A two-stage group-sequential design for delayed treatment responses with the possibility of trial restart.

Common statistical theory applicable to confirmatory phase III trial designs usually assumes that patients are enrolled simultaneously and there is no time gap between enrollment and outcome observation. However, in practice, patients are enrolled successively and there is a lag between the enrollment of a patient and the measurement of the primary outcome. For single-stage designs, the difference between theory and practice only impacts on the trial duration but not on the statistical analysis and its interpretation. For designs with interim analyses, however, the number of patients already enrolled into the trial and the number of patients with available outcome measurements differ, which can cause issues regarding the statistical analyses of the data. The main issue is that current methodologies either imply that at the time of the interim analysis there are so-called pipeline patients whose data are not used to make a statistical decision (like stopping early for efficacy) or the enrollment into the trial needs to be at least paused for interim analysis to avoid pipeline patients. There are methods for delayed responses available that introduced error-spending stopping boundaries for the enrollment of patients followed by critical values to reject the null hypothesis in case the stopping boundaries have been crossed beforehand. Here, we will discuss other solutions, considering different boundary determination algorithms using conditional power and introducing a design allowing for recruitment restart while keeping the type I error rate controlled.

Familywise error for multiple time-to-event endpoints in a group sequential design.

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.

Adaptive designs were primarily used but inadequately reported in early phase drug trials.

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 ß = 0.14, p < 0.01) and the multicenter trials (estimated ß = 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.

Optimal futility stopping boundaries for binary endpoints.

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.

A Bayesian adaptive design approach for stepped-wedge cluster randomized trials.

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.

Group sequential designs for cancer immunotherapy trial with delayed treatment effect.

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-(ρ,γ) weighted log-rank test and a new weighted log-rank test are also discussed.

Incorporating external real-world data (RWD) in confirmatory adaptive design.

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.

Using an early outcome as the sole source of information of interim decisions regarding treatment effect on a long-term endpoint: The non-Gaussian case.

In randomized clinical trials that use a long-term efficacy endpoint, the follow-up time necessary to observe the endpoint may be substantial. In such trials, an attractive option is to consider an interim analysis based solely on an early outcome that could be used to expedite the evaluation of treatment's efficacy. Garcia Barrado et al. (Pharm Stat. 2022; 21: 209-219) developed a methodology that allows introducing such an early interim analysis for the case when both the early outcome and the long-term endpoint are normally-distributed, continuous variables. We extend the methodology to any combination of the early-outcome and long-term-endpoint types. As an example, we consider the case of a binary outcome and a time-to-event endpoint. We further evaluate the potential gain in operating characteristics (power, expected trial duration, and expected sample size) of a trial with such an interim analysis in function of the properties of the early outcome as a surrogate for the long-term endpoint.

Futility Interim Analysis Based on Probability of Success Using a Surrogate Endpoint.

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.

Beta spending function based on conditional power in group sequential design.

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.

Group sequential multi-arm multi-stage trial design with treatment selection.

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.

A gated group sequential design for seamless Phase II/III trial with subpopulation selection.

BACKGROUND: Due to the high cost and high failure rate of Phase III trials where a classical group sequential design (GSD) is usually used, seamless Phase II/III designs are more and more popular to improve trial efficiency. A potential attraction of Phase II/III design is to allow a randomized proof-of-concept stage prior to committing to the full cost of a Phase III trial. Population selection during the trial allows a trial to adapt and focus investment where it is most likely to provide patient benefit. Previous methods have been developed for this problem when there is a single primary endpoint and two possible populations. METHODS: To find the population that potentially benefits with one or two primary endpoints (e.g., progression free survival (PFS), overall survival (OS)), we propose a gated group sequential design for a seamless Phase II/III trial design with adaptive population selection. RESULTS: The investigated design controls the familywise error rate and allows multiple interim analyses to enable early stopping for efficacy or futility. Simulations and an illustrative example suggest that the proposed gated group sequential design has more power and requires less time and resources compared to the group sequential design and adaptive design. CONCLUSIONS: Combining the group sequential design and adaptive design, the gated group sequential design has more power and higher efficiency while controlling for the familywise error rate. It has the potential to save drug development cost and more quickly fulfill unmet medical needs.

Adaptive designs in critical care trials: a simulation study.

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.

Sequential monitoring of cancer immunotherapy trial with random delayed treatment effect.

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.

Group sequential multi-arm multi-stage survival trial design with treatment selection.

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.

Adaptive designs for IVPT data with mixed scaled average bioequivalence.

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.

Group sequential design for randomized trials using "first hitting time" model.

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.

Using an interim analysis based exclusively on an early outcome in a randomized clinical trial with a long-term clinical endpoint.

In RCTs with an interest in a long-term efficacy endpoint, the follow-up time necessary to observe the endpoint may be substantial. In order to reduce the expected duration of such trials, early-outcome data may be collected to enrich an interim analysis aimed at stopping the trial early for efficacy. We propose to extend such a design with an additional interim analysis using solely early-outcome data in order to expedite the evaluation of treatment's efficacy. We evaluate the potential gain in operating characteristics (power, expected trial duration, and expected sample size) when introducing such an early interim analysis, in function of the properties of the early outcome as a surrogate for the long-term endpoint. In the context of a longitudinal age-related macular degeneration (ARMD) ophthalmology trial, results show potentially substantial gains in both the expected trial duration and the expected sample size. A prerequisite, though, is that the treatment effect on the early outcome has to be strongly correlated with the treatment effect on the long-term endpoint, that is, that the early outcome is a validated surrogate for the long-term endpoint.

A unified framework for weighted parametric group sequential design.

Group sequential design (GSD) is widely used in clinical trials in which correlated tests of multiple hypotheses are used. Multiple primary objectives resulting in tests with known correlations include evaluating (1) multiple experimental treatment arms, (2) multiple populations, (3) the combination of multiple arms and multiple populations, or (4) any asymptotically multivariate normal tests. In this paper, we focus on the first three of these and extend the framework of the weighted parametric multiple test procedure from fixed designs with a single analysis per objective to a GSD setting where different objectives may be assessed at the same or different times, each in a group sequential fashion. Pragmatic methods for design and analysis of weighted parametric group sequential design under closed testing procedures are proposed to maintain the strong control of the family-wise Type I error rate when correlations between tests are incorporated. This results in the ability to relax testing bounds compared to designs not fully adjusting for known correlations, increasing power, or allowing decreased sample size. We illustrate the proposed methods using clinical trial examples and conduct a simulation study to evaluate the operating characteristics.

Robust group sequential designs for trials with survival endpoints and delayed response.

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.