Two-stage Adaptive Design Research Articles

A parametric multiple test procedure to adaptive group-sequential trials allowing for mid-term modifications

Adaptive group-sequential trials incorporating mid-term design modifications, such as selection of hypotheses or treatment groups, or sample size reestimation during the interim analysis, provide efficient tools to utilize the data from enrolled patients. A graphical multiple test procedure using weighted Bonferroni test has been proposed in adaptive group-sequential designs based on a marginal p-value combination approach.Multiple test procedures using weighted Bonferroni test may result in potential power loss when the test statistics are positively correlated. This paper proposes a graphical approach for adaptive group-sequential trials using weighted parametric test which utilizes the correlation structure between test statistics. The proposed parametric approach is more powerful than the Bonferroni-based approach and preserves the familywise Type I error. The proposed approach is appealing in adaptive designs with the option of treatment selection during the interim analysis and seamless combination of the dose finding and confirmatory stage, because it can utilize the natural correlations between the test statistics resulting from comparing a few treatment groups to a common control group.Simulations are conducted to evaluate the power and Type I error. The proposed parametric approach is illustrated with a confirmatory two-stage adaptive design with a dose selection stage and confirmatory stage with the selected treatment groups.

Admissible and minimax estimation of the parameters of the selected normal population in two-stage adaptive designs under reflected normal loss function

In clinical research, one of the key problems is to estimate the effect of the best treatment among the given k treatments in two-stage adaptive design. Suppose the effects of two treatments have normal distributions with means θ1 and θ2, respectively, and common known variance σ2. In the first stage, random samples of size n1 with means X1 and X2 are chosen from the two populations. Then the population with the larger or smaller sample mean XM is selected, and a random sample of size n2 with mean YM is chosen from this population in the second stage of design. Our aim is to estimate the mean θM or θJ of the selected population based on XM and YM in two-stage adaptive design under the reflected normal loss function. We obtain minimax estimators of θM and θJ, and then provide some sufficient conditions for the inadmissibility of estimators of θM and θJ. Theoretical results are augmented with a simulation study as well as a real data application.

Exact tests using binary data in adaptive two or multi-stage designs.

When establishing an effective treatment with binary data in a two-stage design, one-sided tests for a proportion p are employed. Researchers use the parameter configuration at the boundary of the null hypothesis space to determine a rejection region and an optimal design. However, it is unclear whether the (maximum) Type I error rate is achieved at the boundary especially when the sample size in stage 2 varies. In this paper, we first prove that this is true for a large family of tests in adaptive two-stage designs by showing that any test in the family has a nondecreasing power in p and then derive optimal designs. Second, similar results are established for m-stage designs with m > 2. Supplementary materials for this article are available online.

Subgroup identification based on an accelerated failure time model combined with adaptive elastic net

We propose a strategy for identifying subgroups with the treatment effect from the survival data of a randomized clinical trial based on accelerated failure time (AFT) model. We applied adaptive elastic net to the AFT model (designated as the penalized model) and identified the candidate covariates based on covariate-treatment interactions. To classify the patient subgroups, we utilized a likelihood-based change-point algorithm to determine the threshold cutoff point. A two-stage adaptive design was adopted to verify if the treatment effect existed within the identified subgroups. The penalized model with the main effect of the covariates considerably outperformed the univariate model without the main effect for the trial data with a small sample size, a high censoring rate, a small subgroup size, or a sample size that did not exceed the number of covariates; in other scenarios, the latter model showed better performances. Compared with the traditional design, the adaptive design improved the power for detecting the treatment effect where subgroup effect exists with a well-controlled type Ⅰ error. The penalized AFT model with the main effect of the covariates has advantages in subgroup identification from the survival data of clinical trials. Compared with the traditional design, the two-stage adaptive design has better performance in evaluation of the treatment effect when a subgroup effect exists.

Random norming aids analysis of non-linear regression models with sequential informative dose selection

A two-stage adaptive optimal design is an attractive option for increasing the efficiency of clinical trials. In these designs, based on interim data, the locally optimal dose is chosen for further exploration, which induces dependencies between data from the two stages. When the maximum likelihood estimator (MLE) is used under nonlinear regression models with independent normal errors in a pilot study where the first stage sample size is fixed, and the second stage sample size is large, the Fisher information fails to normalize the estimator adequately asymptotically, because of dependencies. In this situation, three alternative random information measures are presented and are shown to provide better normalization of the MLE asymptotically. The performance of random information measures is investigated in simulation studies, and the results suggest that the observed information performs best when the sample size is small.

Two-Stage Adaptive Designs for Three-Treatment Bioequivalence Studies

Bioequivalence (BE) studies are most often conducted as crossover trials, and therefore establishing their required sample size necessitates specification of the within-person variance. Given that this specification is often difficult in practice, there has been great interest in recent years in the use of adaptive designs for BE trials. However, while numerous methods for this have now been presented, their focus has been solely on two-treatment BE studies. In some instances, it will be desired to incorporate more than a single test and reference formulation into a BE trial. It would therefore be useful to establish methodology for the design of adaptive multi-treatment BE trials, to acquire the benefits in the two-treatment setting in this more complex situation. Here, we achieve this for three-treatment studies by extending previously proposed designs for two-treatment trials. First, we discuss the additional design considerations that arise when multiple comparisons are made. Next, an extensive simulation study is employed to compare the performance of the proposed procedures. With this, we demonstrate that two-stage designs with desirable statistical operating characteristics can be readily identified for three-treatment BE trials. Supplementary materials for this article are available online.

Criteria for dose-finding in two-stage seamless adaptive design

ABSTRACTIn pharmaceutical/clinical development, two-stage seamless adaptive designs are commonly considered. Such designs include a two-stage phase I/II or phase II/III adaptive trial that combines one phase IIb study for dose-finding or treatment selection and one phase III study for efficacy confirmation into a single study. At the end of stage 1, promising dose(s) will be selected based on pre-specified selection criteria. In practice, since there is little power with limited subjects available at interim, commonly considered selection criteria for critical decision-making include (i) conditional power, (ii) precision analysis, (iii) predictive probability of success, and (iv) probability of being the best dose or treatment. The selected promising dose(s) will then proceed to the next stage for efficacy confirmation. In this article, we introduce, compare, and evaluate these criteria. Simulation studies and a numeric example are given to illustrate those criteria. Besides, we attempt to address some concerns for the two-stage seamless adaptive clinical trial.

Bayesian Two-Stage Adaptive Design in Bioequivalence.

Bioequivalence (BE) studies are an integral component of new drug development process, and play an important role in approval and marketing of generic drug products. However, existing design and evaluation methods are basically under the framework of frequentist theory, while few implements Bayesian ideas. Based on the bioequivalence predictive probability model and sample re-estimation strategy, we propose a new Bayesian two-stage adaptive design and explore its application in bioequivalence testing. The new design differs from existing two-stage design (such as Potvin's method B, C) in the following aspects. First, it not only incorporates historical information and expert information, but further combines experimental data flexibly to aid decision-making. Secondly, its sample re-estimation strategy is based on the ratio of the information in interim analysis to total information, which is simpler in calculation than the Potvin's method. Simulation results manifested that the two-stage design can be combined with various stop boundary functions, and the results are different. Moreover, the proposed method saves sample size compared to the Potvin's method under the conditions that type I error rate is below 0.05 and statistical power reaches 80 %.

A variational approach to optimal two-stage designs.

Recalculating the sample size in adaptive two-stage designs is a well-established method to gain flexibility in a clinical trial. Jennison and Turnbull (2015) proposed an "optimal" adaptive two-stage design based on the inverse normal combination test, which minimizes a mixed criterion of expected sample size under the alternative and conditional power. We demonstrate that the use of a combination test is not necessary to control the type one error rate and use variational techniques to develop a general adaptive design that is globally optimal under predefined optimality criteria. This approach yields to more efficient designs and furthermore allows to investigate the efficiency of the inverse normal method and the relation between local (interim-based) recalculation rules and global (unconditional) optimality of adaptive two-stage designs.

Optimizing Sample Size Allocation and Power in a Bayesian Two-Stage Drop-the-Losers Design

When a researcher desires to test several treatment arms against a control arm, a two-stage adaptive design can be more efficient than a single-stage design where patients are equally allocated to all treatment arms and the control. We see this type of approach in clinical trials as a seamless Phase II–Phase III design. These designs require more statistical support and are less straightforward to plan and analyze than a standard single-stage design. To diminish the barriers associated with a Bayesian two-stage drop-the-losers design, we built a user-friendly point-and-click graphical user interface with R Shiny to aid researchers in planning such designs by allowing them to easily obtain trial operating characteristics, estimate statistical power and sample size, and optimize patient allocation in each stage to maximize power. We assume that endpoints are distributed normally with unknown but common variance between treatments. We recommend this software as an easy way to engage statisticians and researchers in two-stage designs as well as to actively investigate the power of two-stage designs relative to more traditional approaches. The software is freely available at https://github.com/stefangraw/Allocation-Power-Optimizer.

Two-stage adaptive enrichment design for testing an active factor

ABSTRACTWe propose an adaptive enrichment approach to test an active factor, which is a factor whose effect is non-zero in at least one subpopulation. We implement a two-stage play-the-winner design where all subjects in the second stage are enrolled from the subpopulation that has the highest observed effect in the first stage. We recommend a weighted Fisher’s combination of the most powerful test for each stage, respectively: the first stage Hotelling’s test and the second stage noncentral chi-square test. The test is further extended to cover binary outcomes and time-to-event outcomes.

Adaptive two-stage optimal designs for phase II clinical studies that allow early futility stopping

Adaptive designs play an important role in contemporary clinical trials to make designs flexible and efficient. In cancer clinical trials, given a relatively small sample size, it is important to obtain as much information as possible during this phase. We propose a new adaptive optimal design that stops for futility only in the first stage as Simon’s two-stage design. The existing adaptive two-stage designs are often allowed to be stopped for futility or efficacy due to computational advantage. It is difficult to search for an optimal design with futility stopping only in the first stage by using efficient search algorithms; for example, the branch-and-bound algorithm. We have to use multiple computational techniques to search for the optimal design. The proposed adaptive design meets the important property of the monotonic property that the second stage sample size is a nonincreasing function of the number of responses from the first stage. In this article, we show that the proposed adaptive design always has a smaller expected sample size than Simon’s optimal design. We recommend it for use in practice as an alternative to the commonly used Simon’s design.

A Critical Review on Adaptive Sample Size Re-estimation (SSR) Designs for Superiority Trials with Continuous Endpoints

Adaptive sample size re-estimation (SSR) methods have been widely used for designing clinical trials, especially during the past two decades. We give a critical review for several commonly used two-stage adaptive SSR designs for superiority trials with continuous endpoints. The objective, design and some of our suggestions and concerns of each design will be discussed in this paper. Keywords: Adaptive Design; Sample Size Re-estimation; Review Introduction Sample size determination is a key part of designing clinical trials. The objective of a good clinical trial design is to achieve the balance between efficiently spending resources and enrolling enough patients to achieve a desired power. At the designing stage of a clinical trial, there usually only have limited information available about the population, so that the sample size calculated at this stage may not be sufficient to address the study objective. Assumed that the data from two parallel treatment groups (e.g. treatment and control groups) are normally distributed with mean treatment effect μ_1 and μ_2, and equal within-group variance 𝜎2. Let the mean difference (treatment effect) . The efficacy of the treatment will be evaluated by testing the hypothesis.

A distribution-free approach for selecting better treatment through an ethical allocation

ABSTRACTThe present article provides a statistical inference on comparative performances of two treatments in a clinical trial under a two-stage adaptive allocation design. Suppose a fixed number (2m+n, say) of subjects are available for treatment by any of the two competing treatments, say, A and B for a particular ailment. As per the proposed allocation design, incoming subjects are randomised equally between A and B at the first stage. Then, at the second stage, the remaining n subjects are exclusively assigned to the treatment which has higher observed median response evaluated in the first stage. Under such an ethical allocation design we decide on the better treatment through an asymptotically distribution-free test procedure. The related asymptotic results are also studied.

Abstract OT1-05-02: OPTIMA: A prospective randomized trial to validate the clinical utility and cost-effectiveness of gene expression test-directed chemotherapy decisions in high clinical risk early breast cancer

Abstract Background:Multi-parameter tumour gene expression assays (MPAs) are widely used to estimate individual patient residual risk and to guide chemotherapy use in hormone-sensitive, HER2-negative early breast cancer. The TAILORx trial supports MPA use in a node-negative population. Evidence for MPA use in node-positive breast cancer is limited. OPTIMA (Optimal Personalised Treatment of early breast cancer usIng Multi-parameter Analysis) (ISRCTN42400492) aims to validate MPAs as predictors of chemotherapy sensitivity in a largely node-positive breast cancer population where prospective RCT (Randomised Controlled Trial) evidence is lacking. Methods: OPTIMA is a partially blinded multi-center RCT with an adaptive two-stage design. The main eligibility criteria are women and men age 40 or older with resected ER-positive, HER2-negative invasive breast cancer and up to 9 involved axillary lymph nodes. Randomisation is to standard management (chemotherapy and endocrine therapy) or to MPA-directed treatment using the Prosigna (PAM50) test. Those with a Prosigna tumour score (ROR_PT) >60 receive standard management whilst those with a low score (≤60) are treated with endocrine therapy alone. Endocrine therapy for pre-menopausal women includes ovarian suppression. The co-primary outcomes are (1) Invasive Disease Free Survival (IDFS) and (2) cost-effectiveness of test-directed treatment. Secondary outcomes include IDFS in patients with low-score tumours and quality of life. An integrated qualitative recruitment study addresses challenges to consent and recruitment and will build on experience from the feasibility study that a multidisciplinary approach at sites is important for recruitment success. Tumour blocks will be banked to allow evaluation of additional MPA technologies. Recruitment of 4500 patients over 5 years will permit demonstration of 3% non-inferiority of test-directed treatment, assuming 5-year IDFS of 85% with standard management, equivalent to a HR of 1.22. Inclusion of patients from the feasibility study will increase the power to test for non-inferiority. Results: The OPTIMA main trial opened in January 2017. Overall recruitment (including the feasibility study) will reach 1000 in August 2018. Recruitment in Norway will commence in July 2018. Characteristics of the OPTIMA main participants recruited to 31st May 2018 are shown in the table. Main study patient characteristicsCharacteristic %Median age in years (range)57 (40-80) Menopause statusPre34 Post66 Male1Tumour size<30mm58 >=30mm42Node statuspN04 pN1mi(sn)7 pN1(sn)20 pN155 pN214Historic grade16 258 336 Conclusion: OPTIMA is one of two large scale prospective trials validating the use of test-guided chemotherapy decisions in node-positive early breast cancer. It is expected to have a global impact on breast cancer treatment. Experience from the preliminary study and close engagement with centres will aid trial success. Funding: OPTIMA is funded by the UK NIHR HTA Programme (10/34/501). Views expressed are those of the authors and not those of the HTA Programme, NIHR, NHS or the DoH. Citation Format: Stein RC, Hughes-Davies L, Makris A, Macpherson IR, Conefrey C, Rooshenas L, Pinder SE, Thomas J, Hall PS, Cameron DA, Earl HM, Naume B, Poole CJ, Rea DW, MacIntosh SA, Harmer V, Morgan A, Hulme C, McCabe C, Stallard N, Higgins H, Donovan JL, Bartlett JM, Marshall A, Dunn JA. OPTIMA: A prospective randomized trial to validate the clinical utility and cost-effectiveness of gene expression test-directed chemotherapy decisions in high clinical risk early breast cancer [abstract]. In: Proceedings of the 2018 San Antonio Breast Cancer Symposium; 2018 Dec 4-8; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2019;79(4 Suppl):Abstract nr OT1-05-02.

A nonparametric Bayesian continual reassessment method in single-agent dose-finding studies

BackgroundThe main purpose of dose-finding studies in Phase I trial is to estimate maximum tolerated dose (MTD), which is the maximum test dose that can be assigned with an acceptable level of toxicity. Existing methods developed for single-agent dose-finding assume that the dose-toxicity relationship follows a specific parametric potency curve. This assumption may lead to bias and unsafe dose escalations due to the misspecification of parametric curve.MethodsThis paper relaxes the parametric assumption of dose-toxicity relationship by imposing a Dirichlet process prior on unknown dose-toxicity curve. A hybrid algorithm combining the Gibbs sampler and adaptive rejection Metropolis sampling (ARMS) algorithm is developed to estimate the dose-toxicity curve, and a two-stage Bayesian nonparametric adaptive design is presented to estimate MTD.ResultsFor comparison, we consider two classical continual reassessment methods (CRMs) (i.e., logistic and power models). Numerical results show the flexibility of the proposed method for single-agent dose-finding trials, and the proposed method behaves better than two classical CRMs under our considered scenarios.ConclusionsThe proposed dose-finding procedure is model-free and robust, and behaves satisfactorily even in small sample cases.

Two-Stage Negative Adaptive Cluster Sampling

If the population is rare and clustered, then simple random sampling gives a poor estimate of the population total. For such type of populations, adaptive cluster sampling is useful. But it loses control on the final sample size. Hence, the cost of sampling increases substantially. To overcome this problem, the surveyors often use auxiliary information which is easy to obtain and inexpensive. An attempt is made through the auxiliary information to control the final sample size. In this article, we have proposed two-stage negative adaptive cluster sampling design. It is a new design, which is a combination of two-stage sampling and negative adaptive cluster sampling designs. In this design, we consider an auxiliary variable which is highly negatively correlated with the variable of interest and auxiliary information is completely known. In the first stage of this design, an initial random sample is drawn by using the auxiliary information. Further, using Thompson’s (J Am Stat Assoc 85:1050–1059, 1990) adaptive procedure networks in the population are discovered. These networks serve as the primary-stage units (PSUs). In the second stage, random samples of unequal sizes are drawn from the PSUs to get the secondary-stage units (SSUs). The values of the auxiliary variable and the variable of interest are recorded for these SSUs. Regression estimator is proposed to estimate the population total of the variable of interest. A new estimator, Composite Horwitz–Thompson (CHT)-type estimator, is also proposed. It is based on only the information on the variable of interest. Variances of the above two estimators along with their unbiased estimators are derived. Using this proposed methodology, sample survey was conducted at Western Ghat of Maharashtra, India. The comparison of the performance of these estimators and methodology is presented and compared with other existing methods. The cost–benefit analysis is given.

Reasonable two-stage adaptive designs for single-arm phase II clinical trials.

In cancer phase II trials, determining the sample size of a single-arm two-stage design remains a challenge. To overcome this problem, Simon's two-stage design was extended to an adaptive design: at the interim analysis, the total sample size can be set to either of the two preplanned values. However, without any restriction on design construction, an optimal or suboptimal design derived may have counter-intuitive or unreasonable design features, which make the chosen design less persuasive and inefficient. Thus, we thoroughly examined how the expected, total, and maximum sample sizes of the optimal or suboptimal designs are affected by excluding the counter-intuitive or unreasonable designs. We adopted the four optimality criteria: minimizing the expected sample size at the null hypothesis (O1), minimizing the maximum expected sample size over the hypotheses (O2), and minimizing the maximum sample sizes with additional adaption of either of the former two (O3 or O4, respectively). We found that focusing on reasonable design may drastically reduce the maximum sample size when the first optimality criterion is applied. Under the other optimality criteria, although the impact on optimality brought by our proposed strategy may be slight, exclusion of unreasonable design is still useful to reduce the candidate designs, which will considerably reduce the computational time for design search and can facilitate the design choice among optimal and suboptimal designs. We further discuss the utility of our proposal in an example of a real clinical trial and conclude the paper with general recommendations.

Designing phase II clinical trials to target subgroup of interest in a heterogeneous population: A case study using an R package

Phase II trials that evaluate target therapies based on a biomarker must be well designed in order to assess anti-tumor activity as well as clinical utility of the biomarker. Classical phase II designs do not deal with this molecular heterogeneity and can lead to an erroneous conclusion in the whole population, whereas a subgroup of patients may well benefit from the new therapy. Moreover, the target population to be evaluated in a phase III trial may be incorrectly specified. Alternative approaches are proposed in the literature that make it possible to include two subgroups according to biomarker status (negative/positive) in the same study.Jones, Parashar and Tournoux et al. propose different stratified adaptive two-stage designs to identify a subgroup of interest in a heterogeneous population that could possibly benefit from the experimental treatment at the end of the first or second stage. Nevertheless, these designs are rarely used in oncology research. After introducing these stratified adaptive designs, we present an R package (ph2hetero) implementing these methods. A case study is provided to illustrate both the designs and the use of the R package.These stratified adaptive designs provide a useful alternative to classical two-stage designs and may also provide options in contexts other than biomarker studies.

A two-stage adaptive allocation design for survival outcome with informative censoring

An adaptive two-stage allocation design is developed for survival responses subject to independent informative censoring. The asymptotic p value of a score test related to a hypothesis of treatment effectiveness is used to set the assignment probability of the second stage. Several characteristics of the design and the follow-up inference are studied, both numerically and theoretically, and are compared with those of an existing competitor. Applicability of the proposed design is also illustrated through a real data.