Choice of futility boundaries for group sequential designs with two endpoints

Background: In clinical trials, the opportunity for an early stop during an interim analysis (either for efficacy or for futility) may relevantly save time and financial resources. This is especially important, if the planning assumptions required for power calculation are based on a low level of evidence. For example, when including two primary endpoints in the confirmatory analysis, the power of the trial depends on the effects of both endpoints and on their correlation. Assessing the feasibility of such a trial is therefore difficult, as the number of parameter assumptions to be correctly specified is large. For this reason, so-called ‘group sequential designs’ are of particular importance in this setting. Whereas the choice of adequate boundaries to stop a trial early for efficacy has been broadly discussed in the literature, the choice of optimal futility boundaries has not been investigated so far, although this may have serious consequences with respect to performance characteristics. Methods: In this work, we propose a general method to construct ‘optimal’ futility boundaries according to predefined criteria. Further, we present three different group sequential designs for two endpoints applying these futility boundaries. Our methods are illustrated by a real clinical trial example and by Monte-Carlo simulations. Results: By construction, the provided method of choosing futility boundaries maximizes the probability to correctly stop in case of small or opposite effects while limiting the power loss and the probability of stopping the study ‘wrongly’. Our results clearly demonstrate the benefit of using such ‘optimal’ futility boundaries, especially compared to futility boundaries commonly applied in practice. Conclusions: As the properties of futility boundaries are often not considered in practice and unfavorably chosen futility boundaries may imply bad properties of the study design, we recommend assessing the performance of these boundaries according to the criteria proposed in here

To test or not to test:Preliminary assessment of normality when comparing two independent samples

BACKGROUND: Student’s two-sample t test is generally used for comparing the means of two independent samples, for example, two treatment arms. Under the null hypothesis, the t test assumes that the two samples arise from the same normally distributed population with unknown variance. Adequate control of the Type I error requires that the normality assumption holds, which is often examined by means of a preliminary Shapiro-Wilk test. The following two-stage procedure is widely accepted: If the preliminary test for normality is not significant, the t test is used; if the preliminary test rejects the null hypothesis of normality, a nonparametric test is applied in the main analysis. METHODS: Equally sized samples were drawn from exponential, uniform, and normal distributions. The two-sample t test was conducted if either both samples (Strategy I) or the collapsed set of residuals from both samples (Strategy II) had passed the preliminary Shapiro-Wilk test for normality; otherwise, Mann-Whitney’s U test was conducted. By simulation, we separately estimated the conditional Type I error probabilities for the parametric and nonparametric part of the two-stage procedure. Finally, we assessed the overall Type I error rate and the power of the two-stage procedure as a whole. RESULTS: Preliminary testing for normality seriously altered the conditional Type I error rates of the subsequent main analysis for both parametric and nonparametric tests. We discuss possible explanations for the observed results, the most important one being the selection mechanism due to the preliminary test. Interestingly, the overall Type I error rate and power of the entire two-stage procedure remained within acceptable limits. CONCLUSION: The two-stage procedure might be considered incorrect from a formal perspective; nevertheless, in the investigated examples, this procedure seemed to satisfactorily maintain the nominal significance level and had acceptable power properties

Basket trial designs based on power priors

In basket trials a treatment is investigated in several subgroups. They are primarily used in oncology in early clinical phases as single-arm trials with a binary endpoint. For their analysis primarily Bayesian methods have been suggested, as they allow partial sharing of information based on the observed similarity between subgroups. Fujikawa et al. (2020) suggested an approach using empirical Bayes methods that allows flexible sharing based on easily interpreteable weights derived from the Jensen-Shannon divergence between the subgroupwise posterior distributions. We show that this design is closely related to the method of power priors and investigate several modifications of Fujikawa's design using methods from the power prior literature. While in Fujikawa's design, the amount of information that is shared between two baskets is only determined by their pairwise similarity, we also discuss extensions where the outcomes of all baskets are considered in the computation of the sharing-weights. The results of our comparison study show that the power prior design has compareable performance to fully Bayesian designs in a range of different scenarios. At the same time, the power prior design is computationally cheap and even allows analytical computation of operating characteristics in some settings

A systematic comparison of recurrent event models for application to composite endpoints

Background: Many clinical trials focus on the comparison of the treatment effect between two or more groups concerning a rarely occurring event. In this situation, showing a relevant effect with an acceptable power requires the observation of a large number of patients over a long period of time. For feasibility issues, it is therefore often considered to include several event types of interest, non-fatal or fatal, and to combine them within a composite endpoint. Commonly, a composite endpoint is analyzed with standard survival analysis techniques by assessing the time to the first occurring event. This approach neglects that an individual may experience more than one event which leads to a loss of information. As an alternative, composite endpoints could be analyzed by models for recurrent events. There exists a number of such models, e.g. regression models based on count data or Cox-based models such as the approaches of Andersen and Gill, Prentice, Williams and Peterson or, Wei, Lin and Weissfeld. Although some of the methods were already compared within the literature there exists no systematic investigation for the special requirements regarding composite endpoints. Methods: Within this work a simulation-based comparison of recurrent event models applied to composite endpoints is provided for different realistic clinical trial scenarios. Results: We demonstrate that the Andersen-Gill model and the Prentice- Williams-Petersen models show similar results under various data scenarios whereas the Wei-Lin-Weissfeld model delivers effect estimators which can considerably deviate under commonly met data scenarios. Conclusion: Based on the conducted simulation study, this paper helps to understand the pros and cons of the investigated methods in the context of composite endpoints and provides therefore recommendations for an adequate statistical analysis strategy and a meaningful interpretation of results

Sample Size Calculation and Blinded Recalculation for Analysis of Covariance Models with Multiple Random Covariates

When testing for superiority in a parallel-group setting with a continuous outcome, adjusting for covariates is usually recommended. For this purpose, the analysis of covariance is frequently used, and recently several exact and approximate sample size calculation procedures have been proposed. However, in case of multiple covariates, the planning might pose some practical challenges and pitfalls. Therefore, we propose a method, which allows for blinded re-estimation of the sample size during the course of the trial. Simulations confirm that the proposed method provides reliable results in many practically relevant situations, and applicability is illustrated by a real-life data example

Two-stage phase II oncology designs using short-term endpoints for early stopping

Phase II oncology trials are conducted to evaluate whether the tumour activity of a new treatment is promising enough to warrant further investigation. The most commonly used approach in this context is a two-stage single-arm design with binary endpoint. As for all designs with interim analysis, its efficiency strongly depends on the relation between recruitment rate and follow-up time required to measure the patients’ outcomes. Usually, recruitment is postponed after the sample size of the first stage is achieved up until the outcomes of all patients are available. This may lead to a considerable increase of the trial length and with it to a delay in the drug development process. We propose a design where an intermediate endpoint is used in the interim analysis to decide whether or not the study is continued with a second stage. Optimal and minimax versions of this design are derived. The characteristics of the proposed design in terms of type I error rate, power, maximum and expected sample size as well as trial duration are investigated. Guidance is given on how to select the most appropriate design. Application is illustrated by a phase II oncology trial in patients with advanced angiosarcoma, which motivated this research

A new conditional performance score for the evaluation of adaptive group sequential designs with sample size recalculation

In standard clinical trial designs, the required sample size is fixed in the planning stage based on initial parameter assumptions. It is intuitive that the correct choice of the sample size is of major importance for an ethical justification of the trial. The required parameter assumptions should be based on previously published results from the literature. In clinical practice, however, historical data often do not exist or show highly variable results. Adaptive group sequential designs allow a sample size recalculation after a planned unblinded interim analysis in order to adjust the sample size during the ongoing trial. So far, there exist no unique standards to assess the performance of sample size recalculation rules. Single performance criteria commonly reported are given by the power and the average sample size; the variability of the recalculated sample size and the conditional power distribution are usually ignored. Therefore, the need for an adequate performance score combining these relevant performance criteria is evident. To judge the performance of an adaptive design, there exist two possible perspectives, which might also be combined: Either the global performance of the design can be addressed, which averages over all possible interim results, or the conditional performance is addressed, which focuses on the remaining performance conditional on a specific interim result. In this work, we give a compact overview of sample size recalculation rules and performance measures. Moreover, we propose a new conditional performance score and apply it to various standard recalculation rules by means of Monte-Carlo simulations