSTRACT FROM AUTHOR]

Group sequential designs with multiple endpoints are widely used in clinical trials and medical research. In the literature of group sequential designs with a single primary hypothesis, it was recommended to calculate the critical boundary for a symmetric non-directional two-sided test at the significance level α by constructing a one-sided critical boundary at the significance level α / 2 . As a natural but unvalidated extension, researchers may think the same conclusion holds for testing multiple endpoints in group sequential designs, that is, the critical boundary calculated to control the type I error at level α / 2 for one-sided test also controls the type I error at level α for non-directional two-sided tests. In this paper, we demonstrate that using one-sided α / 2 -level critical boundaries for non-directional two-sided α -level tests leads to notable and unnecessary conservativeness when multiple endpoints are hierarchically tested in group sequential designs. To the best of our knowledge, we are the first to reveal the relationship between the type I error rates of the two-sided and one-sided tests in hierarchical testing of multiple endpoints in group sequential designs. We consider three commonly used hierarchical structures for the primary and secondary endpoints, namely the stagewise hierarchical, overall hierarchical, and partially hierarchical structures. Under all three hierarchical structures, we refine the critical boundary for the secondary hypothesis. In addition, we prove that our boundary refinement methods yield enhanced statistical power. The proposed methodology is illustrated using a randomized clinical trial examining the effect of energy-reduced diets with different macronutrient compositions on body weight. [ABSTRACT FROM AUTHOR]

In this article, we illustrate the method of designing a group-sequential randomized clinical trial based on the difference in restricted mean survival time (RMST). The procedure is based on theoretical formulations of Murray and Tsiatis. We also present a numerical example in designing a cardiology surgical trial. Various practical considerations are discussed. R codes are provided in the . We conclude that the group-sequential design for RMST is a viable option in practice. A simulation study is performed to compare the proposed method to the Max-Combo and conventional log-rank tests. The simulation result shows that when there is a delayed treatment benefit and the proportional hazards assumption is untrue, the sequential design based on the RMST can be more efficient than that based on the log-rank test but less efficient than that based on the Max-Combo test. Compared with Max-Combo test, the RMST-based study design yield coherent estimand, statistical inference and result interpretation. [ABSTRACT FROM AUTHOR]

A delayed treatment effect is often observed in the confirmatory trials for immunotherapies and is reflected by a delayed separation of the survival curves of the immunotherapy groups versus the control groups. This phenomenon makes the design based on the log-rank test not applicable because this design would violate the proportional hazard assumption and cause loss of power. Thus, we propose a group sequential design allowing early termination on the basis of efficacy based on a more powerful piecewise weighted log-rank test for an immunotherapy trial with a delayed treatment effect. We present an approach on the group sequential monitoring, in which the information time is defined based on the number of events occurring after the delay time. Furthermore, we developed a one-dimensional search algorithm to determine the required maximum sample size for the proposed design, which uses an analytical estimation obtained by the inflation factor as an initial value and an empirical power function calculated by a simulation-based procedure as an objective function. In the simulation, we tested the unstable accuracy of the analytical estimation, the consistent accuracy of the maximum sample size determined by the search algorithm and the advantages of the proposed design on saving sample size. [ABSTRACT FROM AUTHOR]

Objectives: To investigate the design, conduct, and analysis of adaptive trials through a systematic survey and provide recommendations for future adaptive trials., Study Design and Setting: We systematically searched MEDLINE, EMBASE, Cochrane Central Register of Controlled Trials, and ClinicalTrials.gov databases up to January 2020. We included trials that were self-described as adaptive trials or applied adaptive designs. We identified three frequently used adaptive designs and summarized their methodological details in terms of design, conduct, and analysis. Lastly, we provided recommendations for future adaptive trials., Results: We included a total of 128 trials in this study. The primary motivations for using adaptive design were to speed up the trials and facilitate decision-making (n = 29, 31.5%). The three most frequently used methods were group sequential design (GSD) (n = 71, 55.5%), adaptive dose-finding design (ADFD) (n = 35, 27.3%), and adaptive randomization design (ARD) (n = 26, 20.3%). The timing and frequency of interim analysis were detailed in three-fourths of the GSD trials (n = 55, 77.5%) and in half of the ADFD trials (n = 19, 54.3%); however, more than half of the ARD trials (n = 15, 57.7%) did not provide this information. Some trials selected a different outcome than the primary outcome for interim analysis (GSD: n = 7, 12.7%; ADFD: n = 8, 27.6%; ARD: n = 7, 50.0%), but the majority of these trials did not provide explicit reasons for this choice (GSD: n = 7, 100.0%; ADFD: n = 7, 87.5%; ARD: n = 5, 71.4%). More than half (n = 76, 59.4%) of trials did not mention the accessibility of supporting documents, and two-thirds (n = 86, 67.2%) did not state the establishment of independent data monitoring committees (IDMCs). Moreover, unplanned adjustments were observed during the conduct of one-sixth adaptive trials (n = 22, 17.2%). Based on our findings, we provide 14 recommendations for improving adaptive trials in the future., Conclusion: Substantial improvements were needed in methods of adaptive trials, particularly in the areas of interim analysis, the establishment of independent data monitoring committees, and unplanned adjustments. In this study, we offer recommendations from both general and specific aspects for researchers to carefully design, conduct, and analyze adaptive trials., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier Inc. All rights reserved.)

An important step in the development of targeted therapies is the identification and confirmation of sub-populations where the treatment has a positive treatment effect compared to a control. These sub-populations are often based on continuous biomarkers, measured at baseline. For example, patients can be classified into biomarker low and biomarker high subgroups, which are defined via a threshold on the continuous biomarker. However, if insufficient information on the biomarker is available, the a priori choice of the threshold can be challenging and it has been proposed to consider several thresholds and to apply appropriate multiple testing procedures to test for a treatment effect in the corresponding subgroups controlling the family-wise type 1 error rate. In this manuscript we propose a framework to select optimal thresholds and corresponding optimized multiple testing procedures that maximize the expected power to identify at least one subgroup with a positive treatment effect. Optimization is performed over a prior on a family of models, modelling the relation of the biomarker with the expected outcome under treatment and under control. We find that for the considered scenarios 3 to 4 thresholds give the optimal power. If there is a prior belief on a small subgroup where the treatment has a positive effect, additional optimization of the spacing of thresholds may result in a large benefit. The procedure is illustrated with a clinical trial example in depression. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has led to an unprecedented response in terms of clinical research activity. An important part of this research has been focused on randomized controlled clinical trials to evaluate potential therapies for COVID-19. The results from this research need to be obtained as rapidly as possible. This presents a number of challenges associated with considerable uncertainty over the natural history of the disease and the number and characteristics of patients affected, and the emergence of new potential therapies. These challenges make adaptive designs for clinical trials a particularly attractive option. Such designs allow a trial to be modified on the basis of interim analysis data or stopped as soon as sufficiently strong evidence has been observed to answer the research question, without compromising the trial's scientific validity or integrity. In this article, we describe some of the adaptive design approaches that are available and discuss particular issues and challenges associated with their use in the pandemic setting. Our discussion is illustrated by details of four ongoing COVID-19 trials that have used adaptive designs. [ABSTRACT FROM AUTHOR]

Abstract–The aim of this work is to present an adaptive two-stage seamless design for a Phase II/III clinical trial in chronic obstructive pulmonary disease (COPD). This approach implies sample size re-estimation based on the primary outcome efficacy variable, namely the annual acute exacerbation rate. Patient recruitment in COPD trials can be slow; the proposed statistical approach may allow for a faster completion of the trial by reducing the time between interim analysis (IA) (Phase II) and new recruitment (Phase III). In addition, an adaptive design with re-estimation of the sample size during the study may increase its likelihood of success, especially in cases where estimated interim vaccine efficacy is lower than expected. By applying the proposed approach, at the time of the IA (end of Phase II), a decision can be taken to stop the trial for futility, to continue the trial (by advancing to Phase III) with the planned sample size or to continue the study and increase the sample size. We carried out simulations to evaluate the performance of the method. [ABSTRACT FROM AUTHOR]

Medical research frequently involves comparing an event time of interest between treatment groups. Rather than comparing the entire survival or cumulative incidence curves, it is sometimes preferable to evaluate these probabilities at a fixed point in time. Performing a covariate adjusted analysis can improve efficiency, even in randomized clinical trials, but no currently available group sequential test for fixed point analysis provides this adjustment. This paper introduces covariate adjusted group sequential pointwise comparisons of survival and cumulative incidence probabilities. Their test statistics have an asymptotic distribution with independent increments, permitting use of common stopping boundary specification methods. These tests are demonstrated through a redesign of BMT CTN 0402, a clinical trial that evaluated a prophylactic treatment for adverse outcomes following blood and marrow transplantation. A simulation study demonstrates that these tests maintain the type I error rate and power at nominal levels under a variety of settings involving influential covariates. [ABSTRACT FROM AUTHOR]

Clinical studies of predictive diagnostic tests consider the evaluation of a single test and comparison of two tests regarding their predictive accuracy of disease status. The positive predictive value (PPV) curve is used for assessing the probability of predicting the disease given a positive test result. The sequential property of one PPV curve had been studied. However, in later stages of diagnostic test development, it is more interesting to compare predictive accuracy of two tests. In this article, we propose a group sequential test for the comparison of PPV curves for paired designs when both diagnostic tests are applied to the same subject. We first derive asymptotic properties of the sequential differences of two correlated empirical PPV curves under the common case-control sampling. We then apply these results to develop a group sequential test procedure. The asymptotic results are also critical for deriving both the optimal sample size ratio and minimal required sample sizes for the proposed procedure. Our simulation studies show that the proposed sequential testing maintains the nominal type I error rate in finite samples. The proposed design is illustrated in a hypothetical lung cancer predictive trial and in a cancer diagnostic trial. [ABSTRACT FROM AUTHOR]

Multiple testing problems are often seen in clinical trials. An appropriate testing procedure should be specified to deal with the potential inflation of type I error rate due to multiplicity. In this article, we propose a stepwise progressive parametric multiple (SPPM) testing procedure, which constructs the testing using the products of all the combinations of local p -values and the critical values are determined by numerical integrations progressively using the closure principle. We have compared the performance of SPPM to several other procedures, and demonstrate the advantage of SPPM procedure, in terms of power, for the certain situations of multiple testing. [ABSTRACT FROM AUTHOR]

Background/aims: In a stepped wedge study design, study clusters usually start with the baseline treatment and then cross over to the intervention at randomly determined times. Such designs are useful when the intervention must be delivered at the cluster level and are becoming increasingly common in practice. In these trials, if the outcome is death or serious morbidity, one may have an ethical imperative to monitor the trial and stop before maximum enrollment if the new therapy is proven to be beneficial. In addition, because formal monitoring allows for the stoppage of trials when a significant benefit for new therapy has been ruled out, their use can make a research program more efficient. However, use of the stepped wedge cluster randomized study design complicates the implementation of standard group sequential monitoring methods. Both the correlation of observations introduced by the clustered randomization and the timing of crossover from one treatment to the other impact the rate of information growth, an important component of an interim analysis. Methods: We simulated cross-sectional stepped wedge study data in order to evaluate the impact of sequential monitoring on the Type I error and power when the true intracluster correlation is unknown. We studied the impact of varying intracluster correlations, treatment effects, methods of estimating the information growth, and boundary shapes. Results: While misspecified information growth can impact both the Type I error and power of a study in some settings, we observed little inflation of the Type I error and only moderate reductions in power across a range of misspecified information growth patterns in our simulations. Conclusion: Taking the study design into account and using either an estimate of the intracluster correlation from the ongoing study or other data in the same clusters should allow for easy implementation of group sequential methods in future stepped wedge designs. [ABSTRACT FROM AUTHOR]

Group sequential designs using Lan-DeMets error spending functions are proposed for historical control trials with time-to-event endpoints. Both O'Brien–Fleming and Gamma family types of sequential decision boundaries are derived based on sequential log-rank tests, which follow a Brownian motion in a transformed information time. Simulation results show that the proposed group sequential designs using historical controls preserve the overall type I error and power. [ABSTRACT FROM AUTHOR]