The design of a sequential clinical trial for the comparison of two lung cancer treatments

Continuous safety monitoring for randomized controlled clinical trials with blinded treatment information. Part 3: Design considerations

Ongoing safety monitoring of clinical trials of investigational treatments must operate at levels that range from the minute and detailed - namely, mathematical treatment of trial data - to the philosophical and societal - namely, ethical concerns for individuals and populations. Between those two poles lies a realm of environmental and pragmatic considerations that reflect the goals, biases, risk-tolerance, and constraints of study sponsors and organizers. These factors, while more difficult to quantify or, at times, to justify, also have a meaningful impact on the approach to safety monitoring and the resulting actions and outcomes. This paper considers the influence and interaction of two such factors, study design and statistical framework, on continuous safety monitoring procedures. Group sequential designs have been generally preferred for clinical trials over continuous sequential designs because of practical considerations. The group means and greater time for deliberation when using a group sequential procedure, as opposed to a continuous sequential procedure, can improve the quality of the analyses with minimal loss in sensitivity. However, undertaking any sequential analysis within a frequentist framework provokes considerable theoretical and practical difficulties. Continuous monitoring with a likelihood based method, on the other hand, has the advantages that all available information, including new data, can be used; sample sizes need not be fixed; and decisions can be made at any time without statistical penalty, irrespective of trial design. Such responsive statistical rules are needed to provide guidance to the human beings charged with trial monitoring.

A 25-year review of sequential methodology in clinical studies

This paper explores the theoretical developments and subsequent uptake of sequential methodology in clinical studies in the 25 years since Statistics in Medicine was launched. The review examines the contributions which have been made to all four phases into which clinical trials are traditionally classified and highlights major statistical advancements, together with assessing application of the techniques. The vast majority of work has been in the setting of phase III clinical trials and so emphasis will be placed here. Finally, comments are given indicating how the subject area may develop in the future.

A unified theory for sequential clinical trials

The theory underlying sequential clinical trials is now well developed, and the methodology is increasingly being implemented in practice, both by the pharmaceutical industry and in the public sector. The consequences of conducting interim analyses for frequentist interpretations of data are now well understood. A large number of approaches are available for the calculation of stopping boundaries and for the eventual terminal analysis. In this paper, the principles of the design and analysis of sequential clinical trials will be presented. Existing methods will be reviewed, and their relationships with the general principles will be clarified. Controversies and gaps within the methodology will be highlighted. It is intended that presentation of the subject as a single unified theory will allow the few essential underlying features to be better appreciated.

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.

Interim analyses and stopping rules in cancer clinical trials

A clinical trial conducted according to a schedule of interim analyses written into the protocol, and stopped according to a predetermined rule, is known to statisticians as a sequential clinical trial. This methodology is becoming more widely used in trials concerning life-threatening diseases because of its ability to adjust the sample size to the emerging information on treatment efficacy. When treatments under comparison differ appreciably, small samples will be sufficient; for more subtle differences larger numbers of patients need to be recruited. Sequential methods have already been used in certain cancer clinical trials, and they are especially appropriate for such studies. In this paper the principles of sample size determination are reviewed, and the essential aspects of designing sequential trials are described. The necessity for a special form of statistical analysis following a sequential trial is explained, and the consequences of early or late stopping on the analysis are investigated. Compromises which have to be made between the formal requirements of theory and the practical realities of trial conduct are discussed.

Overrunning and underrunning in sequential clinical trials

In a sequential (or group sequential) clinical trial the fulfillment of some pre-specified stopping rule will cause recruitment to be terminated. However, for various reasons, data on patients treated according to protocol may continue to accumulate for some time afterward. This phenomenon is called overrunning. On the other hand, a sequential clinical trial might be abandoned before the stopping rule has been fulfilled. This is called underrunning. In both of these situations the procedure for validly analyzing the study is unclear. In this paper we first review the arguments for sequential methodology and the practical way in which it can be integrated with normal clinical trial conduct. Turning next to the special situations of overrunning and underrunning, the conditions under which a valid analysis is possible are identified, and a method of analysis based on the frequentist philosophy is presented. The likelihood of first gaining and then losing significance due to overrunning and its consequences are examined. Examples based on experience with real studies are presented.

Application of the triangular test to phase II cancer clinical trials

Phase II cancer clinical trials are primarily designed to determine whether the response rate p to the treatment under study is greater than a specified value p0, that is to test the null hypothesis H0: p less than or equal to p0 against an alternative hypothesis H1 : p greater than p0 specified by p = p1. As an alternative to the single and multistage procedures and to Wald's continuous sequential probability ratio test (SPRT), we applied the group sequential methods proposed by Jones and Whitehead, namely the triangular test (TT) and the discrete SPRT, to the comparison of p with p0, and we expressed H0 and H1 in terms of the log odds-ratio statistic log [p(1 - p0)/p0(1 - p)]. A stimulation study showed that both the TT and the discrete SPRT had type I error and power close to the nominal values, and they compared favourably with multistage methods in terms of the average sample size.

The application of a two-stage design for clinical trials in patients with recurrent head and neck cancer

Cytotoxic chemotherapy produces modest benefits for patients with recurrent and metastatic squamous cell carcinoma of the head and neck (SCCHN). Prospective randomized clinical trials have failed to demonstrate unequivocal superiority of aggressive multidrug regimens over single agents. Despite this, phase II trials frequently result in encouraging preliminary observations that compare favorably to historical single-agent data. While providing for a useful method of screening for anti-tumor activity, phase II studies have limited use in determining the relative value of a new treatment program. Results of phase II studies are considerably influenced by patient selection factors and criteria used to establish therapeutic benefits (responses). Furthermore, estimations of true levels of efficacy (response rates) are dependent on sample sizes, which are usually limited in such trials. We propose that newly developed combinations containing at least one known active agent in this disease should be tested in a controlled setting after their toxicity pattern has been well established. The conduct of the usual phase II study in these situations will probably not provide useful new information, since responses are likely to be observed. We describe a two-stage design applied to terminate a trial if at the first stage there is no evidence of improvement over the control arm. This method allows for early termination of studies involving relatively inefficient treatment regimens and, at the same time, continuation of those with a high likelihood to result in significant therapeutic improvements over a control arm. Loss of power is negligible and sample sizes can be reduced significantly. The rationale behind this method and its simplicity are attractive features for a widespread application for new drug development strategies in this and other diseases.

A simulation study of three sequential methods for the comparison of two treatment groups when the response criterion is censored

Three recent sequential methods, group sequential analysis (GSA), the sequential probability ratio test (SPRT) and the triangular test (TT) are well suited to randomized clinical trials with a censored response criterion, as they do not require matched pairs of patients. We undertook a simulation study to investigate their statistical properties and to compare these three methods with the fixed-sample design. Our results suggest that the three methods have the expected statistical properties for size and power; they allow an important reduction of the average number of events before stopping, except with GSA when there is no treatment difference; the triangular test (closed design) appears the optimal design, as the variance of the number of events is smaller than with the sequential probability ratio test (open design) and analysis after every twenty new events does not alter the statistical properties of these sequential methods and enhances their usefulness.

The design of phase III palliative chemotherapy trials in head and neck cancer

This paper describes a series of 2447 patients with squamous carcinoma of the head and neck treated personally over 22 years; 276 patients with advanced untreatable disease and 498 with recurrent untreatable disease are analysed. The median survival for the first group was 13 weeks and for the second 11 weeks. The data fitted an exponential curve. Prognostic factors included general condition and N status for the first group, and site of the primary tumour, site of the recurrence and length of time to recurrence for the second group. However, these factors only explained 5% of the variance; the remaining 95% was unexplained, emphasizing the futility of stratification for prognostic factors, and the necessity for large trials. Using the above facts the number of patients required for a trial, and the length of the trial, can be worked out, and tables of these are given.

The analysis of a sequential clinical trial for the comparison of two lung cancer treatments

Methods adopted in the analysis of data from a randomized controlled trial of a new treatment for inoperable lung cancer are described. The trial design employed the sequential logrank test using length of survival from time of randomization as the principal outcome measure. We describe the practical arrangements for regular inspections of the accumulating data as required by the sequential design, and also for more extensive but less formal interim analyses, and present some of the results. On termination of the trial the survival patterns of the two treatment groups were compared using methods of analysis developed specifically to allow for the sequential nature of the trial design. The role of prognostic factors was investigated using fixed sample methods which are approximately independent of the sequential design.