Group Sequential Methods Research Articles

Exact calculations for the repeated many-one test

When group sequential methods are applied to compare several treatments with a control, multiplicity from the repeated significance testing as well as from the multiple comparison has to be accounted for properly to control the overall type I error. This often involves a multidimensional integration procedure to compute group sequential boundaries. Liu (1996, J. Appl. Statist. 23 (4)) proposed some group sequential procedures for comparing several treatments with a control. The group sequential boundaries needed to apply these procedures were estimated by simulation to two decimal places for specified α-levels. In this paper, we describe an algorithm that allows efficient calculation of these boundaries by combining a newly developed software in Genz and Keister (1996, J. Comput Appl. Math 71) and the dynamic programming technique described, for example, in Cormen et al. (1990, Introduction to Algorithms, MIT Press, Cambridge). The algorithm is then implemented to successfully solve the computation problem which is previously stated by Liu (1996) as “no simple exact calculation method is available”.

Clinical Trial Designs Based on Sequential Conditional Probability Ratio Tests and Reverse Stochastic Curtailing

We propose a group sequential method based on the sequential conditional probability ratio test and show that it has the conservatism desired in practice. We also propose calculating the discordant probability, that is, the probability that the sequential test concludes differently from a fixed-sample test at the planned end of the trial, recognizing that this probability could be substantial, even if the sequential test has the same size and power as the fixed-sample size test at the planned end of the study. In addition, we show that the proposed method can be used as a stochastic curtailing tool. Thus, the method accommodates unplanned interim analyses as well as those deemed necessary based on data trends, virtually without inflating the type I error, but it is less conservative than the usual stochastic curtailing. The method is implemented through an interactive computer program.

An overview of group sequential methods in longitudinal clinical trials

An overview of group sequential methods in longitudinal clinical trials

Group-Sequential Analysis Incorporating Covariate Information

In this article we survey existing results concerning the joint distribution of the sequence of estimates of the parameter vector when a model is fitted to accumulating data and provide a unified theory that explains the “independent increments” structure commonly seen in group-sequential test statistics. Our theory covers normal linear models, including the case of correlated observations, and asymptotic results extend to generalized linear models and the proportional hazards regression model for survival data. The asymptotic results are derived using standard methods for the nonsequential case, and they hold as long as these nonsequential techniques are applicable at each individual analysis. In all cases, the joint distribution of the sequence of parameter estimates has the same form, exactly or asymptotically, as that of the sequence of means of an increasing number of independent, identically distributed normal variables. Thus our results provide the formal basis for extending the scope of standard group-sequential methods to a wide range of problems.

Incorporation of a stopping criterion for futility into the design of a clinical trial with one interim analysis

We examine the efficiency of clinical trial designs with one interim analysis and prespecified overall type I and II error probabilities. The designs incorporate a stopping criterion for a positive result as well as one for having interim data which indicate that continuation of the trial is futile. The classical Pocock or O'Brien-Fleming group sequential method is applied for early stopping with a positive result. The other stopping criterion is based on the idea of stochastic curtailment: given the interim data, the conditional power is calculated under an optimistic but plausible alternative; if this conditional power is less than a predetermined value, the trial is stopped due to futility.

A group sequential approach to crossover trials for average bioequivalence

Group sequential methods to allow the possibility of early termination of a trial due to sufficiently convincing results are a standard in therapeutic clinical trials but have been little considered in bioequivalence trials. We investigate the statistical properties of one group sequential approach to bioequivalence trials. In particular, we are interested in maintenance of level (5%), quantification of any loss of power, and the probability of early stopping. These properties are assessed via data simulated according to a pharmacokinetic model. We find that there are cases where a group sequential approach has a substantial probability of early stopping, with essentially no loss of power.

Sequential monitoring of clinical trials with multiple survival endpoints.

Many clinical trials follow patients for several different types of survival endpoints, such as mortality, disease progression, and time until dose-limiting toxicity. Conduct of such trials often requires that the accumulating data be reviewed periodically to protect the safety of participating patients and possibly identify early treatment differences. This paper proposes a group sequential method for assessing multiple survival endpoints using repeated confidence intervals. Counting processes for each survival endpoint are used to estimate both the correlation between outcomes and between times of interim analysis. The methods are illustrated using a clinical trial comparing two treatments for PCP prevention in AIDS patients. The operating characteristics of three strategies for constructing confidence intervals are assessed and compared in a simulation study.

The group sequential triangular test for phase II cancer clinical trials.

In cancer, phase II clinical trials are usually noncomparative. Their purpose is to determine whether a new chemotherapy is effective enough to warrant further evaluation in phase III. Therefore, in order to meet ethical requirements, decision-making methods must allow for early termination when inefficacy (or efficacy) is clear. We previously extended the Triangular Test, a group sequential method initially proposed for phase III trials, to phase II trials and demonstrated its advantages (i.e., type I error rate alpha and power close to the nominal values, reduction of the sample size) over other methods. The aim of this paper is to present the Triangular Test from a practical standpoint that will facilitate its application to phase II clinical trials in oncology. After summarizing the minimal theoretical knowledge required to use the method appropriately, we discuss its use in the design and analysis of a phase II cancer trial.

Statistical Packages for Group Sequential Methods

Statistical Packages for Group Sequential Methods

Statistical Packages for Group Sequential Methods

Abstract EaSt, Version 2 Primary developers: Kyungman Kim, Cyrus Mehta, Sandro Pampallona, Anastasios Tsiatis, and Shailesh Vasundhra. Available from Cytel Software Corporation, 675 Massachusetts Ave., Cambridge, MA 98195. Standard price $895; academic price $695. PEST3 (Planning and Evaluation of Sequential Trials), Version 3 Primary developers: Hazel Brunier and John Whitehead. Available from the MPS Research Unit, University of Reading, Earley Gate, Reading RG6 6FN, United Kingdom. Standard price £700 (approx. $1,124); academic price £400 (approx. $642).

Group Sequential Methods for Comparison of Cure Rates in Clinical Trials

Since a subset of the patient population may be cured of disease in some clinical trials, one might be more interested in testing the differences in cure rates rather than other types of differences in failure distributions. Also, the monitoring of clinical trial results frequently necessitates the use of repeated examination of outcome for ethical and efficiency reasons. Parametric and non-parametric group sequential methods are proposed for comparing the cure rates between two treatment groups at the interim analyses during the trial. In both methods, construction of the group sequential boundaries is based on the asymptotic joint distribution of the sequentially computed statistics and their covariance matrix. The proposed methods are illustrated with a pediatric cancer trial which had been conducted by the Childrens Cancer Group.

Group Sequential Comparison of Changes: Ad-hoc Versus More Exact Method

There are many clinical trials in which we are interested in comparing changes in responses between two treatment groups sequentially. Investigators might assume a simple linear model, take the average of the ordinary least square estimators of slope within each treatment group, and use the standardized difference between these two averages as the test statistic at each interim analysis. Ad-hoc construction of the boundary values for interim analysis might be based on group sequential methods which assume that the interim test statistics have independent increments even though it may not be true when a response variable is measured repeatedly over time for each subject. This ad-hoc method is very simple and appealing, and thus has been used in a clinical trial setting. Lee and DeMets (1991, Journal of the American Statistical Association 86, 757-762) have proposed a more exact group sequential method for comparing rates of change. Under the assumption that the response follows the linear mixed effects model, they have derived the asymptotic joint distribution of the sequentially computed statistics. Construction of group sequential boundaries is based on this distribution theory. By simulation studies, we first study the robustness of the more exact method to violations of the typical assumptions. In addition, we compare the ad-hoc method with the more exact method and examine how well these two methods work for various situations. The relationship between two different information times, Fisher information and a surrogate information, are also discussed from the simulation studies.

Sequential methods for parametric survival models

SUMMARY The asymptotic sequential distribution is derived for score tests and maximum likelihood estimates in parametric survival models in the presence of nuisance parameters where individuals enter over time and the data are subject to right censoring. It is shown that these sequential tests and estimates have an independent increments structure. This allows the use of standard group sequential methods for early stopping.

A unified method for monitoring and analysing controlled trials.

Group sequential methods are becoming increasingly popular for monitoring and analysing large controlled trials, especially clinical trials. They not only allow trialists to monitor the data as it accumulates, but also reduce the expected sample size. Such methods are traditionally based on preserving the overall type I error by increasing the conservatism of the hypothesis tests performed at any single analysis. Using methods which are based on hypothesis testing in this way makes point estimation and the calculation of confidence intervals difficult and controversial. We describe a class of group sequential procedures based on a single parameter which reflects initial scepticism towards unexpectedly large effects. These procedures have good expected and maximum sample sizes, and lead to natural point and interval estimates of the treatment difference. Hypothesis tests, point estimates and interval estimates calculated using this procedure are consistent with each other, and tests and estimates made at the end of the trial are consistent with interim tests and estimates. This class of sequential tests can be considered in both a traditional group sequential manner or as a Bayesian solution to the problem.

Interim analysis: the alpha spending function approach.

Interim analysis of accumulating data in a clinical trial is now an established practice for ethical and scientific reasons. Repeatedly testing interim data can inflate false positive error rates if not handled appropriately. Group sequential methods are a commonly used frequentist approach to control this error rate. Motivated by experience of clinical trials, the alpha spending function is one way to implement group sequential boundaries that control the type I error rate while allowing flexibility in how many interim analyses are to be conducted and at what times. In this paper, we review the alpha spending function approach, and detail its applicability to a variety of commonly used statistical procedures, including survival and longitudinal methods.

The what, why and how of Bayesian clinical trials monitoring.

We discuss the advantages and limitations of group sequential methods for monitoring clinical trials data. We describe a Bayesian approach, based upon the use of sceptical prior distributions, that avoids some of the limitations of group sequential methods. We illustrate its use with data from a trial of levamisole plus 5-Fluorouracil for colorectal cancer.

A comparison of methods for Phase II cancer clinical trials: advantages of the triangular test, a group sequential method

In cancer, the purpose of Phase II studies is to determine whether the response rate p to a new treatment is greater than a prespecified value p 0, defined as the largest response rate for which Phase III studies are not worthwhile. It concerns, for example, determining whether the response rate to a new drug is greater than 20%. The main problem is of a decision making nature, and amounts to the comparison of an observed percentage with a theoretical percentage. One way of resolving it is to perform a single statistical analysis after the inclusion of a predetermined number of patients N, but it is not always possible because of high values of N. Furthermore, this approach presents ethical problems when elements in favor of inefficacy or efficacy are available early in the trial. For these reasons, several authors have developed methods which allow to perform repeated analyses and possibly to reach an early conclusion of the study: two-stage, multistage, sequential and group sequential methods. This article considers the main decision making methods proposed in the literature for Phase II studies in oncology. The bibliographic study, which highlights the interest of using group sequential methods, and especially the Triangular Test, is confirmed by a comparative study of the statistical properties of the different methods.

A Microcomputer Program for the Design and Analysis of Phase II Cancer Clinical Trials with Two Group Sequential Methods, the Sequential Probability Ratio Test, and the Triangular Test

We developed an interactive and menu-driven computer program to help investigators design and analyze phase II cancer clinical trials with a group sequential method, namely the sequential probability ratio test or the triangular test. Based on the values selected for the parameters of the trial, the "Design" option allows one to obtain, using simulations, the statistical properties (type I and II error rates and the probability that the test accepts the hypothesis of inefficacy under 21 different assumptions) and the average sample size (under the same assumptions) of the selected test. The "Analysis" option (i) computes, at each analysis, the two statistics V and Z on which the sequential method is based and plots the sample path from the number of successes observed, and (ii), using asymptotic properties, gives the significance level of the test and a point estimate (with its 95% confidence interval) of the parameter of interest at the last analysis.

Group sequential testing in clinical trials with multivariate observations: a review.

Most group sequential testing procedures assume that each patient has only one response. Thus interim test statistics have independent increments. In many clinical trials, however, a response variable is measured at each follow-up visit. In this article, I review some recently developed group sequential methods for repeated measures and for other types of multivariate responses. Six parametric methods and three non-parametric methods are included. My review focuses on the comparison of the assumptions made and the applications of each of these methods.

A Group Sequential Method for one Standard Control and more than one Experimental Treatment

AbstractMany group‐sequential test procedures have been proposed to meet the ethical need for interim analyses. All of these papers, however, focus their discussion on the situation where there are only one standard control and one experimental treatment. In this paper, we consider a trial with one standard control, but with more than one experimental treatment. We have developed a group‐sequential test procedure to accommodate any finite number of experimental treatments. To facilitate the practical application of the proposed test procedure, on the basis of Monte Carlo simulation, we have derived the critical values of α‐levels equal to 0.01, 0.05 and 0.10 for the number of experimental treatments ranging from 2 to 4 and the number of multiple group sequential analysis ranging from 1 to 10. Comparing with a single non‐sequential analysis that has a reasonable power (say, 0.80), we have demonstrated that the application of the proposed test procedure may substantially reduce the required sample size without seriously sacrificing the original power.