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: Sample size calculation is a central aspect in planning of clinical trials. The sample size is calculated based on parameter assumptions, like the treatment effect and the endpoint\'s variance. A fundamental problem of this approach is that the true distribution parameters are not known before the trial. Hence, sample size calculation always contains a certain degree of uncertainty, leading to the risk of underpowering or oversizing a trial. One way to cope with this uncertainty are adaptive designs. Adaptive designs allow to adjust the sample size during an interim analysis. There is a large number of such recalculation rules to choose from. To guide the choice of a suitable adaptive design with sample size recalculation, previous literature suggests a conditional performance score for studies with a normally distributed endpoint. However, binary endpoints are also frequently applied in clinical trials and the application of the conditional performance score to binary endpoints is not yet investigated.
METHODS: We extend the theory of the conditional performance score to binary endpoints by suggesting a related one-dimensional score parametrization. We moreover perform a simulation study to evaluate the operational characteristics and to illustrate application.
RESULTS: We find that the score definition can be extended without modification to the case of binary endpoints. We represent the score results by a single distribution parameter, and therefore derive a single effect measure, which contains the difference in proportions [Formula: see text] between the intervention and the control group, as well as the endpoint proportion [Formula: see text] in the control group.
CONCLUSIONS: This research extends the theory of the conditional performance score to binary endpoints and demonstrates its application in practice.

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.

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.

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.

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.

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.

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.

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.