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When a clinical trial is subject to a series of interim analyses as a result of which the study may be terminated or modified, final frequentist analyses need to take account of the design used. Failure to do so may result in overstated levels of significance, biased effect estimates and confidence intervals with inadequate coverage probabilities. A wide variety of valid methods of frequentist analysis have been devised for sequential designs comparing a single experimental treatment with a single control treatment. It is less clear how to perform the final analysis of a sequential or adaptive design applied in a more complex setting, for example, to determine which treatment or set of treatments amongst several candidates should be recommended. This article has been motivated by consideration of a trial in which four treatments for sepsis are to be compared, with interim analyses allowing the dropping of treatments or termination of the trial to declare a single winner or to conclude that there is little difference between the treatments that remain. The approach taken is based on the method of Rao-Blackwellization which enhances the accuracy of unbiased estimates available from the first interim analysis by taking their conditional expectations given final sufficient statistics. Analytic approaches to determine such expectations are difficult and specific to the details of the design: instead "reverse simulations" are conducted to construct replicate realizations of the first interim analysis from the final test statistics. The method also provides approximate confidence intervals for the differences between treatments., (© 2020 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.)

In this paper, a Bayesian approach is developed for simultaneously comparing multiple experimental treatments with a common control treatment in an exploratory clinical trial. The sample size is set to ensure that, at the end of the study, there will be at least one treatment for which the investigators have a strong belief that it is better than control, or else they have a strong belief that none of the experimental treatments are substantially better than control. This criterion bears a direct relationship with conventional frequentist power requirements, while allowing prior opinion to feature in the analysis with a consequent reduction in sample size. If it is concluded that at least one of the experimental treatments shows promise, then it is envisaged that one or more of these promising treatments will be developed further in a definitive phase III trial. The approach is developed in the context of normally distributed responses sharing a common standard deviation regardless of treatment. To begin with, the standard deviation will be assumed known when the sample size is calculated. The final analysis will not rely upon this assumption, although the intended properties of the design may not be achieved if the anticipated standard deviation turns out to be inappropriate. Methods that formally allow for uncertainty about the standard deviation, expressed in the form of a Bayesian prior, are then explored. Illustrations of the sample sizes computed from the new method are presented, and comparisons are made with frequentist methods devised for the same situation., (Copyright © 2015 John Wiley & Sons, Ltd.)

Conventional phase II trials using binary endpoints as early indicators of a time-to-event outcome are not always feasible. Uveal melanoma has no reliable intermediate marker of efficacy. In pancreatic cancer and viral clearance, the time to the event of interest is short, making an early indicator unnecessary. In the latter application, Weibull models have been used to analyse corresponding time-to-event data. Bayesian sample size calculations are presented for single-arm and randomised phase II trials assuming proportional hazards models for time-to-event endpoints. Special consideration is given to the case where survival times follow the Weibull distribution. The proposed methods are demonstrated through an illustrative trial based on uveal melanoma patient data. A procedure for prior specification based on knowledge or predictions of survival patterns is described. This enables investigation into the choice of allocation ratio in the randomised setting to assess whether a control arm is indeed required. The Bayesian framework enables sample sizes consistent with those used in practice to be obtained. When a confirmatory phase III trial will follow if suitable evidence of efficacy is identified, Bayesian approaches are less controversial than for definitive trials. In the randomised setting, a compromise for obtaining feasible sample sizes is a loss in certainty in the specified hypotheses: the Bayesian counterpart of power. However, this approach may still be preferable to running a single-arm trial where no data is collected on the control treatment. This dilemma is present in most phase II trials, where resources are not sufficient to conduct a definitive trial., (Copyright © 2015 John Wiley & Sons, Ltd.)

This paper considers the design and interpretation of clinical trials comparing treatments for conditions so rare that worldwide recruitment efforts are likely to yield total sample sizes of 50 or fewer, even when patients are recruited over several years. For such studies, the sample size needed to meet a conventional frequentist power requirement is clearly infeasible. Rather, the expectation of any such trial has to be limited to the generation of an improved understanding of treatment options. We propose a Bayesian approach for the conduct of rare-disease trials comparing an experimental treatment with a control where patient responses are classified as a success or failure. A systematic elicitation from clinicians of their beliefs concerning treatment efficacy is used to establish Bayesian priors for unknown model parameters. The process of determining the prior is described, including the possibility of formally considering results from related trials. As sample sizes are small, it is possible to compute all possible posterior distributions of the two success rates. A number of allocation ratios between the two treatment groups can be considered with a view to maximising the prior probability that the trial concludes recommending the new treatment when in fact it is non-inferior to control. Consideration of the extent to which opinion can be changed, even by data from the best feasible design, can help to determine whether such a trial is worthwhile., (© 2014 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.)

This work is motivated by trials in rapidly lethal cancers or cancers for which measuring shrinkage of tumours is infeasible. In either case, traditional phase II designs focussing on tumour response are unsuitable. Usually, tumour response is considered as a substitute for the more relevant but longer-term endpoint of death. In rapidly lethal cancers such as pancreatic cancer, there is no need to use a surrogate, as the definitive endpoint is (sadly) available so soon. In uveal cancer, there is no counterpart to tumour response, and so, mortality is the only realistic response available. Cytostatic cancer treatments do not seek to kill tumours, but to mitigate their effects. Trials of such therapy might also be based on survival times to death or progression, rather than on tumour shrinkage. Phase II oncology trials are often conducted with all study patients receiving the experimental therapy, and this approach is considered here. Simple extensions of one-stage and two-stage designs based on binary responses are presented. Outcomes based on survival past a small number of landmark times are considered: here, the case of three such times is explored in examples. This approach allows exact calculations to be made for both design and analysis purposes. Simulations presented here show that calculations based on normal approximations can lead to loss of power when sample sizes are small. Two-stage versions of the procedure are also suggested., (Copyright © 2014 John Wiley & Sons, Ltd.)

In phase III cancer clinical trials, overall survival is commonly used as the definitive endpoint. In phase II clinical trials, however, more immediate endpoints such as incidence of complete or partial response within 1 or 2 months or progression-free survival (PFS) are generally used. Because of the limited ability to detect change in overall survival with response, the inherent variability of PFS and the long wait for progression to be observed, more informative and immediate alternatives to overall survival are desirable in exploratory phase II trials. In this paper, we show how comparative trials can be designed and analysed using change in tumour size as the primary endpoint. The test developed is based on the framework of score statistics and will formally incorporate the information of whether patients survive until the time at which change in tumour size is assessed. Using an example in non-small cell lung cancer, we show that the sample size requirements for a trial based on change in tumour size are favourable compared with alternative randomized trials and demonstrate that these conclusions are robust to our assumptions., (Copyright © 2012 John Wiley & Sons, Ltd.)

The Cancer Research UK study CR0720-11 is a trial to determine the tolerability and effect on survival of using two agents in combination in patients with advanced pancreatic cancer. In particular, the trial is designed first to identify the most suitable combination of doses of the two agents in terms of the incidence of dose-limiting toxicities. Then, the survival of all patients who have received that dose combination in the study so far, together with additional patients assigned to that dose combination to ensure that the total number is sufficient, will be analysed. If the survival outcomes show promise, then a definitive randomised study of that dose combination will be recommended. The first two patients in the trial will be treated with the lowest doses of each agent in combination. An adaptive Bayesian procedure based only on monotonicity constraints concerning the risks of toxicity at different dose levels will then be used to suggest dose combinations for subsequent patients. The survival analysis will concern only patients who received the chosen dose combination, and will compare observed mortality with that expected from an exponential model based on the known survival rates associated with current treatment. In this paper, the Bayesian dose-finding procedure is described and illustrated, and its properties are evaluated through simulation. Computation of the appropriate sample size for the survival investigation is also discussed., (Copyright © 2012 John Wiley & Sons, Ltd.)

Many formal statistical procedures for phase I dose-finding studies have been proposed. Most concern a single novel agent available at a number of doses and administered to subjects participating in a single treatment period and returning a single binary indicator of toxicity. Such a structure is common when evaluating cytotoxic drugs for cancer. This paper concerns studies of combinations of two agents, both available at several doses. Subjects participate in one treatment period and provide two binary responses: one an indicator of benefit and the other of harm. The word 'benefit' is used loosely here: the response might be an early indicator of physiological change which, if induced in patients, is of potential therapeutic value. The context need not be oncology, but might be any study intended to meet both the phase I aim of establishing which doses are safe and the phase II goal of exploring potential therapeutic activity. A Bayesian approach is used based on an assumption of monotonicity in the relationship between the strength of the dose-combination and the distribution of the bivariate outcome. Special cases are described, and the procedure is evaluated using simulation. The parameters that define the model have immediate and simple interpretation. Graphical representations of the posterior opinions about model parameters are shown, and these can be used to inform the discussions of the trial safety committee., (Copyright © 2011 John Wiley & Sons, Ltd.)

This paper presents an exact method for the analysis of a phase II cancer clinical trial conducted using a two-stage design in which early stopping may be allowed for either futility or efficacy. The method provides a point and interval estimate of the response probability associated with the treatment under investigation and a p-value for testing whether this exceeds some standard null value. Two-stage designs are often used in phase II trials in oncology for reasons of ethics and efficiency, but this design feature is seldom taken into account when the results are analyzed. After any two-stage design or multi-stage design, the method for analysis should take into account the previous interim analyses performed, otherwise the results will be biased. In this paper, an approximate approach based on a log-odds ratio parameterisation will be compared with an exact method through the calculation of the precise coverage probabilities of each approach., (Copyright © 2010 John Wiley & Sons, Ltd.)

Despite an enormous and growing statistical literature, formal procedures for dose-finding are only slowly being implemented in phase I clinical trials. Even in oncology and other life-threatening conditions in which a balance between efficacy and toxicity has to be struck, model-based approaches, such as the Continual Reassessment Method, have not been universally adopted. Two related concerns have limited the adoption of the new methods. One relates to doubts about the appropriateness of models assumed to link the risk of toxicity to dose, and the other is the difficulty of communicating the nature of the process to clinical investigators responsible for early phase studies. In this paper, we adopt a new Bayesian approach involving a simple model assuming only monotonicity in the dose-toxicity relationship. The parameters that define the model have immediate and simple interpretation. The approach can be applied automatically, and we present a simulation investigation of its properties when it is. More importantly, it can be used in a transparent fashion as one element in the expert consideration of what dose to administer to the next patient or group of patients. The procedure serves to summarize the opinions and the data concerning risks of a binary characterization of toxicity which can then be considered, together with additional and less tidy trial information, by the clinicians responsible for making decisions on the allocation of doses. Graphical displays of these opinions can be used to ease communication with investigators., (Copyright (c) 2010 John Wiley & Sons, Ltd.)

There is growing interest, especially for trials in stroke, in combining multiple endpoints in a single clinical evaluation of an experimental treatment. The endpoints might be repeated evaluations of the same characteristic or alternative measures of progress on different scales. Often they will be binary or ordinal, and those are the cases studied here. In this paper we take a direct approach to combining the univariate score statistics for comparing treatments with respect to each endpoint. The correlations between the score statistics are derived and used to allow a valid combined score test to be applied. A sample size formula is deduced and application in sequential designs is discussed. The method is compared with an alternative approach based on generalized estimating equations in an illustrative analysis and replicated simulations, and the advantages and disadvantages of the two approaches are discussed., ((c) 2010 John Wiley & Sons, Ltd.)

Phase II clinical trials are performed to investigate whether a novel treatment shows sufficient promise of efficacy to justify its evaluation in a subsequent definitive phase III trial, and they are often also used to select the dose to take forward. In this paper we discuss different design proposals for a phase II trial in which three active treatment doses and a placebo control are to be compared in terms of a single-ordered categorical endpoint. The sample size requirements for one-stage and two-stage designs are derived, based on an approach similar to that of Dunnett. Detailed computations are prepared for an illustrative example concerning a study in stroke. Allowance for early stopping for futility is made. Simulations are used to verify that the specified type I error and power requirements are valid, despite certain approximations used in the derivation of sample size. The advantages and disadvantages of the different designs are discussed, and the scope for extending the approach to different forms of endpoint is considered., (Copyright (c) 2008 John Wiley & Sons, Ltd.)

This paper presents a simple Bayesian approach to sample size determination in clinical trials. It is required that the trial should be large enough to ensure that the data collected will provide convincing evidence either that an experimental treatment is better than a control or that it fails to improve upon control by some clinically relevant difference. The method resembles standard frequentist formulations of the problem, and indeed in certain circumstances involving 'non-informative' prior information it leads to identical answers. In particular, unlike many Bayesian approaches to sample size determination, use is made of an alternative hypothesis that an experimental treatment is better than a control treatment by some specified magnitude. The approach is introduced in the context of testing whether a single stream of binary observations are consistent with a given success rate p(0). Next the case of comparing two independent streams of normally distributed responses is considered, first under the assumption that their common variance is known and then for unknown variance. Finally, the more general situation in which a large sample is to be collected and analysed according to the asymptotic properties of the score statistic is explored., ((c) 2007 John Wiley & Sons, Ltd.)

Assaying a large number of genetic markers from patients in clinical trials is now possible in order to tailor drugs with respect to efficacy. The statistical methodology for analysing such massive data sets is challenging. The most popular type of statistical analysis is to use a univariate test for each genetic marker, once all the data from a clinical study have been collected. This paper presents a sequential method for conducting an omnibus test for detecting gene-drug interactions across the genome, thus allowing informed decisions at the earliest opportunity and overcoming the multiple testing problems from conducting many univariate tests. We first propose an omnibus test for a fixed sample size. This test is based on combining F-statistics that test for an interaction between treatment and the individual single nucleotide polymorphism (SNP). As SNPs tend to be correlated, we use permutations to calculate a global p-value. We extend our omnibus test to the sequential case. In order to control the type I error rate, we propose a sequential method that uses permutations to obtain the stopping boundaries. The results of a simulation study show that the sequential permutation method is more powerful than alternative sequential methods that control the type I error rate, such as the inverse-normal method. The proposed method is flexible as we do not need to assume a mode of inheritance and can also adjust for confounding factors. An application to real clinical data illustrates that the method is computationally feasible for a large number of SNPs., (Copyright (c) 2007 John Wiley & Sons, Ltd.)

In clinical trials with a long period of time between randomization and the primary assessment of the patient, the same assessments are often undertaken at intermediate times. When an interim analysis is conducted, in addition to the patients who have completed the primary assessment, there will be those who have till then undergone only intermediate assessments. The efficiency of the interim analysis can be increased by the inclusion of data from these additional patients. This paper compares four methods of increasing information based on model-free estimates of transition probabilities to incorporate intermediate assessments from patients who have not completed the trial. It is assumed that the observations are binary and that there is one intermediate assessment. The methods are the score and Wald approaches, each with the log-odds ratio and probability difference parameterizations. Simulations show that all four approaches have good properties in moderate to large sample sizes.

A sequential study design generally makes more efficient use of available information than a fixed sample counterpart of equal power. This feature is gradually being exploited by researchers in genetic and epidemiological investigations that utilize banked biological resources and in studies where time, cost and ethics are prominent considerations. Recent work in this area has focussed on the sequential analysis of matched case-control studies with a dichotomous trait. In this paper, we extend the sequential approach to a comparison of the associations within two independent groups of paired continuous observations. Such a comparison is particularly relevant in familial studies of phenotypic correlation using twins. We develop a sequential twin method based on the intraclass correlation and show that use of sequential methodology can lead to a substantial reduction in the number of observations without compromising the study error rates. Additionally, our approach permits straightforward allowance for other explanatory factors in the analysis. We illustrate our method in a sequential heritability study of dysplasia that allows for the effect of body mass index and compares monozygotes with pairs of singleton sisters., (Copyright 2006 John Wiley & Sons, Ltd.)

Pharmacovigilance, the monitoring of adverse events (AEs), is an integral part in the clinical evaluation of a new drug. Until recently, attempts to relate the incidence of AEs to putative causes have been restricted to the evaluation of simple demographic and environmental factors. The advent of large-scale genotyping, however, provides an opportunity to look for associations between AEs and genetic markers, such as single nucleotides polymorphisms (SNPs). It is envisaged that a very large number of SNPs, possibly over 500,000, will be used in pharmacovigilance in an attempt to identify any genetic difference between patients who have experienced an AE and those who have not. We propose a sequential genome-wide association test for analysing AEs as they arise, allowing evidence-based decision-making at the earliest opportunity. This gives us the capability of quickly establishing whether there is a group of patients at high-risk of an AE based upon their DNA. Our method provides a valid test which takes account of linkage disequilibrium and allows for the sequential nature of the procedure. The method is more powerful than using a correction, such as Sidák, that assumes that the tests are independent.

In this paper a robust method is developed for the analysis of data consisting of repeated binary observations taken at up to three fixed time points on each subject. The primary objective is to compare outcomes at the last time point, using earlier observations to predict this for subjects with incomplete records. A score test is derived. The method is developed for application to sequential clinical trials, as at interim analyses there will be many incomplete records occurring in non-informative patterns. Motivation for the methodology comes from experience with clinical trials in stroke and head injury, and data from one such trial is used to illustrate the approach. Extensions to more than three time points and to allow for stratification are discussed.

In this paper, Bayesian decision procedures previously proposed for dose-escalation studies in healthy volunteers are reviewed and evaluated. Modifications are made to the expression of the prior distribution in order to make the procedure simpler to implement and a more relevant criterion for optimality is introduced. The results of an extensive simulation exercise to establish the properties of the procedure and to aid choice between designs are summarized, and the way in which readers can use simulation to choose a design for their own trials is described. The influence of the value of the within-subject correlation on the procedure is investigated and the use of a simple prior to reflect uncertainty about the correlation is explored.

In this paper, Bayesian decision procedures are developed for dose-escalation studies based on bivariate observations of undesirable events and signs of therapeutic benefit. The methods generalize earlier approaches taking into account only the undesirable outcomes. Logistic regression models are used to model the two responses, which are both assumed to take a binary form. A prior distribution for the unknown model parameters is suggested and an optional safety constraint can be included. Gain functions to be maximized are formulated in terms of accurate estimation of the limits of a 'therapeutic window' or optimal treatment of the next cohort of subjects, although the approach could be applied to achieve any of a wide variety of objectives. The designs introduced are illustrated through simulation and retrospective implementation to a completed dose-escalation study., (Copyright 2005 John Wiley & Sons, Ltd.)

A role for sequential test procedures is emerging in genetic and epidemiological studies using banked biological resources. This stems from the methodology's potential for improved use of information relative to comparable fixed sample designs. Studies in which cost, time and ethics feature prominently are particularly suited to a sequential approach. In this paper sequential procedures for matched case-control studies with binary data will be investigated and assessed. Design issues such as sample size evaluation and error rates are identified and addressed. The methodology is illustrated and evaluated using both real and simulated data sets.

A score test is developed for binary clinical trial data, which incorporates patient non-compliance while respecting randomization. It is assumed in this paper that compliance is 'all-or-nothing', in the sense that a patient either accepts all of the treatment assigned as specified in the protocol, or none of it. Direct analytic comparisons of the adjusted test statistic for both the score test and the likelihood ratio test are made with the corresponding test statistics that adhere to the intention-to-treat principle. It is shown that no gain in power is possible over the intention-to-treat analysis, by adjusting for patient non-compliance. Sample size formulae are derived and simulation studies are used to demonstrate that the sample size approximation holds., (Copyright 2003 John Wiley & Sons, Ltd.)

This paper introduces a simple futility design that allows a comparative clinical trial to be stopped due to lack of effect at any of a series of planned interim analyses. Stopping due to apparent benefit is not permitted. The design is for use when any positive claim should be based on the maximum sample size, for example to allow subgroup analyses or the evaluation of safety or secondary efficacy responses. A final frequentist analysis can be performed that is valid for the type of design employed. Here the design is described and its properties are presented. Its advantages and disadvantages relative to the use of stochastic curtailment are discussed., (Copyright 2003 John Wiley & Sons, Ltd.)

For disease indications such as Acquired Immune Deficiency Syndrome (AIDS) and various cancers, randomization to a pure control treatment may be scientifically desirable but not ethically acceptable. Clinicians may insist that the experimental treatment be made available, at least as a rescue medication, for all patients in the control arm. A method for estimating a treatment effect in survival data from randomized clinical trials of this type is developed under an accelerated failure time model. This approach retains all patients in the groups to which they were randomized and is not based on an ad hoc subgroup analysis. By conditioning on having observed patient switch times, this method avoids the need to model patient switching patterns in the analysis. This new approach is evaluated using simulation studies, and is illustrated through analysing data from a Medical Research Council lung cancer trial., (Copyright 2002 John Wiley & Sons, Ltd.)

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.

Sequential designs are increasingly being used in major clinical trials concerning life-threatening diseases. So far most applications have concerned trials designed to establish whether an experimental treatment is superior to a control. However, many trials are conducted with the objective of showing that an experimental treatment is equivalent to a control. This paper concerns the application of sequential designs to equivalence trials. Criteria for claiming equivalence are reviewed and compared, and methods first developed in the context of bioequivalence are described. Appropriate sequential procedures are identified. A simulated example, based on a clinical comparison of bronchodilators, is used to illustrate both the double triangular test and a comparable procedure constructed from alpha-spending functions.

This paper describes the Bayesian decision procedure and illustrates the methodology through an application to dose determination in early phase clinical trials. The situation considered is quite specific: a fixed number of patients are available, to be treated one at a time, with the choice of dose for any patient requiring knowledge of the responses of all previous patients. A continuous range of possible doses is available. The prior beliefs about the dose-response relationship are of a particular form and the gain from investigation is measured in terms of statistical information gathered. How all of these specifications may be varied is discussed. A comparison with the continual reassessment method is made.

In early phase clinical trials of a new medical treatment, patients are treated to decide whether there is sufficient promise to justify additional studies. A decision theoretic approach is proposed to help determine the number of patients that should be treated. The optimal sample size is obtained by maximizing a utility function which incorporates both the number of 'gained successes' and the costs of treatment. The method extends work of Sylvester and Staquet, and adopts a Bayesian formulation. Numbers of patients in later studies and in eventual routine use of the treatment are taken into account. We allow for the possibility that a later study might lead to an erroneous conclusion. The effects of these various influences on the recommended sampling plan for the early phase clinical trial are explored.

The earliest formal sequential procedure, the sequential probability ratio test, involved the plotting of certain test statistics and comparison with straight line parallel boundaries. The boundaries approach can now be used with a wide variety of test statistics, including those appropriate to the analysis of survival data. The boundaries can take various forms, although the use of straight lines still eases the underlying mathematical theory while at least approximating to the requirements of the majority of clinical trials. The implementation of sequential methods needs to be made flexibly and sensitively, with each clinical trial meriting an individualized approach.

When failure times are observed, additional information concerning the type of failure is often recorded. A method which simultaneously models the failure times and additional information in the form of ordinal categories is discussed. An application to clinical trial data, in which the failure times are times of onset of headache, and the headaches are classified into the ordinal categories mild, moderate and severe, illustrates how this method may be used and how the final model can be interpreted. The continuation ratio model, which is used in this method, is described in detail.

Meta-analysis provides a systematic and quantitative approach to the summary of results from randomized studies. Whilst many authors have published actual meta-analyses concerning specific therapeutic questions, less has been published about comprehensive methodology. This article presents a general parametric approach, which utilizes efficient score statistics and Fisher's information, and relates this to different methods suggested by previous authors. Normally distributed, binary, ordinal and survival data are considered. Both the fixed effects and random effects model for treatments are described.

Crossover studies have been successfully conducted in the case of continuous responses. Existing procedures of analysis for ordinal responses, on the other hand, are rarely satisfactory unless strict, usually unrealistic, assumptions are made. In this paper we investigate a random effects model and show that the model is simple and general. Interpretation of parameters is easy, though with a complicated fitting procedure.

A method for the calculation of confidence intervals following a sequential clinical trial is proposed which is more accurate than methods based solely on continuous monitoring assumptions, but is not as computationally laborious as previous methods suggested for group sequential trials. The calculation takes account of the excess of the sample path over the boundary at the final inspection of the trial, which may be substantial after group sequential monitoring, and is ignored when continuous monitoring is assumed. Accuracy of such confidence intervals after a triangular test is investigated by simulation of coverage probabilities, individual confidence limit probabilities and p-value curves.

In this paper the following problem of clinical research is explored. Several potential new treatments are available for use against a certain disease. These are evaluated in a series of pilot studies which will constitute phase II clinical trials. The most promising will then be compared with a standard treatment in a phase III trial. Of interest will be the number of patients needed for the complete research programme, the proportions of these that should be involved in each phase, and the number of treatments which should be tried. Optimal strategies are found which maximize the probability that the overall programme identifies a treatment which is significantly better than the standard.