Point estimation, confidence intervals, and P-values for optimal adaptive two-stage designs with normal endpoints

Due to the dependency structure in the sampling process, adaptive trial designs create challenges in point and interval estimation and in the calculation of P-values. Optimal adaptive designs, which are designs where the parameters governing the adaptivity are chosen to maximize some performance criterion, suffer from the same problem. Various analysis methods which are able to handle this dependency structure have already been developed. In this work, we aim to give a comprehensive summary of these methods and show how they can be applied to the class of designs with planned adaptivity, of which optimal adaptive designs are an important member. The defining feature of these kinds of designs is that the adaptive elements are completely prespecified. This allows for explicit descriptions of the calculations involved, which makes it possible to evaluate different methods in a fast and accurate manner. We will explain how to do so, and present an extensive comparison of the performance characteristics of various estimators between an optimal adaptive design and its group-sequential counterpart.

Adaptive sequential design for phase II single-arm oncology trials: an expansion of Simon's design

Single-arm phase II trials are very common in oncology. A fixed sample trial may lack sufficient power if the true efficacy is less than the assumed one. Adaptive designs have been proposed in the literature. We propose a Simon's design based, adaptive sequential design. Simon's design is the most used fixed sample design for single-arm phase II oncology trials. A prominent feature of Simon's design is that it minimizes the sample size when there is no clinically meaningful efficacy. We identify Simon's trial as a special group sequential design. Established methods for sample size re-estimation (SSR) can be readily applied to Simon's design. Simulations show that simply adding SSR to Simon's design may still not provide desirable power. We propose some expansions to Simon's design. The expanded design with SSR can provide even more power.

Most Powerful Test Sequences with Early Stopping Options

We extended the application of uniformly most powerful tests to sequential tests with different stage-specific sample sizes and critical regions. In the one parameter exponential family, likelihood ratio sequential tests are shown to be uniformly most powerful for any predetermined α-spending function and stage-specific sample sizes. To obtain this result, the probability measure of a group sequential design is constructed with support for all possible outcome events, as is useful for designing an experiment prior to having data. This construction identifies impossible events that are not part of the support. The overall probability distribution is dissected into components determined by the stopping stage. These components are the sub-densities of interim test statistics first described by Armitage, McPherson and Rowe (1969) that are commonly used to create stopping boundaries given an α-spending function and a set of interim analysis times. Likelihood expressions conditional on reaching a stage are given to connect pieces of the probability anatomy together. The reduction of support caused by the adoption of an early stopping rule induces sequential truncation (not nesting) in the probability distributions of possible events. Multiple testing induces mixtures on the adapted support. Even asymptotic distributions of inferential statistics that are typically normal, are not. Rather they are derived from mixtures of truncated multivariate normal distributions.

Optimization of adaptive designs with respect to a performance score

Adaptive designs are an increasingly popular method for the adaptation of design aspects in clinical trials, such as the sample size. Scoring different adaptive designs helps to make an appropriate choice among the numerous existing adaptive design methods. Several scores have been proposed to evaluate adaptive designs. Moreover, it is possible to determine optimal two-stage adaptive designs with respect to a customized objective score by solving a constrained optimization problem. In this paper, we use the conditional performance score by Herrmann et al. (2020) as the optimization criterion to derive optimal adaptive two-stage designs. We investigate variations of the original performance score, for example, by assigning different weights to the score components and by incorporating prior assumptions on the effect size. We further investigate a setting where the optimization framework is extended by a global power constraint, and additional optimization of the critical value function next to the stage-two sample size is performed. Those evaluations with respect to the sample size curves and the resulting design's performance can contribute to facilitate the score's usage in practice.

Bland–Altman Limits of Agreement from a Bayesian and Frequentist Perspective

Bland–Altman agreement analysis has gained widespread application across disciplines, last but not least in health sciences, since its inception in the 1980s. Bayesian analysis has been on the rise due to increased computational power over time, and Alari, Kim, and Wand have put Bland–Altman Limits of Agreement in a Bayesian framework (Meas. Phys. Educ. Exerc. Sci. 2021, 25, 137–148). We contrasted the prediction of a single future observation and the estimation of the Limits of Agreement from the frequentist and a Bayesian perspective by analyzing interrater data of two sequentially conducted, preclinical studies. The estimation of the Limits of Agreement θ1 and θ2 has wider applicability than the prediction of single future differences. While a frequentist confidence interval represents a range of nonrejectable values for null hypothesis significance testing of H0: θ1 ≤ −δ or θ2 ≥ δ against H1: θ1 > −δ and θ2 < δ, with a predefined benchmark value δ, Bayesian analysis allows for direct interpretation of both the posterior probability of the alternative hypothesis and the likelihood of parameter values. We discuss group-sequential testing and nonparametric alternatives briefly. Frequentist simplicity does not beat Bayesian interpretability due to improved computational resources, but the elicitation and implementation of prior information demand caution. Accounting for clustered data (e.g., repeated measurements per subject) is well-established in frequentist, but not yet in Bayesian Bland–Altman analysis.

Optimal planning of adaptive two-stage designs

Adaptive designs are playing an increasingly important role in the planning of clinical trials. While there exists various research on the optimal determination of a two-stage design, non-optimal versions still are frequently applied in clinical research. In this article, we strive to motivate the application of optimal adaptive designs and give guidance on how to determine them. It is demonstrated that optimizing a trial design with respect to particular objective criteria can have a substantial benefit over the application of conventional adaptive sample size recalculation rules. Furthermore, we show that in many practical situations, optimal group-sequential designs show an almost negligible performance loss compared to optimal adaptive designs. Finally, we illustrate how optimal designs can be tailored to specific operational requirements by customizing the underlying optimization problem.

Follow up after sample size re-estimation in a breast cancer randomized trial for disease-free survival

BACKGROUND

While the clinical trials and statistical methodology literature on sample size re-estimation (SSRE) is robust, evaluation of SSRE procedures following the completion of a clinical trial has been sparsely reported. In blinded sample size re-estimation, only nuisance parameters are re-estimated, and the blinding of the current trial treatment effect is preserved. Blinded re-estimation procedures are well-accepted by regulatory agencies and funders. We review our experience of sample size re-estimation in a large international, National Institutes of Health funded clinical trial for adjuvant breast cancer treatment, and evaluate our blinded sample size re-estimation procedure for this time-to-event trial. We evaluated the SSRE procedure by examining assumptions made during the re-estimation process, estimates resulting from re-estimation, and the impact on final trial results with and without the addition of participants, following sample size re-estimation.

METHODS

We compared the control group failure probabilities estimated at the time of SSRE to estimates used in the original planning, to the final un-blinded control group failure probability estimates for those included in the SSRE procedure (SSRE cohort), and to the final total control group failure probability estimates. The impact of re-estimation on the final comparison between randomized treatment groups is evaluated for those in the originally planned cohort (n = 340) and for the combination of those recruited in the originally planned cohort and those added after re-estimation (n = 509).

RESULTS

Very little difference is observed between the originally planned cohort and all randomized patients in the control group failure probabilities over time or in the overall hazard ratio estimating treatment effect (originally planned cohort HR 1.25 (0.86, 1.79); all randomized cohort HR 1.24 95% CI (0.91, 1.68)). At the time of blinded SSRE, the estimated control group failure probabilities at 3 years (0.24) and 5 years (0.40) were similar to those for the SSRE cohort once un-blinded (3 years, 0.22 (0.16, 0.30); 5 years, 0.33 (0.26, 0.41)).

CONCLUSIONS

We found that our re-estimation procedure performed reasonably well in estimating the control group failure probabilities at the time of re-estimation. Particularly for time-to-event outcomes, pre-planned blinded SSRE procedures may be the best option to aid in maintaining power.

TRIAL REGISTRATION

ClinicalTrials.gov, NCT00201851 . Registered on 9 September 2005. Retrospectively registered.

Interim analysis incorporating short- and long-term binary endpoints

Designs incorporating more than one endpoint have become popular in drug development. One of such designs allows for incorporation of short‐term information in an interim analysis if the long‐term primary endpoint has not been yet observed for some of the patients. At first we consider a two‐stage design with binary endpoints allowing for futility stopping only based on conditional power under both fixed and observed effects. Design characteristics of three estimators: using primary long‐term endpoint only, short‐term endpoint only, and combining data from both are compared. For each approach, equivalent cut‐off point values for fixed and observed effect conditional power calculations can be derived resulting in the same overall power. While in trials stopping for futility the type I error rate cannot get inflated (it usually decreases), there is loss of power. In this study, we consider different scenarios, including different thresholds for conditional power, different amount of information available at the interim, different correlations and probabilities of success. We further extend the methods to adaptive designs with unblinded sample size reassessments based on conditional power with inverse normal method as the combination function. Two different futility stopping rules are considered: one based on the conditional power, and one from P‐values based on Z‐statistics of the estimators. Average sample size, probability to stop for futility and overall power of the trial are compared and the influence of the choice of weights is investigated.

Adaptive designs in clinical trials: from scientific advice to marketing authorisation to the European Medicine Agency

Background

In recent years, experience on the application of adaptive designs in confirmatory clinical trials has accumulated. Although planning such trials comes at the cost of additional operational complexity, adaptive designs offer the benefit of flexibility to update trial design and objectives as data accrue. In 2007, the European Medicines Agency (EMA) provided guidance on confirmatory clinical trials with adaptive (or flexible) designs. In order to better understand how adaptive trials are implemented in practice and how they may impact medicine approval within the EMA centralised procedure, we followed on 59 medicines for which an adaptive clinical trial had been submitted to the EMA Scientific Advice (SA) and analysed previously in a dedicated EMA survey of scientific advice letters. We scrutinized in particular the submission of the corresponding medicines for a marketing authorisation application (MAA). We also discuss the current regulatory perspective as regards the implementation of adaptive designs in confirmatory clinical trials.

Methods

Using the internal EMA MAA database, the AdisInsight database and related trial registries, we analysed how many of these 59 trials actually started, the completion status, results, the time to trial start, the adaptive elements finally implemented after SA, their possible influence on the success of the trial and corresponding product approval.

Results

Overall 31 trials out of 59 (53%) were retrieved. Thirty of them (97%) have been started and 23 (74%) concluded. Nine of these trials (39% out of 23) demonstrated a significant treatment effect on their primary endpoint and 4 (17% out of 23) supported a marketing authorisation (MA). An additional two trials were stopped using pre-defined criteria for futility, efficiently identifying trials on which further resources should not be spent. Median time to trial start after SA letter was given by EMA was 5 months. In the investigated trial registries, at least 18 trial (58% of 31 retrieved trials) designs were implemented with adaptive elements, which were predominantly dose selection, sample size reassessment (SSR) and stopping for futility (SFF). Among the 11 completed trials including adaptive elements, 6 demonstrated a significant treatment effect on their primary endpoint (55%).

Conclusions

Adaptive designs are now well established in the drug development landscape. If properly pre-planned, adaptations can play a key role in the success of some of these trials, for example to help successfully select the most promising dose regimens for phase II/III trials. Interim analyses can also enable stopping of trials for futility when they do not hold their promises. Type I error rate control, trial integrity and results consistency between the different stages of the analyses are fundamental aspects to be discussed thoroughly. Engaging early dialogue with regulators and implementing the scientific advice received is strongly recommended, since much experience in discussing adaptive designs and assessing their results has been accumulated.

An evaluation of increasing sample size based on conditional power

We evaluate properties of sample size re-estimation (SSR) designs similar to the promising zone design considered by Mehta and Pocock (2011). We evaluate these designs under the assumption of a true effect size of 1.1 down to 0.4 of the protocol-specified effect size by six measures: 1. The probability of a sample size increase, 2. The mean proportional increase in sample size given an increase; 3 and 4. The mean true conditional power with and without a sample size increase; 5 and 6. The expected increase in sample size and power due to the SSR procedure. These measures show the probability of a sample size increase and the cost/benefit for given true effect sizes, particularly when the SSR may either be pursuing a small effect size of little clinical importance or be unnecessary when the true effect size is close to the protocol-specified effect size. The results show the clear superiority of conducting the SSR late in the study and the inefficiency of a mid-study SSR. The results indicate that waiting until late in the study for the SSR yields a smaller, better targeted set of studies with a greater increase in overall power than a mid-study SSR.

Adaptive designs from a Data Safety Monitoring Board perspective: Some controversies and some case studies

This article describes vignettes concerning interactions with Data Safety Monitoring Boards during the design and monitoring of some clinical trials with an adaptive design. Most reflect personal experiences by the author.

Sample Size Reassessment and Hypothesis Testing in Adaptive Survival Trials

Mid-study design modifications are becoming increasingly accepted in confirmatory clinical trials, so long as appropriate methods are applied such that error rates are controlled. It is therefore unfortunate that the important case of time-to-event endpoints is not easily handled by the standard theory. We analyze current methods that allow design modifications to be based on the full interim data, i.e., not only the observed event times but also secondary endpoint and safety data from patients who are yet to have an event. We show that the final test statistic may ignore a substantial subset of the observed event times. An alternative test incorporating all event times is found, where a conservative assumption must be made in order to guarantee type I error control. We examine the power of this approach using the example of a clinical trial comparing two cancer therapies.

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.

Flexible selection of a single treatment incorporating short-term endpoint information in a phase II/III clinical trial

Seamless phase II/III clinical trials in which an experimental treatment is selected at an interim analysis have been the focus of much recent research interest. Many of the methods proposed are based on the group sequential approach. This paper considers designs of this type in which the treatment selection can be based on short-term endpoint information for more patients than have primary endpoint data available. We show that in such a case, the familywise type I error rate may be inflated if previously proposed group sequential methods are used and the treatment selection rule is not specified in advance. A method is proposed to avoid this inflation by considering the treatment selection that maximises the conditional error given the data available at the interim analysis. A simulation study is reported that illustrates the type I error rate inflation and compares the power of the new approach with two other methods: a combination testing approach and a group sequential method that does not use the short-term endpoint data, both of which also strongly control the type I error rate. The new method is also illustrated through application to a study in Alzheimer's disease.

The Potential of Adaptive Design in Animal Studies

Clinical trials are the backbone of medical research, and are often the last step in the development of new therapies for use in patients. Prior to human testing, however, preclinical studies using animal subjects are usually performed in order to provide initial data on the safety and effectiveness of prospective treatments. These studies can be costly and time consuming, and may also raise concerns about the ethical treatment of animals when potentially harmful procedures are involved. Adaptive design is a process by which the methods used in a study may be altered while it is being conducted in response to preliminary data or other new information. Adaptive design has been shown to be useful in reducing the time and costs associated with clinical trials, and may provide similar benefits in preclinical animal studies. The purpose of this review is to summarize various aspects of adaptive design and evaluate its potential for use in preclinical research.

Adaptive sample size modification in clinical trials: start small then ask for more?

We consider sample size re-estimation in a clinical trial, in particular when there is a significant delay before the measurement of patient response. Mehta and Pocock have proposed methods in which sample size is increased when interim results fall in a 'promising zone' where it is deemed worthwhile to increase conditional power by adding more subjects. Our analysis reveals potential pitfalls in applying this approach. Mehta and Pocock use results of Chen, DeMets and Lan to identify when increasing sample size, but applying a conventional level α significance test at the end of the trial does not inflate the type I error rate: we have found the greatest gains in power per additional observation are liable to lie outside the region defined by this method. Mehta and Pocock increase sample size to achieve a particular conditional power, calculated under the current estimate of treatment effect: this leads to high increases in sample size for a small range of interim outcomes, whereas we have found it more efficient to make moderate increases in sample size over a wider range of cases. If the aforementioned pitfalls are avoided, we believe the broad framework proposed by Mehta and Pocock is valuable for clinical trial design. Working in this framework, we propose sample size rules that apply explicitly the principle of adding observations when they are most beneficial. The resulting trial designs are closely related to efficient group sequential tests for a delayed response proposed by Hampson and Jennison.

Adaptive design of confirmatory trials: Advances and challenges

The past decade witnessed major developments in innovative designs of confirmatory clinical trials, and adaptive designs represent the most active area of these developments. We give an overview of the developments and associated statistical methods in several classes of adaptive designs of confirmatory trials. We also discuss their statistical difficulties and implementation challenges, and show how these problems are connected to other branches of mainstream Statistics, which we then apply to resolve the difficulties and bypass the bottlenecks in the development of adaptive designs for the next decade.

A Rejection Principle for Sequential Tests of Multiple Hypotheses Controlling Familywise Error Rates

We present a unifying approach to multiple testing procedures for sequential (or streaming) data by giving sufficient conditions for a sequential multiple testing procedure to control the familywise error rate (FWER). Together we call these conditions a "rejection principle for sequential tests," which we then apply to some existing sequential multiple testing procedures to give simplified understanding of their FWER control. Next the principle is applied to derive two new sequential multiple testing procedures with provable FWER control, one for testing hypotheses in order and another for closed testing. Examples of these new procedures are given by applying them to a chromosome aberration data set and to finding the maximum safe dose of a treatment.

Adaptive choice of patient subgroup for comparing two treatments

This paper is motivated by a randomized controlled trial to compare an endovascular procedure with conventional medical treatment for stroke patients, in which the endovascular procedure may be effective only in a subgroup of patients. Since the subgroup is not known at the design stage but can be learned statistically from the data collected during the course of the trial, we develop a novel group sequential design that incorporates adaptive choice of the patient subgroup among several possibilities which include the entire patient population as a choice. We define the type I and type II errors of a test in this design and show how a prescribed type I error can be maintained by using the closed testing principle in multiple testing. We also show how asymptotically optimal tests can be constructed by using generalized likelihood ratio statistics for parametric problems and analogous standardized or Studentized statistics for nonparametric tests such as Wilcoxon's rank sum test commonly used for treatment comparison in stroke patients.

Maximum type 1 error rate inflation in multiarmed clinical trials with adaptive interim sample size modifications

Sample size modifications in the interim analyses of an adaptive design can inflate the type 1 error rate, if test statistics and critical boundaries are used in the final analysis as if no modification had been made. While this is already true for designs with an overall change of the sample size in a balanced treatment-control comparison, the inflation can be much larger if in addition a modification of allocation ratios is allowed as well. In this paper, we investigate adaptive designs with several treatment arms compared to a single common control group. Regarding modifications, we consider treatment arm selection as well as modifications of overall sample size and allocation ratios. The inflation is quantified for two approaches: a naive procedure that ignores not only all modifications, but also the multiplicity issue arising from the many-to-one comparison, and a Dunnett procedure that ignores modifications, but adjusts for the initially started multiple treatments. The maximum inflation of the type 1 error rate for such types of design can be calculated by searching for the "worst case" scenarios, that are sample size adaptation rules in the interim analysis that lead to the largest conditional type 1 error rate in any point of the sample space. To show the most extreme inflation, we initially assume unconstrained second stage sample size modifications leading to a large inflation of the type 1 error rate. Furthermore, we investigate the inflation when putting constraints on the second stage sample sizes. It turns out that, for example fixing the sample size of the control group, leads to designs controlling the type 1 error rate.

A review and re-interpretation of a group-sequential approach to sample size re-estimation in two-stage trials

In this paper, we review the adaptive design methodology of Li et al. (Biostatistics 3:277-287) for two-stage trials with mid-trial sample size adjustment. We argue that it is closer in principle to a group sequential design, in spite of its obvious adaptive element. Several extensions are proposed that aim to make it even more attractive and transparent alternative to a standard (fixed sample size) trial for funding bodies to consider. These enable a cap to be put on the maximum sample size and for the trial data to be analysed using standard methods at its conclusion. The regulatory view of trials incorporating unblinded sample size re-estimation is also discussed.

Sample size and screening size trade-off in the presence of subgroups with different expected treatment effects

When designing clinical trials, sometimes we may expect a larger treatment effect in one group while others exhibit an attenuated effect. In these settings there can be a trade-off between a smaller average treatment effect with broader enrollment criteria and a larger effect with restricted criteria but longer enrollment duration. Identification of subgroups will often use a clinical decision rule, for example, biomarker cutoff, but may be imprecise, that is, with sensitivity and specificity not simultaneously 100%. We evaluate the impact of including attenuated subgroups on design operating characteristics and illustrate scenarios where overall trial duration may be shorter by not being restrictive.

An efficient sequential design of clinical trials

We propose an efficient group sequential monitoring rule for clinical trials. At each interim analysis both efficacy and futility are evaluated through a specified loss structure together with the predicted power. The proposed design is robust to a wide range of priors, and achieves the specified power with a saving of sample size compared to existing adaptive designs. A method is also proposed to obtain a reduced-bias estimator of treatment difference for the proposed design. The new approaches hold great potential for efficiently selecting a more effective treatment in comparative trials. Operating characteristics are evaluated and compared with other group sequential designs in empirical studies. An example is provided to illustrate the application of the method.

Adaptive clinical trial designs with pre-specified rules for modifying the sample size: understanding efficient types of adaptation

Adaptive clinical trial design has been proposed as a promising new approach that may improve the drug discovery process. Proponents of adaptive sample size re-estimation promote its ability to avoid 'up-front' commitment of resources, better address the complicated decisions faced by data monitoring committees, and minimize accrual to studies having delayed ascertainment of outcomes. We investigate aspects of adaptation rules, such as timing of the adaptation analysis and magnitude of sample size adjustment, that lead to greater or lesser statistical efficiency. Owing in part to the recent Food and Drug Administration guidance that promotes the use of pre-specified sampling plans, we evaluate alternative approaches in the context of well-defined, pre-specified adaptation. We quantify the relative costs and benefits of fixed sample, group sequential, and pre-specified adaptive designs with respect to standard operating characteristics such as type I error, maximal sample size, power, and expected sample size under a range of alternatives. Our results build on others' prior research by demonstrating in realistic settings that simple and easily implemented pre-specified adaptive designs provide only very small efficiency gains over group sequential designs with the same number of analyses. In addition, we describe optimal rules for modifying the sample size, providing efficient adaptation boundaries on a variety of scales for the interim test statistic for adaptation analyses occurring at several different stages of the trial. We thus provide insight into what are good and bad choices of adaptive sampling plans when the added flexibility of adaptive designs is desired.

Adaptive trial designs

We review adaptive designs for clinical trials, giving special attention to the control of the Type I error in late-phase confirmatory trials, when the trial planner wishes to adjust the final sample size of the study in response to an unblinded analysis of interim estimates of treatment effects. We point out that there is considerable inefficiency in using the adaptive designs that employ conditional power calculations to reestimate the sample size and that maintain the Type I error by using certain weighted test statistics. Although these adaptive designs have little advantage over familiar group-sequential designs, our review also describes recent developments in adaptive designs that are both flexible and efficient. We also discuss the use of Bayesian designs, when the context of use demands control over operating characteristics (Type I and II errors) and correction of the bias of estimated treatment effects.

Exploring the benefits of adaptive sequential designs in time-to-event endpoint settings

Sequential analysis is frequently employed to address ethical and financial issues in clinical trials. Sequential analysis may be performed using standard group sequential designs, or, more recently, with adaptive designs that use estimates of treatment effect to modify the maximal statistical information to be collected. In the general setting in which statistical information and clinical trial costs are functions of the number of subjects used, it has yet to be established whether there is any major efficiency advantage to adaptive designs over traditional group sequential designs. In survival analysis, however, statistical information (and hence efficiency) is most closely related to the observed number of events, while trial costs still depend on the number of patients accrued. As the number of subjects may dominate the cost of a trial, an adaptive design that specifies a reduced maximal possible sample size when an extreme treatment effect has been observed may allow early termination of accrual and therefore a more cost-efficient trial. We investigate and compare the tradeoffs between efficiency (as measured by average number of observed events required), power, and cost (a function of the number of subjects accrued and length of observation) for standard group sequential methods and an adaptive design that allows for early termination of accrual. We find that when certain trial design parameters are constrained, an adaptive approach to terminating subject accrual may improve upon the cost efficiency of a group sequential clinical trial investigating time-to-event endpoints. However, when the spectrum of group sequential designs considered is broadened, the advantage of the adaptive designs is less clear.

Optimal group-sequential designs for simultaneous testing of superiority and non-inferiority

Confirmatory clinical trials comparing the efficacy of a new treatment with an active control typically aim at demonstrating either superiority or non-inferiority. In the latter case, the objective is to show that the experimental treatment is not worse than the active control by more than a pre-specified non-inferiority margin. We consider two classes of group-sequential designs that combine the superiority and non-inferiority objectives: non-adaptive designs with fixed group sizes and adaptive designs where future group sizes may be based on the observed treatment effect. For both classes, we derive group-sequential designs meeting error probability constraints that have the lowest possible expected sample size averaged over a set of values of the treatment effect. These optimized designs provide an efficient means of reducing expected sample size under a range of treatment effects, even when the separate objectives of proving superiority and non-inferiority would require quite different fixed sample sizes. We also present error spending versions of group-sequential designs that are easily implementable and can handle unpredictable group sizes or information levels. We find the adaptive choice of group sizes to yield some modest efficiency gains; alternatively, expected sample size may be reduced by adding another interim analysis to a non-adaptive group-sequential design.

Flexible designs for genomewide association studies

Genomewide association studies attempting to unravel the genetic etiology of complex traits have recently gained attention. Frequently, these studies employ a sequential genotyping strategy: A large panel of markers is examined in a subsample of subjects, and the most promising markers are genotyped in the remaining subjects. In this article, we introduce a novel method for such designs enabling investigators to, for example, modify marker densities and sample proportions while strongly controlling the family-wise type I error rate. Loss of efficiency is avoided by redistributing conditional type I error rates of discarded markers. Our approach can be combined with cost optimal designs and entails a greater flexibility than all previously suggested designs. Among other features, it allows for marker selections based upon biological criteria instead of statistical criteria alone, or the option to modify the sample size at any time during the course of the project. For practical applicability, we develop a new algorithm, subsequently evaluate it by simulations, and illustrate it using a real data set.

Group sequential and adaptive designs - a review of basic concepts and points of discussion

In recent times, group sequential and adaptive designs for clinical trials have attracted great attention from industry, academia and regulatory authorities. These designs allow analyses on accumulating data - as opposed to classical, "fixed-sample" statistics. The rapid development of a great variety of statistical procedures is accompanied by a lively debate on their potential merits and shortcomings. The purpose of this review article is to ease orientation in both respects. First, we provide a concise overview of the essential technical concepts, with special emphasis on their interrelationships. Second, we give a structured review of the current controversial discussion on practical issues, opportunities and challenges of these new designs.