Sequential design approaches for bioequivalence studies with crossover designs

The planning of bioequivalence (BE) studies, as for any clinical trial, requires a priori specification of an effect size for the determination of power and an assumption about the variance. The specified effect size may be overly optimistic, leading to an underpowered study. The assumed variance can be either too small or too large, leading, respectively, to studies that are underpowered or overly large. There has been much work in the clinical trials field on various types of sequential designs that include sample size reestimation after the trial is started, but these have seen only little use in BE studies. The purpose of this work was to validate at least one such method for crossover design BE studies. Specifically, we considered sample size reestimation for a two-stage trial based on the variance estimated from the first stage. We identified two methods based on Pocock's method for group sequential trials that met our requirement for at most negligible increase in type I error rate.     

Informing the selection of futility stopping thresholds: case study from a late-phase clinical trial

In an environment where (i) potential risks to subjects participating in clinical studies need to be managed carefully, (ii) trial costs are increasing, and (iii) there are limited research resources available, it is necessary to prioritize research projects and sometimes re-prioritize if early indications suggest that a trial has low probability of success. Futility designs allow this re-prioritization to take place. This paper reviews a number of possible futility methods available and presents a case study from a late-phase study of an HIV therapeutic, which utilized conditional power-based stopping thresholds. The two most challenging aspects of incorporating a futility interim analysis into a trial design are the selection of optimal stopping thresholds and the timing of the analysis, both of which require the balancing of various risks. The paper outlines a number of graphical aids that proved useful in explaining the statistical risks involved to the study team. Further, the paper outlines a decision analysis undertaken which combined expectations of drug performance with conditional power calculations in order to produce probabilities of different interim and final outcomes, and which ultimately led to the selection of the final stopping thresholds.     

Testing bioequivalence for multiple formulations with power and sample size calculations

Bioequivalence (BE) trials play an important role in drug development for demonstrating the BE between test and reference formulations. The key statistical analysis for BE trials is the use of two one‐sided tests (TOST), which is equivalent to showing that the 90% confidence interval of the relative bioavailability is within a given range. Power and sample size calculations for the comparison between one test formulation and the reference formulation has been intensively investigated, and tables and software are available for practical use. From a statistical and logistical perspective, it might be more efficient to test more than one formulation in a single trial. However, approaches for controlling the overall type I error may be required. We propose a method called multiplicity‐adjusted TOST (MATOST) combining multiple comparison adjustment approaches, such as Hochberg's or Dunnett's method, with TOST. Because power and sample size calculations become more complex and are difficult to solve analytically, efficient simulation‐based procedures for this purpose have been developed and implemented in an R package. Some numerical results for a range of scenarios are presented in the paper. We show that given the same overall type I error and power, a BE crossover trial designed to test multiple formulations simultaneously only requires a small increase in the total sample size compared with a simple 2 × 2 crossover design evaluating only one test formulation. Hence, we conclude that testing multiple formulations in a single study is generally an efficient approach. The R package MATOST is available at https://sites.google.com/site/matostbe/ . Copyright © 2012 John Wiley & Sons, Ltd.     

Stopping for efficacy in single-arm phase II clinical trials

Phase II clinical trials investigate whether a new drug or treatment has sufficient evidence of effectiveness against the disease under study. Two-stage designs are popular for phase II since they can stop in the first stage if the drug is ineffective. Investigators often face difficulties in determining the target response rates, and adaptive designs can help to set the target response rate tested in the second stage based on the number of responses observed in the first stage. Popular adaptive designs consider two alternate response rates, and they generally minimise the expected sample size at the maximum uninterested response rate. Moreover, these designs consider only futility as the reason for early stopping and have high expected sample sizes if the provided drug is effective. Motivated by this problem, we propose an adaptive design that enables us to terminate the single-arm trial at the first stage for efficacy and conclude which alternate response rate to choose. Comparing the proposed design with a popular adaptive design from literature reveals that the expected sample size decreases notably if any of the two target response rates are correct. In contrast, the expected sample size remains almost the same under the null hypothesis.     

Integrating phase 2 into phase 3 based on an intermediate endpoint while accounting for a cure proportion—With an application to the design of a clinical trial in acute myeloid leukemia

For a trial with primary endpoint overall survival for a molecule with curative potential, statistical methods that rely on the proportional hazards assumption may underestimate the power and the time to final analysis. We show how a cure proportion model can be used to get the necessary number of events and appropriate timing via simulation. If phase 1 results for the new drug are exceptional and/or the medical need in the target population is high, a phase 3 trial might be initiated after phase 1. Building in a futility interim analysis into such a pivotal trial may mitigate the uncertainty of moving directly to phase 3. However, if cure is possible, overall survival might not be mature enough at the interim to support a futility decision. We propose to base this decision on an intermediate endpoint that is sufficiently associated with survival. Planning for such an interim can be interpreted as making a randomized phase 2 trial a part of the pivotal trial: If stopped at the interim, the trial data would be analyzed, and a decision on a subsequent phase 3 trial would be made. If the trial continues at the interim, then the phase 3 trial is already underway. To select a futility boundary, a mechanistic simulation model that connects the intermediate endpoint and survival is proposed. We illustrate how this approach was used to design a pivotal randomized trial in acute myeloid leukemia and discuss historical data that informed the simulation model and operational challenges when implementing it.     

Optimal adaptive sequential designs for crossover bioequivalence studies

In prior works, this group demonstrated the feasibility of valid adaptive sequential designs for crossover bioequivalence studies. In this paper, we extend the prior work to optimize adaptive sequential designs over a range of geometric mean test/reference ratios (GMRs) of 70–143% within each of two ranges of intra‐subject coefficient of variation (10–30% and 30–55%). These designs also introduce a futility decision for stopping the study after the first stage if there is sufficiently low likelihood of meeting bioequivalence criteria if the second stage were completed, as well as an upper limit on total study size. The optimized designs exhibited substantially improved performance characteristics over our previous adaptive sequential designs. Even though the optimized designs avoided undue inflation of type I error and maintained power at 80%, their average sample sizes were similar to or less than those of conventional single stage designs. Copyright © 2015 John Wiley & Sons, Ltd.     

Information fraction estimation: Strategies for a phase 3 non-inferiority maximum duration design with time to event outcome

There is considerable debate surrounding the choice of methods to estimate information fraction for futility monitoring in a randomized non-inferiority maximum duration trial. This question was motivated by a pediatric oncology study that aimed to establish non-inferiority for two primary outcomes. While non-inferiority was determined for one outcome, the futility monitoring of the other outcome failed to stop the trial early, despite accumulating evidence of inferiority. For a one-sided trial design for which the intervention is inferior to the standard therapy, futility monitoring should provide the opportunity to terminate the trial early. Our research focuses on the Total Control Only (TCO) method, which is defined as a ratio of observed events to total events exclusively within the standard treatment regimen. We investigate its properties in stopping a trial early in favor of inferiority. Simulation results comparing the TCO method with alternative methods, one based on the assumption of an inferior treatment effect (TH0), and the other based on a specified hypothesis of a non-inferior treatment effect (THA), were provided under various pediatric oncology trial design settings. The TCO method is the only method that provides unbiased information fraction estimates regardless of the hypothesis assumptions and exhibits a good power and a comparable type I error rate at each interim analysis compared to other methods. Although none of the methods is uniformly superior on all criteria, the TCO method possesses favorable characteristics, making it a compelling choice for estimating the information fraction when the aim is to reduce cancer treatment-related adverse outcomes.     

Bioequivalence and the pharmaceutical industry

Since the early 1990s, average bioequivalence (ABE) studies have served as the international regulatory standard for demonstrating that two formulations of drug product will provide the same therapeutic benefit and safety profile when used in the marketplace. Population (PBE) and individual (IBE) bioequivalence have been the subject of intense international debate since methods for their assessment were proposed in the late 1980s and since their use was proposed in United States Food and Drug Administration guidance in 1997. Guidance has since been proposed and finalized by the Food and Drug Administration for the implementation of such techniques in the pioneer and generic pharmaceutical industries. The current guidance calls for the use of replicate design and of cross‐over studies (cross‐overs with sequences TRTR, RTRT, where T is the test and R is the reference formulation) for selected drug products, and proposes restricted maximum likelihood and method‐of‐moments techniques for parameter estimation. In general, marketplace access will be granted if the products demonstrate ABE based on a restricted maximum likelihood model. Study sponsors have the option of using PBE or IBE if the use of these criteria can be justified to the regulatory authority. Novel and previously proposed SAS^®‐based approaches to the modelling of pharmacokinetic data from replicate design studies will be summarized. Restricted maximum likelihood and method‐of‐moments modelling results are compared and contrasted based on the analysis of data available from previously performed replicate design studies, and practical issues involved in the application of replicate designs to demonstrate ABE are characterized. It is concluded that replicate designs may be used effectively to demonstrate ABE for highly variable drug products. Statisticians should exercise caution in the choice of modelling procedure. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

Conditional estimation using prior information in 2‐stage group sequential designs assuming asymptotic normality when the trial terminated early

Two‐stage designs are widely used to determine whether a clinical trial should be terminated early. In such trials, a maximum likelihood estimate is often adopted to describe the difference in efficacy between the experimental and reference treatments; however, this method is known to display conditional bias. To reduce such bias, a conditional mean‐adjusted estimator (CMAE) has been proposed, although the remaining bias may be nonnegligible when a trial is stopped for efficacy at the interim analysis. We propose a new estimator for adjusting the conditional bias of the treatment effect by extending the idea of the CMAE. This estimator is calculated by weighting the maximum likelihood estimate obtained at the interim analysis and the effect size prespecified when calculating the sample size. We evaluate the performance of the proposed estimator through analytical and simulation studies in various settings in which a trial is stopped for efficacy or futility at the interim analysis. We find that the conditional bias of the proposed estimator is smaller than that of the CMAE when the information time at the interim analysis is small. In addition, the mean‐squared error of the proposed estimator is also smaller than that of the CMAE. In conclusion, we recommend the use of the proposed estimator for trials that are terminated early for efficacy or futility.     

A Bayesian sequential design with binary outcome

Several researchers have proposed solutions to control type I error rate in sequential designs. The use of Bayesian sequential design becomes more common; however, these designs are subject to inflation of the type I error rate. We propose a Bayesian sequential design for binary outcome using an alpha‐spending function to control the overall type I error rate. Algorithms are presented for calculating critical values and power for the proposed designs. We also propose a new stopping rule for futility. Sensitivity analysis is implemented for assessing the effects of varying the parameters of the prior distribution and maximum total sample size on critical values. Alpha‐spending functions are compared using power and actual sample size through simulations. Further simulations show that, when total sample size is fixed, the proposed design has greater power than the traditional Bayesian sequential design, which sets equal stopping bounds at all interim analyses. We also find that the proposed design with the new stopping for futility rule results in greater power and can stop earlier with a smaller actual sample size, compared with the traditional stopping rule for futility when all other conditions are held constant. Finally, we apply the proposed method to a real data set and compare the results with traditional designs.     

A simple two-stage design for quantitative responses with application to a study in diabetic neuropathic pain

Two-stage designs offer substantial advantages for early phase II studies. The interim analysis following the first stage allows the study to be stopped for futility, or more positively, it might lead to early progression to the trials needed for late phase II and phase III. If the study is to continue to its second stage, then there is an opportunity for a revision of the total sample size. Two-stage designs have been implemented widely in oncology studies in which there is a single treatment arm and patient responses are binary. In this paper the case of two-arm comparative studies in which responses are quantitative is considered. This setting is common in therapeutic areas other than oncology. It will be assumed that observations are normally distributed, but that there is some doubt concerning their standard deviation, motivating the need for sample size review. The work reported has been motivated by a study in diabetic neuropathic pain, and the development of the design for that trial is described in detail.     

Oncology phase II proof‐of‐concept studies with multiple targets: Randomized controlled trial or single arm?

For oncology drug development, phase II proof‐of‐concept studies have played a key role in determining whether or not to advance to a confirmatory phase III trial. With the increasing number of immunotherapies, efficient design strategies are crucial in moving successful drugs quickly to market. Our research examines drug development decision making under the framework of maximizing resource investment, characterized by benefit cost ratios (BCRs). In general, benefit represents the likelihood that a drug is successful, and cost is characterized by the risk adjusted total sample size of the phases II and III studies. Phase III studies often include a futility interim analysis; this sequential component can also be incorporated into BCRs. Under this framework, multiple scenarios can be considered. For example, for a given drug and cancer indication, BCRs can yield insights into whether to use a randomized control trial or a single‐arm study. Importantly, any uncertainty in historical control estimates that are used to benchmark single‐arm studies can be explicitly incorporated into BCRs. More complex scenarios, such as restricted resources or multiple potential cancer indications, can also be examined. Overall, BCR analyses indicate that single‐arm trials are favored for proof‐of‐concept trials when there is low uncertainty in historical control data and smaller phase III sample sizes. Otherwise, especially if the most likely to succeed tumor indication can be identified, randomized controlled trials may be a better option. While the findings are consistent with intuition, we provide a more objective approach.     

Comparison of models for average bioequivalence in replicated crossover designs

Average bioequivalence (ABE) has been the regulatory standard for bioequivalence (BE) since the 1990s. BE studies are commonly two-period crossovers, but may also use replicated designs. The replicated crossover will provide greater power for the ABE assessment. FDA has recommended that ABE analysis of replicated crossovers use a model which includes terms for separate within- and between-subject components for each formulation and which allows for a subject x formulation interaction component. Our simulation study compares the performance of four alternative mixed effects models: the FDA model, a three variance component model proposed by Ekbohm and Melander (EM), a random intercepts and slopes model (RIS) proposed by Patterson and Jones, and a simple model that contains only two variance components. The simple model fails (when not 'true') to provide adequate coverage and it accepts the hypothesis of equivalence too often. FDA and EM models are frequently indistinguishable and often provide the best performance with respect to coverage and probability of concluding BE. The RIS model concludes equivalence too often when both the within- and between-subject variance components differ between formulations. The FDA analysis model is recommended because it provides the most detail regarding components of variability and has a slight advantage over the EM model in confidence interval length.     

Optimal group sequential designs constrained on both overall and stage one error rates

Abstract

Optimized group sequential designs proposed in the literature have designs minimizing average sample size with respect to a prior distribution of treatment effect with overall type I and type II error rates well-controlled (i.e., at final stage). The optimized asymmetric group sequential designs that we present here additionally consider constrains on stopping probabilities at stage one: probability of stopping for futility at stage one when no drug effect exists as well as the probability of rejection when the maximum effect size is true at stage one so that accountability of group sequential design is ensured from the first stage throughout.     

An adaptive biomarker basket design in phase II oncology trials

The phase II basket trial in oncology is a novel design that enables the simultaneous assessment of treatment effects of one anti-cancer targeted agent in multiple cancer types. Biomarkers could potentially associate with the clinical outcomes and re-define clinically meaningful treatment effects. It is therefore natural to develop a biomarker-based basket design to allow the prospective enrichment of the trials with the adaptive selection of the biomarker-positive (BM+) subjects who are most sensitive to the experimental treatment. We propose a two-stage phase II adaptive biomarker basket (ABB) design based on a potential predictive biomarker measured on a continuous scale. At Stage 1, the design incorporates a biomarker cutoff estimation procedure via a hierarchical Bayesian model with biomarker as a covariate (HBMbc). At Stage 2, the design enrolls only BM+ subjects, defined as those with the biomarker values exceeding the biomarker cutoff within each cancer type, and subsequently assesses the early efficacy and/or futility stopping through the pre-defined interim analyses. At the end of the trial, the response rate of all BM+ subjects for each cancer type can guide drug development, while the data from all subjects can be used to further model the relationship between the biomarker value and the clinical outcome for potential future research. The extensive simulation studies show that the ABB design could produce a good estimate of the biomarker cutoff to select BM+ subjects with high accuracy and could outperform the existing phase II basket biomarker cutoff design under various scenarios.     

An efficient sequential design of clinical trials

We propose an efficient group sequential monitoring rule for clinical trials. At each interim analysis both efficacy and futility are evaluated through a specified loss structure together with the predicted power. The proposed design is robust to a wide range of priors, and achieves the specified power with a saving of sample size compared to existing adaptive designs. A method is also proposed to obtain a reduced-bias estimator of treatment difference for the proposed design. The new approaches hold great potential for efficiently selecting a more effective treatment in comparative trials. Operating characteristics are evaluated and compared with other group sequential designs in empirical studies. An example is provided to illustrate the application of the method.     

Designing and analyzing clinical trials for personalized medicine via Bayesian models

Patients with different characteristics (e.g., biomarkers, risk factors) may have different responses to the same medicine. Personalized medicine clinical studies that are designed to identify patient subgroup treatment efficacies can benefit patients and save medical resources. However, subgroup treatment effect identification complicates the study design in consideration of desired operating characteristics. We investigate three Bayesian adaptive models for subgroup treatment effect identification: pairwise independent, hierarchical, and cluster hierarchical achieved via Dirichlet Process (DP). The impact of interim analysis and longitudinal data modeling on the personalized medicine study design is also explored. Interim analysis is considered since they can accelerate personalized medicine studies in cases where early stopping rules for success or futility are met. We apply integrated two-component prediction method (ITP) for longitudinal data simulation, and simple linear regression for longitudinal data imputation to optimize the study design. The designs' performance in terms of power for the subgroup treatment effects and overall treatment effect, sample size, and study duration are investigated via simulation. We found the hierarchical model is an optimal approach to identifying subgroup treatment effects, and the cluster hierarchical model is an excellent alternative approach in cases where sufficient information is not available for specifying the priors. The interim analysis introduction to the study design lead to the trade-off between power and expected sample size via the adjustment of the early stopping criteria. The introduction of the longitudinal modeling slightly improves the power. These findings can be applied to future personalized medicine studies with discrete or time-to-event endpoints.     

Bayesian optimal phase II designs with dual-criterion decision making

The conventional phase II trial design paradigm is to make the go/no-go decision based on the hypothesis testing framework. Statistical significance itself alone, however, may not be sufficient to establish that the drug is clinically effective enough to warrant confirmatory phase III trials. We propose the Bayesian optimal phase II trial design with dual-criterion decision making (BOP2-DC), which incorporates both statistical significance and clinical relevance into decision making. Based on the posterior probability that the treatment effect reaches the lower reference value (statistical significance) and the clinically meaningful value (clinical significance), BOP2-DC allows for go/consider/no-go decisions, rather than a binary go/no-go decision. BOP2-DC is highly flexible and accommodates various types of endpoints, including binary, continuous, time-to-event, multiple, and coprimary endpoints, in single-arm and randomized trials. The decision rule of BOP2-DC is optimized to maximize the probability of a go decision when the treatment is effective or minimize the expected sample size when the treatment is futile. Simulation studies show that the BOP2-DC design yields desirable operating characteristics. The software to implement BOP2-DC is freely available at www.trialdesign.org .