Group sequential, sample size re-estimation and two-stage adaptive designs in clinical trials: a comparison

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.

Effect of sample size re-estimation in adaptive clinical trials for Alzheimer's disease and mild cognitive impairment

Introduction

The sample size re-estimation (SSR) adaptive design allows interim analyses and resultant modifications of the ongoing trial to preserve or increase power. We investigated the applicability of SSR in Alzheimer's disease (AD) trials using a meta-database of clinical studies.

Methods

Based on six studies, we simulated clinical trials using Alzheimer's Disease Assessment Scale-cognitive subscale (ADAS-Cog) as primary outcome. A single SSR based on effect sizes or based on variances was conducted at 6 months and 12 months. Resultant power improvement and sample size adjustments were evaluated.

Results

SSR resulted in highly variable outcomes for both sample size increases and power improvement. The gain in power after SSR varies by initial sample sizes, trial durations, and effect sizes.

Conclusions

SSR adaptive designs can be effective for trials in AD and mild cognitive impairment with small or medium initial sample sizes. However, SSR in larger trials (>200 subjects per arm) generates no major advantages over the typical randomized trials.

Flexible designs for phase II comparative clinical trials involving two response variables

The aim of phase II clinical trials is to determine whether an experimental treatment is sufficiently promising and safe to justify further testing. The need for reduced sample size arises naturally in phase II clinical trials owing to both technical and ethical reasons, motivating a significant part of research in the field during recent years, while another significant part of the research effort is aimed at more complex therapeutic schemes that demand the consideration of multiple endpoints to make decisions. In this paper, our attention is restricted to phase II clinical trials in which two treatments are compared with respect to two dependent dichotomous responses proposing some flexible designs. These designs permit the researcher to terminate the clinical trial when high rates of favorable or unfavorable outcomes are observed early enough requiring in this way a small number of patients. From the mathematical point of view, the proposed designs are defined on bivariate sequences of multi-state trials, and the corresponding stopping rules are based on various distributions related to the waiting time until a certain number of events appear in these sequences. The exact distributions of interest, under a unified framework, are studied using the Markov chain embedding technique, which appears to be very useful in clinical trials for the sample size determination. Tables of expected sample size and power are presented. The numerical illustration showed a very good performance for these new designs.

An insight into the properties of a two-stage design in bioequivalence studies

PURPOSE

Unveil the properties of a two-stage design (TSD) for bioequivalence (BE) studies.

METHODS

A TSD with an upper sample size limit (UL) is described and analyzed under different conditions using Monte Carlo simulations. TSD was split into three branches: A, B1, and B2. The first stage included branches A and B1, while stage two referred to branch B2. Sample size re-estimation at B2 relies on the observed GMR and variability of stage 1. The properties studied were % BE acceptance, % uses and % efficiency of each branch, as well as the reason of BE failure.

RESULTS

No inflation of type I error was observed. Each TSD branch exhibits different performance. Stage two exhibits the greatest % BE acceptances when highly variable drugs are assessed with a low starting number of subjects (N₁) or when formulations differ significantly. Branch A is more frequently used when variability is low, drug products are similar, and a large N₁ is included. BE assessment at branch A is very efficient.

CONCLUSIONS

The overall acceptance profile of TSD resembles the typical pattern observed in single-stage studies, but it is actually different. Inclusion of a UL is necessary to avoid inflation of type I error.

Methodology and Application of Adaptive and Sequential Approaches in Contemporary Clinical Trials

The clinical trial, a prospective study to evaluate the effect of interventions in humans under prespecified conditions, is a standard and integral part of modern medicine. Many adaptive and sequential approaches have been proposed for use in clinical trials to allow adaptations or modifications to aspects of a trial after its initiation without undermining the validity and integrity of the trial. The application of adaptive and sequential methods in clinical trials has significantly improved the flexibility, efficiency, therapeutic effect, and validity of trials. To further advance the performance of clinical trials and convey the progress of research on adaptive and sequential methods in clinical trial design, we review significant research that has explored novel adaptive and sequential approaches and their applications in Phase I, II, and III clinical trials and discuss future directions in this field of research.

Adaptive design clinical trials: Methodology, challenges and prospect

New drug development is a time-consuming and expensive process. Recently, there has been stagnation in the development of novel compounds. Moreover, the attrition rate in clinical research is also on the rise. Fearing more stagnation, the Food and Drug Administration released the critical path initiative in 2004 and critical path opportunity list in 2006 thus highlighting the need of advancing innovative trial designs. One of the innovations suggested was the adaptive designed clinical trials, a method promoting introduction of pre-specified modifications in the design or statistical procedures of an on-going trial depending on the data generated from the concerned trial thus making a trial more flexible. The adaptive design trials are proposed to boost clinical research by cutting on the cost and time factor. Although the concept of adaptive designed clinical trials is round-the-corner for the last 40 years, there is still lack of uniformity and understanding on this issue. This review highlights important adaptive designed methodologies besides covering the regulatory positions on this issue.

Sample size re-estimation for survival data in clinical trials with an adaptive design

In clinical trials with survival data, investigators may wish to re-estimate the sample size based on the observed effect size while the trial is ongoing. Besides the inflation of the type-I error rate due to sample size re-estimation, the method for calculating the sample size in an interim analysis should be carefully considered because the data in each stage are mutually dependent in trials with survival data. Although the interim hazard estimate is commonly used to re-estimate the sample size, the estimate can sometimes be considerably higher or lower than the hypothesized hazard by chance. We propose an interim hazard ratio estimate that can be used to re-estimate the sample size under those circumstances. The proposed method was demonstrated through a simulation study and an actual clinical trial as an example. The effect of the shape parameter for the Weibull survival distribution on the sample size re-estimation is presented.

Approaches to handling data when a phase II trial deviates from the pre-specified Simon's two-stage design

Simon's 'optimal' and 'minimax' two-stage designs are common methods for conducting phase IIA studies investigating new cancer therapies. However, these designs are rather rigid in their settings because of the pre-specified rejection rules and fixed sample sizes at each stage. In practice, we often encounter the problem that a study is unable to adhere to the event number and sample sizes of the original two-stage design. In this paper, we consider some approaches in handling situations where deviations or interruptions from the original Simon's two-stage design occur because recruitment of patients is slower than expected. We consider four scenarios and use conditional probabilities to address the issues commonly inquired by the scientific review board. We also discuss how to report p-values in these situations.

GLUMIP 2.0: Software for Planning Internal Pilots

Internal pilot designs involve conducting interim power analysis (without interim data analysis) to modify the final sample size. Recently developed techniques have been described to avoid the type I error rate inflation inherent to unadjusted hypothesis tests, while still providing the advantages of an internal pilot design. We present GLUMIP 2.0, the latest version of our free SAS/IML software for planning internal pilot studies in the general linear univariate model (GLUM) framework. The new analytic forms incorporated into the updated software solve many problems inherent to current internal pilot techniques for linear models with Gaussian errors. Hence, the GLUMIP 2.0 software makes it easy to perform exact power analysis for internal pilots under the GLUM framework with independent Gaussian errors and fixed predictors.

Adaptive design methods in clinical trials - a review

In recent years, the use of adaptive design methods in clinical research and development based on accrued data has become very popular due to its flexibility and efficiency. Based on adaptations applied, adaptive designs can be classified into three categories: prospective, concurrent (ad hoc), and retrospective adaptive designs. An adaptive design allows modifications made to trial and/or statistical procedures of ongoing clinical trials. However, it is a concern that the actual patient population after the adaptations could deviate from the originally target patient population and consequently the overall type I error (to erroneously claim efficacy for an infective drug) rate may not be controlled. In addition, major adaptations of trial and/or statistical procedures of on-going trials may result in a totally different trial that is unable to address the scientific/medical questions the trial intends to answer. In this article, several commonly considered adaptive designs in clinical trials are reviewed. Impacts of ad hoc adaptations (protocol amendments), challenges in by design (prospective) adaptations, and obstacles of retrospective adaptations are described. Strategies for the use of adaptive design in clinical development of rare diseases are discussed. Some examples concerning the development of Velcade intended for multiple myeloma and non-Hodgkin's lymphoma are given. Practical issues that are commonly encountered when implementing adaptive design methods in clinical trials are also discussed.

Similarities and differences in design considerations for cell therapy and pharmacologic cardiovascular clinical trials

Cell therapies hold the potential for suppression, modification, or cure of disease. Several unique challenges have been recognized as this field has developed. Many of these involve considerations of trial design. This paper summarizes the discussion and suggestions constructed during the 8th Cardiovascular Clinical Trialists Workshop, a meeting involving cardiovascular clinical trialists, biostatisticians, National Institutes of Health scientists, European and United States regulators, and pharmaceutical industry scientists. Investigators must adapt research methods to accommodate the scientific advances associated with cell therapy. Safety and efficacy of cell therapy for cardiovascular indications should be evaluated with the same degree of scientific rigor required of pharmacologic agents, and the same fundamental regulatory requirements and scientific processes apply to both. Clinical trials for these indications should also meet standards similar to those set for drug therapies. Safety should be determined throughout development, dose responsiveness should be established and, while surrogate endpoints are important development tools, the ultimate demonstration of efficacy must rely on clinical benefit. The establishment of a global safety database for cell therapy would significantly advance the field. Efforts to discover innovative therapies must be balanced by a commitment to comprehensively evaluate the safety and efficacy of the new treatments.

Sample size reestimation by Bayesian prediction

We review a Bayesian predictive approach for interim data monitoring and propose its application to interim sample size reestimation for clinical trials. Based on interim data, this approach predicts how the sample size of a clinical trial needs to be adjusted so as to claim a success at the conclusion of the trial with an expected probability. The method is compared with predictive power and conditional power approaches using clinical trial data. Advantages of this approach over the others are discussed.

Nonconventional clinical trial designs: approaches to provide more precise estimates of treatment effects with a smaller sample size, but at a cost

Statistical sciences have recently made advancements that allow improved precision or reduced sample size in clinical research studies. Herein, we review 4 of the more promising: (1) improvements in approaches for dose selection trials, (2) approaches for sample size adjustment, (3) selection of study end point and associated statistical methods, and (4) frequentist versus Bayesian statistical methods. Whereas each of these holds the opportunity for more efficient trials, each are associated with the need for more stringent assumptions or increased complexity in the interpretation of results. The opportunities for these promising approaches, and their associated "costs," are reviewed.

Plan to be flexible: a commentary on adaptive designs

This is a discussion of the following three papers appearing in this special issue on adaptive designs: 'Nested repeated confidence intervals and switching between noninferiority and superiority' by Joachim Hartung and Guido Knapp; 'Confirmatory Seamless Phase II/III Clinical trials with Hypotheses Selection at Interim: General Concepts' by Frank Bretz, Heinz Schmidli, Franz König, Amy Racine and Willi Maurer; and 'Confirmatory Seamless Phase Il/III Clinical Trials with Hypotheses Selection at Interim: Applications and Practical Considerations' by Heinz Schmidli, Frank Bretz, Amy Racine and Willi Maurer.