Adaptive graph-based multiple testing procedures

Adaptive two-stage seamless sequential design for clinical trials

We propose an adaptive sequential testing procedure for the selection and testing of multiple treatment options, such as dose/regimen, different drugs, sub-populations, endpoints, or a mixture of them in a seamlessly combined phase II/III trial. The selection is to be made at the end of phase 2 stage. Unlike in many of the published literature, the selection rule is not required to be to "select the best", and does not need to be pre-specified, which provides flexibility and allows the trial investigators to use any efficacy and safety information/criteria, or surrogate or intermediate endpoint to make the selection. Sample size and power calculations are provided. The calculations have been confirmed to be accurate by simulations. Interim analysis can be performed after the selection, sample size can be modified if the observed efficacy deviates from the assumed. Inference after the trial, including p-value, median unbiased point estimate and confidence intervals, are provided. By applying a dominance theorem, the procedure can be applied to normal, binary, Poisson, negative binomial distributed endpoints and time-to-event endpoints, and a mixture of these distributions (in trials involving endpoint selection).

Clinical Trials Impacted by the COVID-19 Pandemic: Adaptive Designs to the Rescue?

Very recently the new pathogen severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was identified and the coronavirus disease 2019 (COVID-19) declared a pandemic by the World Health Organization. The pandemic has a number of consequences for ongoing clinical trials in non-COVID-19 conditions. Motivated by four current clinical trials in a variety of disease areas we illustrate the challenges faced by the pandemic and sketch out possible solutions including adaptive designs. Guidance is provided on (i) where blinded adaptations can help; (ii) how to achieve Type I error rate control, if required; (iii) how to deal with potential treatment effect heterogeneity; (iv) how to use early read-outs; and (v) how to use Bayesian techniques. In more detail approaches to resizing a trial affected by the pandemic are developed including considerations to stop a trial early, the use of group-sequential designs or sample size adjustment. All methods considered are implemented in a freely available R shiny app. Furthermore, regulatory and operational issues including the role of data monitoring committees are discussed.

Symmetric graphs for equally weighted tests, with application to the Hochberg procedure

The graphical approach to multiple testing provides a convenient tool for designing, visualizing, and performing multiplicity adjustments in confirmatory clinical trials while controlling the familywise error rate. It assigns a set of weights to each intersection null hypothesis within the closed test framework. These weights form the basis for intersection tests using weighted individual p-values, such as the weighted Bonferroni test. In this paper, we extend the graphical approach to intersection tests that assume equal weights for the elementary null hypotheses associated with any intersection hypothesis, including the Hochberg procedure as well as omnibus tests such as Fisher's combination, O'Brien's, and F tests. More specifically, we introduce symmetric graphs that generate sets of equal weights so that the aforementioned tests can be applied with the graphical approach. In addition, we visualize the Hochberg and the truncated Hochberg procedures in serial and parallel gatekeeping settings using symmetric component graphs. We illustrate the method with two clinical trial examples.

Methods for the analysis of multiple endpoints in small populations: A review

While current guidelines generally recommend single endpoints for primary analyses of confirmatory clinical trials, it is recognized that certain settings require inference on multiple endpoints for comprehensive conclusions on treatment effects. Furthermore, combining treatment effect estimates from several outcome measures can increase the statistical power of tests. Such an efficient use of resources is of special relevance for trials in small populations. This paper reviews approaches based on a combination of test statistics or measurements across endpoints as well as multiple testing procedures that allow for confirmatory conclusions on individual endpoints. We especially focus on feasibility in trials with small sample sizes and do not solely rely on asymptotic considerations. A systematic literature search in the Scopus database, supplemented by a manual search, was performed to identify research papers on analysis methods for multiple endpoints with relevance to small populations. The identified methods were grouped into approaches that combine endpoints into a single measure to increase the power of statistical tests and methods to investigate differential treatment effects in several individual endpoints by multiple testing.

Flexible alpha allocation strategies for confirmatory adaptive enrichment clinical trials with a prespecified subgroup

Adaptive enrichment designs have recently received considerable attention as they have the potential to make drug development process for personalized medicine more efficient. Several statistical approaches have been proposed so far in the literature and the operating characteristics of these approaches are extensively investigated using simulation studies. In this paper, we improve on existing adaptive enrichment designs by assigning unequal weights to the significance levels associated with the hypotheses of the overall population and a prespecified subgroup. More specifically, we focus on the standard combination test, a modified combination test, the marginal combination test, and the partial conditional error rate approach and explore the operating characteristics of these approaches by a simulation study. We show that these approaches can lead to power gains, compared to existing approaches, if the weights are chosen carefully.

Lessons learned from IDeAl - 33 recommendations from the IDeAl-net about design and analysis of small population clinical trials

BACKGROUND

IDeAl (Integrated designs and analysis of small population clinical trials) is an EU funded project developing new statistical design and analysis methodologies for clinical trials in small population groups. Here we provide an overview of IDeAl findings and give recommendations to applied researchers.

METHOD

The description of the findings is broken down by the nine scientific IDeAl work packages and summarizes results from the project's more than 60 publications to date in peer reviewed journals. In addition, we applied text mining to evaluate the publications and the IDeAl work packages' output in relation to the design and analysis terms derived from in the IRDiRC task force report on small population clinical trials.

RESULTS

The results are summarized, describing the developments from an applied viewpoint. The main result presented here are 33 practical recommendations drawn from the work, giving researchers a comprehensive guidance to the improved methodology. In particular, the findings will help design and analyse efficient clinical trials in rare diseases with limited number of patients available. We developed a network representation relating the hot topics developed by the IRDiRC task force on small population clinical trials to IDeAl's work as well as relating important methodologies by IDeAl's definition necessary to consider in design and analysis of small-population clinical trials. These network representation establish a new perspective on design and analysis of small-population clinical trials.

CONCLUSION

IDeAl has provided a huge number of options to refine the statistical methodology for small-population clinical trials from various perspectives. A total of 33 recommendations developed and related to the work packages help the researcher to design small population clinical trial. The route to improvements is displayed in IDeAl-network representing important statistical methodological skills necessary to design and analysis of small-population clinical trials. The methods are ready for use.

Twenty-five years of confirmatory adaptive designs: opportunities and pitfalls

'Multistage testing with adaptive designs' was the title of an article by Peter Bauer that appeared 1989 in the German journal Biometrie und Informatik in Medizin und Biologie. The journal does not exist anymore but the methodology found widespread interest in the scientific community over the past 25 years. The use of such multistage adaptive designs raised many controversial discussions from the beginning on, especially after the publication by Bauer and Köhne 1994 in Biometrics: Broad enthusiasm about potential applications of such designs faced critical positions regarding their statistical efficiency. Despite, or possibly because of, this controversy, the methodology and its areas of applications grew steadily over the years, with significant contributions from statisticians working in academia, industry and agencies around the world. In the meantime, such type of adaptive designs have become the subject of two major regulatory guidance documents in the US and Europe and the field is still evolving. Developments are particularly noteworthy in the most important applications of adaptive designs, including sample size reassessment, treatment selection procedures, and population enrichment designs. In this article, we summarize the developments over the past 25 years from different perspectives. We provide a historical overview of the early days, review the key methodological concepts and summarize regulatory and industry perspectives on such designs. Then, we illustrate the application of adaptive designs with three case studies, including unblinded sample size reassessment, adaptive treatment selection, and adaptive endpoint selection. We also discuss the availability of software for evaluating and performing such designs. We conclude with a critical review of how expectations from the beginning were fulfilled, and - if not - discuss potential reasons why this did not happen.

Overview of multiple testing methodology and recent development in clinical trials

Multiplicity control is an important statistical issue in clinical trials where strong control of the type I error rate is required. Many multiple testing methods have been proposed and applied to address multiplicity issues in clinical trials. This paper provides an application oriented and comprehensive overview of commonly used multiple testing procedures and recent developments in statistical methodology in multiple testing in clinical trials. Commonly used multiple testing procedures are applied to test non-hierarchical hypotheses and gatekeeping procedures can be used to test hierarchically ordered hypotheses while controlling the overall type I error rate. The recently developed graphical approach has the flexibility to integrate hierarchical and non-hierarchical procedures into one framework. A graphical multiple testing procedure with "no-dead-end" provides an opportunity to fully recycle α across hypothesis families. Two hypothetical clinical trial examples are used to illustrate applications of these procedures. The advantages and disadvantages of the different procedures are briefly discussed.

A simple and flexible graphical approach for adaptive group-sequential clinical trials

In this article, we introduce a graphical approach to testing multiple hypotheses in group-sequential clinical trials allowing for midterm design modifications. It is intended for structured study objectives in adaptive clinical trials and extends the graphical group-sequential designs from Maurer and Bretz (Statistics in Biopharmaceutical Research 2013; 5: 311-320) to adaptive trial designs. The resulting test strategies can be visualized graphically and performed iteratively. We illustrate the methodology with two examples from our clinical trial practice. First, we consider a three-armed gold-standard trial with the option to reallocate patients to either the test drug or the active control group, while stopping the recruitment of patients to placebo, after having demonstrated superiority of the test drug over placebo at an interim analysis. Second, we consider a confirmatory two-stage adaptive design with treatment selection at interim.