A confirmatory basket design considering non-inferiority and superiority testing

For multiple rare diseases as defined by a common biomarker signature, or a disease with multiple disease subtypes of low frequency, it is often possible to provide confirmatory evidence for these disease or subtypes (baskets) as a combined group. A novel drug, as a second generation, may have marginal improvement in efficacy overall but superior efficacy in some baskets. In this situation, it is appealing to test hypotheses of both non-inferiority overall and superiority on certain baskets. The challenge is designing a confirmatory study efficient to address multiple questions in one trial. A two-stage adaptive design is proposed to test the non-inferiority hypothesis at the interim stage, followed by pruning and pooling before testing a superiority hypothesis at the final stage. Such a design enables an efficient and novel registration pathway, including an early claim of non-inferiority followed by a potential label extension with superiority on certain baskets and an improved benefit-risk profile demonstrated by longer term efficacy and safety data. Operating characteristics of this design are examined by simulation studies, and its appealing features make it ready for use in a confirmatory setting, especially in emerging markets, where both the need and the possibility for efficient use of resources may be the greatest.

Estimation and expected sample size in Simon's two stage designs that stop as early as possible

In early phase clinical studies in oncology, Simon's two-stage designs are widely used. The trial design could be made more efficient by stopping early in the second stage when the required number of responses is reached, or when it has become clear that this target can no longer be met (a form of non-stochastic curtailment). Early stopping, however, will affect proper estimation of the response rate. We propose a uniformly minimum-variance unbiased estimator (UMVUE) for the response rate in this setting. The estimator is proven to be UMVUE using the Rao-Blackwell theorem. We evaluate the estimator's properties in terms of bias and mean squared error, both analytically and via simulations. We derive confidence intervals based on sample space orderings, and assess the coverage. For various design options, we evaluate the reduction in expected sample size as a function of the true response rate. Our method provides a solution for estimating response rates in case of a non-stochastic curtailment Simon's two-stage design.

Design and analysis of drop-the-losers studies using binary endpoints in the rare disease setting

The drop-the-losers design combines a phase 2 trial of k treatments and a confirmatory phase 3 trial under a single adaptive protocol, thereby gaining efficiency over a traditional clinical development approach. Such designs may be particularly useful in the rare disease setting, where conserving sample size is paramount, and control arms may not be feasible. We propose an unconditional exact likelihood (UEL) testing and inference procedure for these designs for a binary endpoint using small sample sizes, comparing its operating characteristics to existing methods. Additional practical considerations are evaluated, including the choice of stagewise sample sizes and effect of ties.

A Bayesian adaptive design for biosimilar trials with time-to-event endpoint

A biosimilar drug is a biological product that is highly similar to and at the same time has no clinically meaningful difference from licensed product in terms of safety, purity, and potency. Biosimilar study design is essential to demonstrate the equivalence between biosimilar drug and reference product. However, existing designs and assessment methods are primarily based on binary and continuous endpoints. We propose a Bayesian adaptive design for biosimilarity trials with time-to-event endpoint. The features of the proposed design are twofold. First, we employ the calibrated power prior to precisely borrow relevant information from historical data for the reference drug. Second, we propose a two-stage procedure using the Bayesian biosimilarity index (BBI) to allow early stop and improve the efficiency. Extensive simulations are conducted to demonstrate the operating characteristics of the proposed method in contrast with some naive method. Sensitivity analysis and extension with respect to the assumptions are presented.

A confidence function-based posterior probability design for phase II cancer trials

Single‐arm one‐ or multi‐stage study designs are commonly used in phase II oncology development when the primary outcome of interest is tumor response, a binary variable. Both two‐ and three‐outcome designs are available. Simon two‐stage design is a well‐known example of two‐outcome designs. The objective of a two‐outcome trial is to reject either the null hypothesis that the objective response rate (ORR) is less than or equal to a pre‐specified low uninteresting rate or to reject the alternative hypothesis that the ORR is greater than or equal to some target rate. Three‐outcome designs proposed by Sargent et al. allow a middle gray decision zone which rejects neither hypothesis in order to reduce the required study size. We propose new two‐ and three‐outcome designs with continual monitoring based on Bayesian posterior probability that meet frequentist specifications such as type I and II error rates. Futility and/or efficacy boundaries are based on confidence functions, which can require higher levels of evidence for early versus late stopping and have clear and intuitive interpretations. We search in a class of such procedures for optimal designs that minimize a given loss function such as average sample size under the null hypothesis. We present several examples and compare our design with other procedures in the literature and show that our design has good operating characteristics.

Adaptive multiarm multistage clinical trials

Two methods for designing adaptive multiarm multistage (MAMS) clinical trials, originating from conceptually different group sequential frameworks are presented, and their operating characteristics are compared. In both methods pairwise comparisons are made, stage-by-stage, between each treatment arm and a common control arm with the goal of identifying active treatments and dropping inactive ones. At any stage one may alter the future course of the trial through adaptive changes to the prespecified decision rules for treatment selection and sample size reestimation, and notwithstanding such changes, both methods guarantee strong control of the family-wise error rate. The stage-wise MAMS approach was historically the first to be developed and remains the standard method for designing inferentially seamless phase 2-3 clinical trials. In this approach, at each stage, the data from each treatment comparison are summarized by a single multiplicity adjusted P-value. These stage-wise P-values are combined by a prespecified combination function and the resultant test statistic is monitored with respect to the classical two-arm group sequential efficacy boundaries. The cumulative MAMS approach is a more recent development in which a separate test statistic is constructed for each treatment comparison from the cumulative data at each stage. These statistics are then monitored with respect to multiplicity adjusted group sequential efficacy boundaries. We compared the powers of the two methods for designs with two and three active treatment arms, under commonly utilized decision rules for treatment selection, sample size reestimation and early stopping. In our investigations, which were carried out over a reasonably exhaustive exploration of the parameter space, the cumulative MAMS designs were more powerful than the stage-wise MAMS designs, except for the homogeneous case of equal treatment effects, where a small power advantage was discernable for the stage-wise MAMS designs.

Two-stage phase II survival trial design

Recently, molecularly targeted agents and immunotherapy have been advanced for the treatment of relapse or refractory cancer patients, where disease progression-free survival or event-free survival is often a primary endpoint for the trial design. However, methods to evaluate two-stage single-arm phase II trials with a time-to-event endpoint are currently processed under an exponential distribution, which limits application of real trial designs. In this paper, we developed an optimal two-stage design, which is applied to the four commonly used parametric survival distributions. The proposed method has advantages compared with existing methods in that the choice of underlying survival model is more flexible and the power of the study is more adequately addressed. Therefore, the proposed two-stage design can be routinely used for single-arm phase II trial designs with a time-to-event endpoint as a complement to the commonly used Simon's two-stage design for the binary outcome.

FinnTwin12 Cohort: An Updated Review

This review offers an update on research conducted with FinnTwin12 (FT12), the youngest of the three Finnish Twin Cohorts. FT12 was designed as a two-stage study. In the first stage, we conducted multiwave questionnaire research enrolling all eligible twins born in Finland during 1983-1987 along with their biological parents. In stage 2, we intensively studied a subset of these twins with in-school assessments at age 12 and semistructured poly-diagnostic interviews at age 14. At baseline, parents of intensively studied twins were administered the adult version of the interview. Laboratory studies with repeat interviews, neuropsychological tests, and collection of DNA were made of intensively studied twins during follow-up in early adulthood. The basic aim of the FT12 study design was to obtain information on individual, familial and school/neighborhood risks for substance use/abuse prior to the onset of regular tobacco and alcohol use and then track trajectories of use and abuse and their consequences into adulthood. But the longitudinal assessments were not narrowly limited to this basic aim, and with multiwave, multirater assessments from ages 11 to 12, the study has created a richly informative data set for analyses of gene-environment interactions of both candidate genes and genomewide measures with measured risk-relevant environments. Because 25 years have elapsed since the start of the study, we are planning a fifth-wave follow-up assessment.

Phase II Two-Stage Single-Arm Clinical Trials for Testing Toxicity Levels

Simon's two-stage designs are frequently used in phase II single-arm trials for efficacy studies. In safety studies, a main concern is that there may be too many patients who experience an adverse event. We show that Simon's two-stage designs for efficacy studies can be similarly used to design a two-stage safety study by modifying some of the design parameters. Given the type I and II error rates and the proportion of adverse events experienced in the first stage cohort, we prescribe a procedure whether to terminate the trial or proceed with a stage 2 trial by recruiting additional patients. We study the relationship between a two-stage design with a safety endpoint and an efficacy endpoint and use simulation studies to ascertain their properties. We provide a real-life application and a free R package gen2stage to facilitate direct use of such two-stage designs in a safety study.

Optimal design for high-throughput screening via false discovery rate control

High-throughput screening (HTS) is a large-scale hierarchical process in which a large number of chemicals are tested in multiple stages. Conventional statistical analyses of HTS studies often suffer from high testing error rates and soaring costs in large-scale settings. This article develops new methodologies for false discovery rate control and optimal design in HTS studies. We propose a two-stage procedure that determines the optimal numbers of replicates at different screening stages while simultaneously controlling the false discovery rate in the confirmatory stage subject to a constraint on the total budget. The merits of the proposed methods are illustrated using both simulated and real data. We show that, at the expense of a limited budget, the proposed screening procedure effectively controls the error rate and the design leads to improved detection power.

Bayesian sample size determination for phase IIA clinical trials using historical data and semi-parametric prior's elicitation

The Simon's two-stage design is the most commonly applied among multi-stage designs in phase IIA clinical trials. It combines the sample sizes at the two stages in order to minimize either the expected or the maximum sample size. When the uncertainty about pre-trial beliefs on the expected or desired response rate is high, a Bayesian alternative should be considered since it allows to deal with the entire distribution of the parameter of interest in a more natural way. In this setting, a crucial issue is how to construct a distribution from the available summaries to use as a clinical prior in a Bayesian design. In this work, we explore the Bayesian counterparts of the Simon's two-stage design based on the predictive version of the single threshold design. This design requires specifying two prior distributions: the analysis prior, which is used to compute the posterior probabilities, and the design prior, which is employed to obtain the prior predictive distribution. While the usual approach is to build beta priors for carrying out a conjugate analysis, we derived both the analysis and the design distributions through linear combinations of B-splines. The motivating example is the planning of the phase IIA two-stage trial on anti-HER2 DNA vaccine in breast cancer, where initial beliefs formed from elicited experts' opinions and historical data showed a high level of uncertainty. In a sample size determination problem, the impact of different priors is evaluated.

Controlling the type I error rate in two-stage sequential adaptive designs when testing for average bioequivalence

In a 2×2 crossover trial for establishing average bioequivalence (ABE) of a generic agent and a currently marketed drug, the recommended approach to hypothesis testing is the two one-sided test (TOST) procedure, which depends, among other things, on the estimated within-subject variability. The power of this procedure, and therefore the sample size required to achieve a minimum power, depends on having a good estimate of this variability. When there is uncertainty, it is advisable to plan the design in two stages, with an interim sample size reestimation after the first stage, using an interim estimate of the within-subject variability. One method and 3 variations of doing this were proposed by Potvin et al. Using simulation, the operating characteristics, including the empirical type I error rate, of the 4 variations (called Methods A, B, C, and D) were assessed by Potvin et al and Methods B and C were recommended. However, none of these 4 variations formally controls the type I error rate of falsely claiming ABE, even though the amount of inflation produced by Method C was considered acceptable. A major disadvantage of assessing type I error rate inflation using simulation is that unless all possible scenarios for the intended design and analysis are investigated, it is impossible to be sure that the type I error rate is controlled. Here, we propose an alternative, principled method of sample size reestimation that is guaranteed to control the type I error rate at any given significance level. This method uses a new version of the inverse-normal combination of p-values test, in conjunction with standard group sequential techniques, that is more robust to large deviations in initial assumptions regarding the variability of the pharmacokinetic endpoints. The sample size reestimation step is based on significance levels and power requirements that are conditional on the first-stage results. This necessitates a discussion and exploitation of the peculiar properties of the power curve of the TOST testing procedure. We illustrate our approach with an example based on a real ABE study and compare the operating characteristics of our proposed method with those of Method B of Povin et al.

Biomarker threshold adaptive designs for survival endpoints

Due to the importance of precision medicine, it is essential to identify the right patients for the right treatment. Biomarkers, which have been commonly used in clinical research as well as in clinical practice, can facilitate selection of patients with a good response to the treatment. In this paper, we describe a biomarker threshold adaptive design with survival endpoints. In the first stage, we determine subgroups for one or more biomarkers such that patients in these subgroups benefit the most from the new treatment. The analysis in this stage can be based on historical or pilot studies. In the second stage, we sample subjects from the subgroups determined in the first stage and randomly allocate them to the treatment or control group. Extensive simulation studies are conducted to examine the performance of the proposed design. Application to a real data example is provided for implementation of the first-stage algorithms.

Nine-year change in statistical design, profile, and success rates of Phase II oncology trials

We investigated nine-year trends in statistical design and other features of Phase II oncology clinical trials published in 2005, 2010, and 2014 in five leading oncology journals: Cancer, Clinical Cancer Research, Journal of Clinical Oncology, Annals of Oncology, and Lancet Oncology. The features analyzed included cancer type, multicenter vs. single-institution, statistical design, primary endpoint, number of treatment arms, number of patients per treatment arm, whether or not statistical methods were well described, whether the drug was found effective based on rigorous statistical testing of the null hypothesis, and whether the drug was recommended for future studies.

Exact confidence limits for the response rate in two-stage designs with over- or under-enrollment in the second stage

Simon's two-stage design has been widely used in early phase clinical trials to assess the activity of a new investigated treatment. In practice, the actual sample sizes do not always follow the study design precisely, especially in the second stage. When over- or under-enrollment occurs in a study, the original critical values for the study design are no longer valid for making proper statistical inference in a clinical trial. The hypothesis for such studies is always one-sided, and the null hypothesis is rejected when only a few responses are observed. Therefore, a one-sided lower interval is suitable to test the hypothesis. The commonly used approaches for confidence interval construction are based on asymptotic approaches. These approaches generally do not guarantee the coverage probability. For this reason, Clopper-Pearson approach can be used to compute exact confidence intervals. This approach has to be used in conjunction with a method to order the sample space. The frequently used method is based on point estimates for the response rate, but this ordering has too many ties which lead to conservativeness of the exact intervals. We propose developing exact one-sided intervals based on the p-value to order the sample space. The proposed approach outperforms the existing asymptotic and exact approaches. Therefore, it is recommended for use in practice.

Characterization of dose-response for count data using a generalized MCP-Mod approach in an adaptive dose-ranging trial

Understanding the dose-response relationship is a key objective in Phase II clinical development. Yet, designing a dose-ranging trial is a challenging task, as it requires identifying the therapeutic window and the shape of the dose-response curve for a new drug on the basis of a limited number of doses. Adaptive designs have been proposed as a solution to improve both quality and efficiency of Phase II trials as they give the possibility to select the dose to be tested as the trial goes. In this article, we present a 'shapebased' two-stage adaptive trial design where the doses to be tested in the second stage are determined based on the correlation observed between efficacy of the doses tested in the first stage and a set of pre-specified candidate dose-response profiles. At the end of the trial, the data are analyzed using the generalized MCP-Mod approach in order to account for model uncertainty. A simulation study shows that this approach gives more precise estimates of a desired target dose (e.g. ED70) than a single-stage (fixed-dose) design and performs as well as a two-stage D-optimal design. We present the results of an adaptive model-based dose-ranging trial in multiple sclerosis that motivated this research and was conducted using the presented methodology.

Estimation of infection prevalence and sensitivity in a stratified two-stage sampling design employing highly specific diagnostic tests when there is no gold standard

In this work, we describe a two-stage sampling design to estimate the infection prevalence in a population. In the first stage, an imperfect diagnostic test was performed on a random sample of the population. In the second stage, a different imperfect test was performed in a stratified random sample of the first sample. To estimate infection prevalence, we assumed conditional independence between the diagnostic tests and develop method of moments estimators based on expectations of the proportions of people with positive and negative results on both tests that are functions of the tests' sensitivity, specificity, and the infection prevalence. A closed-form solution of the estimating equations was obtained assuming a specificity of 100% for both tests. We applied our method to estimate the infection prevalence of visceral leishmaniasis according to two quantitative polymerase chain reaction tests performed on blood samples taken from 4756 patients in northern Ethiopia. The sensitivities of the tests were also estimated, as well as the standard errors of all estimates, using a parametric bootstrap. We also examined the impact of departures from our assumptions of 100% specificity and conditional independence on the estimated prevalence.

Two-stage designs for cross-over bioequivalence trials

The topic of applying two-stage designs in the field of bioequivalence studies has recently gained attention in the literature and in regulatory guidelines. While there exists some methodological research on the application of group sequential designs in bioequivalence studies, implementation of adaptive approaches has focused up to now on superiority and non-inferiority trials. Especially, no comparison of the features and performance characteristics of these designs has been performed, and therefore, the question of which design to employ in this setting remains open. In this paper, we discuss and compare 'classical' group sequential designs and three types of adaptive designs that offer the option of mid-course sample size recalculation. A comprehensive simulation study demonstrates that group sequential designs can be identified, which show power characteristics that are similar to those of the adaptive designs but require a lower average sample size. The methods are illustrated with a real bioequivalence study example.

Two-stage adaptive cutoff design for building and validating a prognostic biomarker signature

Cancer biomarkers are frequently evaluated using archived specimens collected from previously conducted therapeutic trials. Routine collection and banking of high quality specimens is an expensive and time-consuming process. Therefore, care should be taken to preserve these precious resources. Here, we propose a novel two-stage adaptive cutoff design that affords the possibility to stop the biomarker study early if an evaluation of the model performance is unsatisfactory at an early stage, thereby allowing one to preserve the remaining specimens for future research. In addition, our design integrates important elements necessary to meet statistical rigor and practical demands for developing and validating a prognostic biomarker signature, including maintaining strict separation between the datasets used to build and evaluate the model and producing a locked-down signature to facilitate future validation. We conduct simulation studies to evaluate the operating characteristics of the proposed design. We show that under the null hypothesis when the model performance is deemed undesirable, the proposed design maintains type I error at the nominal level, has high probabilities of terminating the study early, and results in substantial savings in specimens. Under the alternative hypothesis, power is generally high when the total sample size and the targeted degree of improvement in prediction accuracy are reasonably large. We illustrate the use of the procedure with a dataset in patients with diffuse large-B-cell lymphoma. The practical aspects of the proposed designs are discussed. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

Adaptive designs for clinical trials assessing biomarker-guided treatment strategies

BACKGROUND

The Biomarker Strategy Design has been proposed for trials assessing the value of a biomarker in guiding treatment in oncology. In such trials, patients are randomised to either receive the standard chemotherapy treatment or a biomarker-directed treatment arm, in which biomarker status is used to guide treatment.

METHODS

Motivated by a current trial, we consider an adaptive design in which two biomarkers are assessed. The trial is conducted in two stages. In the first stage, patients in the biomarker-guided arm are assessed using a standard and an alternative cheaper biomarker, with the standard biomarker guiding treatment. An analysis comparing biomarker results is then used to choose the biomarker to use for the remainder of the trial. The new biomarker is used if the results for the two biomarkers are sufficiently similar.

RESULTS

We show that in practical situations the first-stage results can be used to adapt the trial without type I error rate inflation. We also show that there can be considerable cost gains with only a small loss in power in the case where the alternative biomarker is highly concordant with the standard one.

CONCLUSIONS

Adaptive designs have an important role in reducing the cost and increasing the clinical utility of trials evaluating biomarker-guided treatment strategies.

Testing for efficacy in adaptive clinical trials with enrichment

Adaptive design of clinical trials has attracted considerable interest because of its potential of reducing costs and saving time in the clinical development process. In this paper, we consider the problem of assessing the effectiveness of a test treatment over a control by a two-arm randomized clinical trial in a potentially heterogenous patient population. In particular, we study enrichment designs that use accumulating data from a clinical trial to adaptively determine patient subpopulation in which the treatment effect is eventually assessed. A hypothesis testing procedure and a lower confidence limit are presented for the treatment effect in the selected patient subgroups. The performances of the new methods are compared with existing approaches through a simulation study.

Phase II clinical trials with time-to-event endpoints: optimal two-stage designs with one-sample log-rank test

Phase II clinical trials are often conducted to determine whether a new treatment is sufficiently promising to warrant a major controlled clinical evaluation against a standard therapy. We consider single-arm phase II clinical trials with right censored survival time responses where the ordinary one-sample logrank test is commonly used for testing the treatment efficacy. For planning such clinical trials, this paper presents two-stage designs that are optimal in the sense that the expected sample size is minimized if the new regimen has low efficacy subject to constraints of the type I and type II errors. Two-stage designs, which minimize the maximal sample size, are also determined. Optimal and minimax designs for a range of design parameters are tabulated along with examples.

On the statistical model of the two-stage designs in bioequivalence assessment

OBJECTIVES

Two-stage clinical designs are currently recommended by the regulatory authorities for the assessment of bioequivalence (BE). A specific statistical methodology was recently proposed by the European Medicines Agency (EMA). The aims of this article are to elaborate on the suggested statistical design from the EMA and to compare it with the existing statistical methods reported in the literature.

METHODS

Monte Carlo simulations were used to simulate the conditions of a two-stage BE design. The starting sample size was either 24 or 48, whereas the coefficient of variation of the within-subject variability was equal to 20% and 40%. Several geometric mean ratio levels of the BE metric were considered. Under each condition, 1,000,000 studies were simulated.

KEY FINDINGS

The overall performance, in terms of percentage of BE acceptance, is identical. The additional term, 'sequence × stage', suggested in the EMA method is in most cases nonsignificant. The same results were obtained regardless of the type (fixed or random) of the effect applied to the 'subjects' term.

CONCLUSIONS

Any BE study either finished or in progress which relies on the existing literature methodology leads to the same percentage of BE acceptance as if it was analysed with the recently proposed EMA method.

Adaptive designs for single-arm phase II trials in oncology

Clinical phase II trials in oncology are conducted to determine whether the activity of a new anticancer treatment is promising enough to merit further investigation. Two-stage designs are commonly used for this situation to allow for early termination. Designs proposed in the literature so far have the common drawback that the sample sizes for the two stages have to be specified in the protocol and have to be adhered to strictly during the course of the trial. As a consequence, designs that allow a higher extent of flexibility are desirable. In this article, we propose a new adaptive method that allows an arbitrary modification of the sample size of the second stage using the results of the interim analysis or external information while controlling the type I error rate. If the sample size is not changed during the trial, the proposed design shows very similar characteristics to the optimal two-stage design proposed by Chang et al. (Biometrics 1987; 43:865-874). However, the new design allows the use of mid-course information for the planning of the second stage, thus meeting practical requirements when performing clinical phase II trials in oncology.

Between-arm comparisons in randomized Phase II trials

In a Phase II trial, we may randomize patients to multiple arms of experimental therapies and evaluate their efficacy to determine if any of them is worthy of a large scale Phase III trial. Usually the primary objective of such a study is to identify experimental therapies that are efficacious compared to a historical control. Each arm is independently evaluated using a standard design a for single-arm Phase II trial, e.g., Simon's optimal or minimax design. When more than one arm is accepted through such a randomized trial, we may want to select the winner(s) among them. There are methods for between-arm comparisons in the literature, but most of them have drawbacks. They have a large false selection (type I error) probability when the competing arms have a small difference in efficacy, or the statistical tests used in the selection procedure do not properly reflect the small sample sizes and multi-stage design of the trials. In this paper, we propose between-arm comparison methods for selection in randomized Phase II trials addressing these issues.