Stopping Boundaries of Flexible Sample Size Design With Flexible Trial Monitoring

In the group sequential (GS) approach with a fixed sample size design, the Type I error is controlled by the additivity of exit spending values. However, in a flexible sample size design where the sample size will be recalculated using the interim data, the overall Type I error rate can be inflated. Therefore, the predefined GS stopping boundaries have to be adjusted to maintain the Type I error level at each interim analysis and the at the overall level. The modified α spending function adjusted for sample size reestimation (SSR) is proposed to maintain the Type I error level. We use a unified approach and mathematically quantify the Type I error with and without sample size adjustment constraints. As a result, stopping boundaries can be obtained by inversely solving the exact Type I error functions. This unified approach, using Brownian motion theory, can be applied to normal, survival, and binary endpoints. Extensive simulations show the adjusted stopping boundaries can control the Type I error at each analysis and at the overall level.     

The Type II Error Probability of a Group Sequential Test of Efficacy and Futility,and Considerations for Power and Sample Size

For a clinical trial incorporating a group sequential test that allows early stopping for efficacy or futility (GSTEF), the primary hypothesis concerns efficacy. However, the type II error probability of the tests of efficacy is neither specified nor known. The type II error probability of a GSTEF is partitioned into the sum of its component type II error probabilities of futility and efficacy. This partitioning provides transparency, allowing researchers flexibility to set these component error probabilities directly and to know the impact on the total type II error probability and vice versa. This transparency and flexibility should improve the application of GSTEF to clinical trials.     

A Revisit of Sample Size Decisions in Confirmatory Trials

When designing a phase III superiority trial, we often compute the sample size to detect a treatment effect observed in a previous trial. In this article, we propose to take into account uncertainties around the estimated treatment effect and the estimated variability in patients’ responses jointly. We argue that it will be better to base the sample size decision for a confirmatory trial on the probability that the trial will produce a positive outcome than the traditional statistical power. We show that sample sizes computed under the traditional method are often too small to yield a desirable success probability. We extend this argument to the “conditional probability” concept that is often the basis for futility decision and sample size reestimation in an adaptive design. We argue that in the latter case, the concept of predictive power is likely to provide a more realistic measure on the prospect of the trial. In our opinion, a trialist should be concerned when the required sample size for a confirmatory trial based on the chance of a positive trial is substantially higher than that calculated under the traditional approach, either at the design stage or at the interim sample size reestimation decision point.     

Sample Size Re-Estimation for Adaptive Sequential Design in Clinical Trials

There is considerable interest in methods that use accumulated data to modify trial sample size. However, sample size re-estimation in group sequential designs has been controversial. We describe a method for sample size re-estimation at the penultimate stage of a group sequential design that achieves specified power against an alternative hypothesis corresponding to the current point estimate of the treatment effect.     

Adaptive Statistical Analysis Following Sample Size Modification Based on Interim Review of Effect Size

ABSTRACT

In designing a comparative clinical trial, the required sample size is a function of the effect size, the value of which is unknown and at best may be estimated from historical data. Insufficiency in sample size as a result of overestimating the effect size can be destructive to the success of the clinical trial. Sample size re-estimation may need to be properly considered as a part of clinical trial planning. This paper is intended to give the motivations for the sample size re-estimation based partly on the effect size observed at an interim analysis and for a resulting simple adaptive test strategy. The performance of this adaptive design strategy is assessed by comparing it with a fixed maximum sample size design that is properly adjusted in anticipation of the possible sample size adjustment.     

Two-Stage Adaptive Design for Clinical Trials with Survival Data

Abstract

In long-term clinical trials we often need to monitor the patients’ enrollment, compliance, and treatment effect during the study. In this paper we take the conditional power approach and consider a two-stage design based on the ideas of Li et al. (2002 Li , G. , Shih , W. J. , Xie , T. , Lu , J. ( 2002 ). A sample size adjustment procedure for clinical trials based on conditional power . Biostatistics 3 : 277 – 287 . [PUBMED] [CROSSREF] [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) for trials with survival endpoints. We make projections and decisions regarding the future course of the trial from the interim data. The decision includes possible early termination of the trial for convincing evidence of futility or efficacy, and projection includes how many additional patients are needed to enroll and how long the enrollment and follow-up may be when continuing the trial. The flexibility of the adaptive design is demonstrated by an example, the Coumadin Aspirin Reinfarction Study.     

Group Sequential Design for Randomized Phase III Trials under the Weibull Model

In this article, a parametric sequential test is proposed under the Weibull model. The proposed test is asymptotically normal with an independent increment structure. The sample size for a fixed sample test is derived for the purpose of group sequential trial design. In addition, a multi-stage group sequential procedure is given under the Weibull model by applying the Brownian motion property of the test statistic and sequential conditional probability ratio test methodology.     

Not Too Big,Not Too Small: A Goldilocks Approach To Sample Size Selection

We present a Bayesian adaptive design for a confirmatory trial to select a trial’s sample size based on accumulating data. During accrual, frequent sample size selection analyses are made and predictive probabilities are used to determine whether the current sample size is sufficient or whether continuing accrual would be futile. The algorithm explicitly accounts for complete follow-up of all patients before the primary analysis is conducted. We refer to this as a Goldilocks trial design, as it is constantly asking the question, “Is the sample size too big, too small, or just right?” We describe the adaptive sample size algorithm, describe how the design parameters should be chosen, and show examples for dichotomous and time-to-event endpoints.     

An Adaptive Group Sequential Phase II Design to Compare Treatments for Survival Endpoints in Rare Patient Entities

For rare diseases, standard treatments are often not available and essential study parameters are difficult or impossible to obtain. Therefore, designs of clinical trials for these diseases are often based on little information. Adaptive designs allow such trials to be started and to gain information during the study. Motivated by a trial for a rare subtype of renal-cell carcinoma, we present a two-stage adaptive design for right-censored time-to-event data and a two-sided test. After the first stage, one can stop for futility or continue with reestimated sample size. The properties of such designs are analyzed by simulation studies.     

THE ATTRACTIVENESS OF THE CONCEPT OF A PROSPECTIVELY DESIGNED TWO-STAGE CLINICAL TRIAL

ABSTRACT

The clinical development process can be viewed as a succession of trials, possibly overlapping in calendar time. The design of each trial may be influenced by results from previous studies and other currently proceeding trials, as well as by external information. Results from all of these trials must be considered together in order to assess the efficacy and safety of the proposed new treatment. Meta-analysis techniques provide a formal way of combining the information. We examine how such methods can be used in combining results from: (1) a collection of separate studies, (2) a sequence of studies in an organized development program, and (3) stages within a single study using a (possibly adaptive) group sequential design. We present two examples. The first example concerns the combining of results from a Phase IIb trial using several dose levels or treatment arms with those of the Phase III trial comparing the treatment selected in Phase IIb against a control. This enables a “seamless transition” from Phase IIb to Phase III. The second example examines the use of combination tests to analyze data from an adaptive group sequential trial.