Some challenges with statistical inference in adaptive designs

A systematic review of the "promising zone" design

Introduction

Sample size calculations require assumptions regarding treatment response and variability. Incorrect assumptions can result in under- or overpowered trials, posing ethical concerns. Sample size re-estimation (SSR) methods investigate the validity of these assumptions and increase the sample size if necessary. The “promising zone” (Mehta and Pocock, Stat Med 30:3267–3284, 2011) concept is appealing to researchers for its design simplicity. However, it is still relatively new in the application and has been a source of controversy.

Objectives

This research aims to synthesise current approaches and practical implementation of the promising zone design.

Methods

This systematic review comprehensively identifies the reporting of methodological research and of clinical trials using promising zone. Databases were searched according to a pre-specified search strategy, and pearl growing techniques implemented.

Results

The combined search methods resulted in 270 unique records identified; 171 were included in the review, of which 30 were trials. The median time to the interim analysis was 60% of the original target sample size (IQR 41–73%). Of the 15 completed trials, 7 increased their sample size. Only 21 studies reported the maximum sample size that would be considered, for which the median increase was 50% (IQR 35–100%).

Conclusions

Promising zone is being implemented in a range of trials worldwide, albeit in low numbers. Identifying trials using promising zone was difficult due to the lack of reporting of SSR methodology. Even when SSR methodology was reported, some had key interim analysis details missing, and only eight papers provided promising zone ranges.

Statistical challenges in a regulatory review of cardiovascular and CNS clinical trials

There are several challenging statistical problems identified in the regulatory review of large cardiovascular (CV) clinical outcome trials and central nervous system (CNS) trials. The problems can be common or distinct due to disease characteristics and the differences in trial design elements such as endpoints, trial duration, and trial size. In schizophrenia trials, heavy missing data is a big problem. In Alzheimer trials, the endpoints for assessing symptoms and the endpoints for assessing disease progression are essentially the same; it is difficult to construct a good trial design to evaluate a test drug for its ability to slow the disease progression. In CV trials, reliance on a composite endpoint with low event rate makes the trial size so large that it is infeasible to study multiple doses necessary to find the right dose for study patients. These are just a few typical problems. In the past decade, adaptive designs were increasingly used in these disease areas and some challenges occur with respect to that use. Based on our review experiences, group sequential designs (GSDs) have borne many successful stories in CV trials and are also increasingly used for developing treatments targeting CNS diseases. There is also a growing trend of using more advanced unblinded adaptive designs for producing efficacy evidence. Many statistical challenges with these kinds of adaptive designs have been identified through our experiences with the review of regulatory applications and are shared in this article.

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.

Methods for flexible sample-size design in clinical trials: Likelihood, weighted, dual test, and promising zone approaches

Sample size plays a crucial role in clinical trials. Flexible sample-size designs, as part of the more general category of adaptive designs that utilize interim data, have been a popular topic in recent years. In this paper, we give a comparative review of four related methods for such a design. The likelihood method uses the likelihood ratio test with an adjusted critical value. The weighted method adjusts the test statistic with given weights rather than the critical value. The dual test method requires both the likelihood ratio statistic and the weighted statistic to be greater than the unadjusted critical value. The promising zone approach uses the likelihood ratio statistic with the unadjusted value and other constraints. All four methods preserve the type-I error rate. In this paper we explore their properties and compare their relationships and merits. We show that the sample size rules for the dual test are in conflict with the rules of the promising zone approach. We delineate what is necessary to specify in the study protocol to ensure the validity of the statistical procedure and what can be kept implicit in the protocol so that more flexibility can be attained for confirmatory phase III trials in meeting regulatory requirements. We also prove that under mild conditions, the likelihood ratio test still preserves the type-I error rate when the actual sample size is larger than the re-calculated one.