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High placebo responses could significantly reduce the treatment effect in a parallel randomized trial. To combat that challenge, several approaches were developed, including the sequential parallel comparison design (SPCD) that was shown to increase the statistical power as compared to the traditional randomized trial. A linear combination of the response rate differences from two phases per the SPCD is commonly used to measure the overall treatment effect size. The traditional approach to calculate the confidence interval for the overall rate difference is based on the delta method using the variance–covariance matrix of all outcomes. As outcomes from a multinomial distribution are correlated, we suggest utilizing a constrained variance–covariance matrix in the delta method. In the observation of anti-conservative coverages from asymptotic intervals, we further propose using importance sampling to develop accurate intervals. Simulation studies show that accurate intervals have better coverage probabilities than others and the interval width of accurate intervals is similar to the interval width of others. Two real trials to treat major depressive disorder are used to illustrate the application of the proposed intervals. [ABSTRACT FROM AUTHOR]

High placebo responses in clinical trial could reduce the treatment effect leading to the failure of a promising drug. Several strategies have been developed to minimize high placebo responses, including the sequential parallel comparison design (SPCD). For a study with binary outcome, the existing statistical methods to test the drug effectiveness always rely on the asymptotic limiting distribution. When a study's sample size is small to medium, the asymptotic approaches do not have satisfactory performance with regard to type I error rate and statistical power. For that reason, we propose utilizing exact conditional approach to calculate sample size based on the existing test statistics to order the sample space. The proposed method controls the type I error rate under the unconditional framework. We compare the proposed exact sample sizes using different test statistics and the sample size for a randomized parallel study. We would recommend using exact sample sizes for the SPCD with small- to medium sample sizes and the SPCD with extreme response rates. [ABSTRACT FROM AUTHOR]

In recent years, adaptive randomization methods have gained significant popularity in clinical research and trial design due to their ability to provide both efficiency and flexibility in adjusting the statistical procedures of ongoing clinical trials. For a study to compare multiple treatments, a multi-arm two-stage design could be utilized to select the best treatment from the first stage and further compare that treatment with control in the second stage. The traditional design used equal randomization in both stages. To better utilize the interim results from the first stage, we propose to develop response adaptive randomization two-stage designs for a multi-arm clinical trial with binary outcome. Two allocation methods are considered: (1) an optimal allocation based on a sequential design; (2) the play-the-winner rule. Optimal multi-arm two-stage designs are obtained under three criteria: minimizing the expected number of failures, minimizing the average expected sample size, and minimizing the expected sample size under the null hypothesis. Simulation studies show that the proposed adaptive design based on the play-the-winner rule has good performance. A phase II trial for patients with pancreas adenocarcinoma and a germline BRCA $/$ / PALB2 mutation was used to illustrate the application of the proposed response adaptive randomization designs. [ABSTRACT FROM AUTHOR]

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

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

During drug development, a biomarker is sometimes identified as separating a patient population into those with more and those with less benefit from evaluated treatments. Consequently, later studies might be targeted, while earlier ones are performed in mixed patient populations. This poses a challenge in evidence synthesis, especially if only aggregated data are available. Starting from this scenario, we investigate three commonly used network meta‐analytic estimation methods, the naive estimation approach, the stand‐alone analysis, and the network meta‐regression. Additionally, we adapt and modify two methods, which are used in evidence synthesis to combine randomized controlled trials with observational studies, the enrichment‐through‐weighting approach, and the informative prior estimation. We evaluate all five methods in a simulation study with 32 scenarios using bias, root‐mean‐squared‐error, coverage, precision, and power. Additionally, we revisit a clinical data set to exemplify and discuss the application. In the simulation study, none of the methods was observed to be clearly favorable over all investigated scenarios. However, the stand‐alone analysis and the naive estimation performed comparably or worse than the other methods in all evaluated performance measures and simulation scenarios and are therefore not recommended. While substantial between‐trial heterogeneity is challenging for all estimation approaches, the performance of the network meta‐regression, the enriching‐through weighting approach and the informative prior approach was dependent on the simulation scenario and the performance measure of interest. Furthermore, as these estimation methods are drawing slightly different assumptions, some of which require the presence of additional information for estimation, we recommend sensitivity‐analyses wherever possible. [ABSTRACT FROM AUTHOR]

The adaptive seamless design combining phases II and III into a single trial has been shown growing interest for improving the efficiency of drug development, becoming the most frequent adaptive design type. It typically consists of two stages, the trial objectives being often different in each stage. The primary objectives are to select optimal experimental treatment group(s) in the first stage and compare the efficacy between the selected treatment and control groups in the second stage. In this article, we focus on a two‐stage adaptive seamless design, for which treatment selection is based on the short‐term binary endpoint and treatment comparison is based on the long‐term binary endpoint. We thus propose an exact conditional test as a final analysis, based on the bivariate binomial distribution and given the selected treatment with the most promising short‐term endpoint response rate from an interim analysis. Additionally, the mid‐p$$ p $$ approach is incorporated to improve conservativeness for an exact test. Simulation studies were conducted to compare the proposed methods with a method based on the combination test. The proposed exact method controlled for type I error rate at the nominal level, regardless of the number of initial treatments or the correlation between short‐ and long‐term endpoints. In terms of the treatment comparison power, the proposed methods are more powerful than that based on the combination test in the scenarios, with only one treatment being effective. [ABSTRACT FROM AUTHOR]

In phase II oncology trials, two‐stage design allowing early stopping for futility and/or efficacy is frequently used. However, this design based on frequentist statistical approaches could not guarantee a high posterior probability of attending the pre‐specified clinically interesting rate from a Bayesian perspective. Here, we proposed a new Bayesian design enabling early terminating for efficacy as well as futility. In addition to the clinically uninteresting and interesting response rate, a prior distribution of response rate, the minimum posterior threshold probabilities and the lengths of the highest posterior density intervals were specified in the design. Finally, we defined the feasible design with the highest total effective predictive probability. We studied the properties of the proposed design and applied it to an oncology trial as an example. The proposed design ensured that the observed response rate fell within prespecified levels of posterior probability. The proposed design provides an alternative design to single‐arm two‐stage trials. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Multiple Comparison Procedure – Modelling (MCP-Mod) method was qaulified by regulatory agencies (e.g., EMA in 2014 and FDA in 2016) as an efficient statistical method for Phase 2 dose-finding studies when there is uncertainty about dose-response relationship. As this is a relatively new approach, there is limited literature providing practical guidance on its application. In this paper, we evaluated the performance of the MCP-Mod method for clinical trials with a binary primary endpoint, focusing on (1) the impact of sample size, data variability and treatment effect size on the performance of the MCP-Mod, (2) the impact of candidate model mis-specification, and (3) optimal sample allocation under a fixed sample size. The evaluation was performed via simulations under different scenarios.

Phase II clinical trials make a critical decision of go or no‐go to a subsequent phase III studies. A considerable proportion of promising drugs identified in phase II trials fail the confirmative efficacy test in phase III. Recognizing the low posterior probabilities of H1 when accepting the drug under Simon's two‐stage design, the Bayesian enhancement two‐stage (BET) design is proposed to strengthen the passing criterion. Under the BET design, the lengths of highest posterior density (HPD) intervals, posterior probabilities of H0 and H1 are computed to calibrate the design parameters, aiming to improve the stability of the trial characteristics and strengthen the evidence for proceeding the drug development forward. However, from a practical perspective, the HPD interval length lacks transparency and interpretability. To circumvent this problem, we propose the BET design with error control (BETEC) by replacing the HPD interval length with the posterior error rate. The BETEC design can achieve a balance between the posterior false positive rate and false negative rate and, more importantly, it has an intuitive and clear interpretation. We compare our method with the BET design and Simon's design through extensive simulation studies. As an illustration, we further apply BETEC to two recent clinical trials, and investigate its performance in comparison with other competitive designs. Being both efficient and intuitive, the BETEC design can serve as an alternative toolbox for implementing phase II single‐arm trials. [ABSTRACT FROM AUTHOR]

Individualized therapies for patients with biomarkers are moving more and more into the focus of research interest when developing new treatments. Hereby, the term individualized (or targeted) therapy denotes a treatment specifically developed for biomarker‐positive patients. A network meta‐analysis model for a binary endpoint combining the evidence for a targeted therapy from individual patient data with the evidence for a non‐targeted therapy from aggregate data is presented and investigated. The biomarker status of the patients is either available at patient‐level in individual patient data or at study‐level in aggregate data. Both types of biomarker information have to be included. The evidence synthesis model follows a Bayesian approach and applies a meta‐regression to the studies with aggregate data. In a simulation study, we address three treatment arms, one of them investigating a targeted therapy. The bias and the root‐mean‐square error of the treatment effect estimate for the subgroup of biomarker‐positive patients based on studies with aggregate data are investigated. Thereby, the meta‐regression approach is compared to approaches applying alternative solutions. The regression approach has a surprisingly small bias even in the presence of few studies. By contrast, the root‐mean‐square error is relatively greater. An illustrative example is provided demonstrating implementation of the presented network meta‐analysis model in a clinical setting. [ABSTRACT FROM AUTHOR]

Single-arm trials with binary endpoint are firmly established in e.g., early clinical oncology. Here, two-stage designs are often employed to allow early termination of the trial in the case of an unexpectedly large or small response rate to the new treatment. Various designs have been proposed over the last few years which usually require strong assumptions about the true response rate during planning. Often, these designs are not robust to deviations from the planning assumptions. In this paper, we define a Bayesian framework for scoring two-stage designs under uncertainty and investigate the characteristics of designs optimizing a commonly employed performance score of Liu et al. The resulting optimal designs are compared with an alternative, utility-based approach incorporating expected power and sample size. We provide insights in the underlying implicit assumptions of using expected power for scoring adaptive designs and relate the global score function to the practice of sample size recalculation based on conditional power. An in-depth comparison of the features of the different performance scores and their respective optimizing designs provides the guidance for practitioners who face the problem of choosing between the various options. A software implementation of the proposed methods is publicly available online. [ABSTRACT FROM AUTHOR]

In the clinical development of some new infectious disease drugs, early clinical pharmacology trials may predict with high confidence that the efficacious doses are well below the range of the safety margin. In this case, a dose-ranging study may be unnecessary after a proof-of-concept (PoC) study testing the highest dose. A multi-stage adaptive design spanning both PoC and confirmatory stages is proposed in this context. The design incorporates two interim analyses allowing strategies for stopping, continuing, or expanding the study. A conditional power threshold for a binary endpoint is proposed to assess futility. Additional components of early efficacy and sample size adjustment are also included to enhance the design's flexibility and robustness. Design operating characteristics are evaluated by numerical calculation. We show that the proposed streamlined trial design has the same statistical rigor as a conventional phase 3 clinical trial with adequate power and a properly controlled type 1 error rate. Additional adaptive design options are also investigated and discussed. [ABSTRACT FROM AUTHOR]

Targeted therapies are becoming more common. In targeted therapy development, suppose its companion diagnostic test divides patients into a marker‐positive subgroup and its complementary marker‐negative subgroup. To find the right patient population for the therapy to target, inference on efficacy in the marker‐positive and marker‐negative subgroups as well as efficacy in the overall mixture population are all of interest. Depending on the type of clinical endpoints, inference on mixture population can be nontrivial and commonly used efficacy measures may not be suitable for a mixture population. Correlations among estimates of efficacy in the marker‐positive, marker‐negative, and overall mixture population play a crucial role in using an earlier phase study to inform on the design of a confirmatory study (e.g., determination of sample size). This article first shows that when the clinical endpoint is binary (such as respond or not), odds ratio is inappropriate as an efficacy measure in this setting, but relative response (RR) is appropriate. We show a safe way of calculating estimated correlations is to consider mixing subgroup response probabilities within each treatment arm first, and then derive the joint distribution of RR estimates. We also show, if one calculates RR within each subgroup first, how wrong the correlations can be if the Delta method derivation fails to take randomness of estimating the mixing coefficient into account. [ABSTRACT FROM AUTHOR]

Enhanced knowledge of the biological and genetic basis of cancer is re-defining the target population for new treatments. In oncology, potential targets for a new therapeutic agent often include various solid and hematologic malignancies that share common signaling pathways. New agents are often tested in multiple tumor types across which information can be borrowed. We propose a hierarchical Bayesian design (HBD) to simultaneously test a novel agent in multiple groups for randomized Phase II clinical trials with binary endpoints. Compared to parallel design for individual tumor groups, the HBD has greatly reduced sample size. Therefore, this improves efficiency and decreases the financial cost of conducting randomized Phase II clinical trials. An R package hbdct has been developed to implement the HBD and streamline the sample size calibration. [ABSTRACT FROM AUTHOR]

Abstract: The choice of a primary endpoint is an important issue when designing a clinical trial. It is common to use composite endpoints as a primary endpoint because it increases the number of observed events, captures more information and is expected to increase the power. However, combining events that have no similar clinical importance and have different treatment effects makes the interpretation of the results cumbersome and might reduce the power of the corresponding tests. Gómez and Lagakos proposed the ARE (asymptotic relative efficiency) method to choose between a composite or one of its components as primary endpoint comparing the efficacy of a treatment based on the times to each of these endpoints. The aim of this paper is to expand the ARE method to binary endpoints. We show that the ARE method depends on six parameters including the degree of association between components, event proportion, and effect of therapy given by the corresponding odds ratio of the single endpoints. A case study is presented to illustrate the methodology. We conclude with efficient guidelines for discerning which could be the best suited primary endpoint given anticipated parameters. [ABSTRACT FROM AUTHOR]

Inference after two-stage single-arm designs with binary endpoint is challenging due to the nonunique ordering of the sampling space in multistage designs. We illustrate the problem of specifying test-compatible confidence intervals for designs with nonconstant second-stage sample size and present two approaches that guarantee confidence intervals consistent with the test decision. Firstly, we extend the well-known Clopper-Pearson approach of inverting a family of two-sided hypothesis tests from the group-sequential case to designs with fully adaptive sample size. Test compatibility is achieved by using a sample space ordering that is derived from a test-compatible estimator. The resulting confidence intervals tend to be conservative but assure the nominal coverage probability. In order to assess the possibility of further improving these confidence intervals, we pursue a direct optimization approach minimizing the mean width of the confidence intervals. While the latter approach produces more stable coverage probabilities, it is also slightly anti-conservative and yields only negligible improvements in mean width. We conclude that the Clopper-Pearson-type confidence intervals based on a test-compatible estimator are the best choice if the nominal coverage probability is not to be undershot and compatibility of test decision and confidence interval is to be preserved. [ABSTRACT FROM AUTHOR]

We study matched pair designs with two binary endpoints under three different approaches. Power approximation and sample size calculation are derived under these situations and facilitated by R programs. An adaptive design with sample size re-estimation is also presented. Through extensive simulations, we provide general guidelines for practitioners to choose the best approach according to the ranges of the interested parameters in the sense of feasibility and robustness. Application to a cancer chemotherapy trial is illustrated. [ABSTRACT FROM AUTHOR]

Background: When designing studies that have a binary outcome as the primary endpoint, the hypothesized proportion of patients in each population experiencing the endpoint of interest (i.e., π 1,π 2) plays an important role in sample size and power calculations. Point estimates for π 1 and π 2 are often calculated using historical data. However, the uncertainty in these estimates is rarely addressed.Methods: This paper presents a hybrid classical and Bayesian procedure that formally integrates prior information on the distributions of π 1 and π 2 into the study's power calculation. Conditional expected power (CEP), which averages the traditional power curve using the prior distributions of π 1 and π 2 as the averaging weight conditional on the presence of a positive treatment effect (i.e., π 2>π 1), is used, and the sample size is found that equates the pre-specified frequentist power (1-β) and the conditional expected power of the trial.Results: Notional scenarios are evaluated to compare the probability of achieving a target value of power with a trial design based on traditional power and a design based on CEP. We show that if there is uncertainty in the study parameters and a distribution of plausible values for π 1 and π 2, the performance of the CEP design is more consistent and robust than traditional designs based on point estimates for the study parameters. Traditional sample size calculations based on point estimates for the hypothesized study parameters tend to underestimate the required sample size needed to account for the uncertainty in the parameters. The greatest marginal benefit of the proposed method is achieved when the uncertainty in the parameters is not large.Conclusions: Through this procedure, we are able to formally integrate prior information on the uncertainty and variability of the study parameters into the design of the study while maintaining a frequentist framework for the final analysis. Solving for the sample size that is necessary to achieve a high level of CEP given the available prior information helps protect against misspecification of hypothesized treatment effect and provides a substantiated estimate that forms the basis for discussion about the study's feasibility during the design phase. [ABSTRACT FROM AUTHOR]

The article discusses the necessity of conducting a definite go/no-go study before making a major investment (phase 3) on a newly developed drug. Topics covered include conducting a study or review of a probable occurrence of an adverse event from previous studies, checking if a dose-limiting adverse event may have occurred that could affect patient tolerance to the drug, and validating a delivery medical device that may have an unacceptable failure rate.

The design of a three-arm trial including the experimental treatment, an active reference treatment, and a placebo is recommended as a useful approach to the assessment of noninferiority of the experimental treatment. The inclusion of the placebo arm enables the assessment of assay sensitivity and internal validation, in addition to testing the noninferiority of the experimental treatment to the reference. Generally, the acceptable noninferiority margin Δ has been defined as the maximum clinically irrelevant difference between treatments in many two-arm noninferiority trials. However, many articles have considered a design in which the noninferiority margin Δ is relatively defined as a prespecified fraction f of the unknown effect size of the reference treatment. Therefore, these methods cannot be applied to cases where the margin is defined as a prespecified difference between treatments, in this article, we propose score-based statistical procedures for a three-arm noninferiority trial with a prespecified margin Δ for inference of the difference in the proportions of binary endpoints, in addition, we derive the approximate sample size and optimal allocation to minimize the total sample size and that of the placebo arm. A randomized controlled trial on major depressive disorder based on the difference in the proportions of remission is used to demonstrate our proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This article reviews the basic principles involved in the design, conduct, and analysis of Phase III treatment trials in prostate cancer. It begins with a brief review of Phase III trials, and subsequently describes the process of hypothesis testing and the types of errors involved in the process of statistical inference. Next, it presents a general discussion of design considerations, including choice of endpoints, patient selection and eligibility criteria, randomization and stratification, methods to determine the required number patients, standard procedures to monitor a study, and finally how to analyze the results from randomized clinical trials. [Copyright &y& Elsevier]

Phase III trials are aimed at assessing whether new treatments have superior efficacy than standards. Sequential methods, such as the single triangular test (STT) and the double triangular test (DTT), allow for early stopping of such trials. They use stopping boundaries which depend, for a binary endpoint, on π0 and π1 (response rates under standard and new treatment, respectively) and α and β (type I and II errors, respectively). Thus, a wrong estimation of π0 at planning phase might have an influence on their statistical properties. We assessed the extent of this influence by simulations regarding α, 1 − β, and average sample number (ASN) and compared the two methods with the one-sided and two-sided single-stage designs (SSD). There was no influence on α for any test and the power achieved by the one-sided or two-sided SSD was moderately affected by a wrong estimation of π0. However, important drifts (whose magnitude depended on chosen design) were observed for sequential methods concerning power and ASN in case of moderate under- or overestimation of π0 (±20% compared with its ‘true’ value). For example, when ‘true’ values of π0 and π1 are 0.30 and 0.40, respectively, using design values of 0.10 and 0.20, the power is 0.57 and 0.50 for the STT and DTT, respectively, instead of 0.95. When ‘true’ values of π0 and π1 are 0.10 and 0.20, respectively, using design values of 0.30 and 0.40, the ASN under H0 is 1309 and 2019 for the STT and DTT, respectively, instead of 392 and 601, respectively, using the right design. Using sequential methods in comparative clinical trials with binary responses requires a precise knowledge of the response rate under standard treatment to avoid losses in power or inappropriate increases in sample size. [ABSTRACT FROM AUTHOR]