A case for Bayesianism in clinical trials

Bayesian evaluation of group sequential clinical trial designs

Clinical trial designs often incorporate a sequential stopping rule to serve as a guide in the early termination of a study. When choosing a particular stopping rule, it is most common to examine frequentist operating characteristics such as type I error, statistical power, and precision of confidence intervals (Statist. Med. 2005, in revision). Increasingly, however, clinical trials are designed and analysed in the Bayesian paradigm. In this paper, we describe how the Bayesian operating characteristics of a particular stopping rule might be evaluated and communicated to the scientific community. In particular, we consider a choice of probability models and a family of prior distributions that allows concise presentation of Bayesian properties for a specified sampling plan.

Practical Bayesian adaptive randomisation in clinical trials

While randomisation is the established method for obtaining scientifically valid treatment comparisons in clinical trials, it sometimes is at odds with what physicians feel is good medical practice. If a physician favours one treatment over another based on personal experience or published data, it may be more appropriate ethically for that physician to use the favoured treatment, rather than enrolling patients on a randomised trial. Still, the randomised trial may later show the physician's favoured treatment to be inferior. This paper reviews a statistical method, Bayesian adaptive randomisation, that provides a practical compromise between the scientific ideal of conventional randomisation and choosing each patient's treatment based on a personal preference that may prove to be incorrect. The method will first be illustrated by a simple hypothetical example, then by a recent trial in which patients with unresectable soft tissue sarcoma were adaptively randomised between two chemotherapy regimens.

Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Frequentist evaluation of group sequential clinical trial designs

Group sequential stopping rules are often used as guidelines in the monitoring of clinical trials in order to address the ethical and efficiency issues inherent in human testing of a new treatment or preventive agent for disease. Such stopping rules have been proposed based on a variety of different criteria, both scientific (e.g. estimates of treatment effect) and statistical (e.g. frequentist type I error, Bayesian posterior probabilities, stochastic curtailment). It is easily shown, however, that a stopping rule based on one of these criteria induces a stopping rule on all other criteria. Thus, the basis used to initially define a stopping rule is relatively unimportant so long as the operating characteristics of the stopping rule are fully investigated. In this paper we describe how the frequentist operating characteristics of a particular stopping rule might be evaluated to ensure that the selected clinical trial design satisfies the constraints imposed by the many different disciplines represented by the clinical trial collaborators.

The contrast and convergence of Bayesian and frequentist statistical approaches in pharmacoeconomic analysis

The application of Bayesian statistical analyses has been facilitated in recent years by methodological advances and an increasing complexity necessitated within research. Substantial debate has historically accompanied this analytic approach relative to the frequentist method, which is the predominant statistical ideology employed in clinical studies. While the essence of the debate between the two branches of statistics centres on differences in the use of prior information and the definition of probability, the ramifications involve the breadth of research design, analysis and interpretation. The purpose of this paper is to discuss the application of frequentist and Bayesian statistics in the pharmacoeconomic assessment of healthcare technology. A description of both paradigms is offered in the context of potential advantages and disadvantages, and applications within pharmacoeconomics are briefly addressed. Additional considerations are presented to stimulate further development and to direct appropriate applications of each method such that the integrity and robustness of scientific inference be strengthened.

Bayesian sample size calculations in phase II clinical trials using a mixture of informative priors

A number of researchers have discussed phase II clinical trials from a Bayesian perspective. A recent article by Mayo and Gajewski focuses on sample size calculations, which they determine by specifying an informative prior distribution and then calculating a posterior probability that the true response will exceed a prespecified target. In this article, we extend these sample size calculations to include a mixture of informative prior distributions. The mixture comes from several sources of information. For example consider information from two (or more) clinicians. The first clinician is pessimistic about the drug and the second clinician is optimistic. We tabulate the results for sample size design using the fact that the simple mixture of Betas is a conjugate family for the Beta- Binomial model. We discuss the theoretical framework for these types of Bayesian designs and show that the Bayesian designs in this paper approximate this theoretical framework.

A phase I/II trial of a WT1 (Wilms' tumor gene) peptide vaccine in patients with solid malignancy: safety assessment based on the phase I data

OBJECTIVE

We conducted a phase I study to investigate the safety of a weekly WT1 tumor vaccine therapy in patients with solid tumors that had been refractory to all other anti-cancer therapies.

METHODS

Skin-test-negative patients were intradermally injected weekly for 12 weeks with 3.0 mg of an HLA-A*2402-restricted modified 9-mer WT1 peptide emulsified in Montanide ISA51 adjuvant. We estimated the Bayesian posterior probability of the occurrence of grade 3 or 4 toxicity when receiving the weekly WT1 vaccination. This analysis provided the basis for making a decision to terminate the phase I study and switch to phase II. Moreover, we performed an exploratory assessment of the anti-tumor effects of WT1 treatment.

RESULTS

Ten patients received 114 vaccinations with WT1 on a weekly schedule. No grade 3 or 4 toxicities were observed. Based on the Bayesian approach, it was highly likely that the probability of grade 3 or 4 toxicity was below 20% (the posterior probability = 0.914). Fifteen grade 2 and two grade 1 toxicities were observed; all of these incidents, however, were determined by the Independent Data and Safety Monitoring Committee to be unrelated to the WT1 treatment. One patient exhibited a partial response; five additional patients had stable disease while receiving weekly WT1 treatment.

CONCLUSION

This paper confirms that the potential toxicities of the treatment schedule of weekly WT1 vaccination are acceptable and suggested a potential anti-tumor effect. Consequently, we validated the decision to continue to the phase II trial.

Use of a Bayesian approach to decide when to stop a therapeutic trial: the case of a chemoprophylaxis trial in human immunodeficiency virus infection

From 1996 to 1998, a phase III, placebo-controlled, therapeutic trial was conducted in Abidjan, Ivory Coast, to assess the efficacy of cotrimoxazole prophylaxis in reducing severe morbidity in adults at early stages of human immunodeficiency virus infection. The authors used the real data from this trial to simulate three Bayesian interim analyses. Three prior distributions were considered: a noninformative one, a skeptical one, and one based on external information. The posterior distribution was calculated by using directed acyclic graphs and Gibbs sampling. This Bayesian approach showed different results according to the prior distribution chosen. Although use of the noninformative prior would have led to stopping the trial at the same time that the frequentist approach would have, the skeptical prior would have led to continuing it, and the prior based on external data would have led to stopping it 1 year earlier.

Seven items were identified for inclusion when reporting a Bayesian analysis of a clinical study

OBJECTIVE

(1) To generate a list of items that experts consider most important when reporting a Bayesian analysis of a clinical study, (2) to report on the extent to which we found these items in the literature, and (3) to identify factors related to the number of items in a report.

STUDY DESIGN AND SETTING

Based on opinions from 23 international experts, we determined the items considered most important when publishing a Bayesian analysis. We then performed a literature search to identify articles in which a Bayesian analysis was performed and determined the extent to which we found these items in each report. Finally, we examined the relationship between the number of items in a report and journal- and article-specific attributes.

RESULTS

Our final set of seven items described the prior distribution (specification, justification, and sensitivity analysis), analysis (statistical model and analytic technique), and presentation of results (central tendency and variance). There was >99% probability that more items were reported in studies with a noncontrolled study design and in journals with a methodological focus, lower impact factor, and absence of a word count limit.

CONCLUSION

We developed a set of seven items that experts believe to be most important when reporting a Bayesian analysis.

Bayesian sample size calculations in phase II clinical trials using informative conjugate priors

A number of researchers have discussed phase II clinical trials from a Bayesian perspective. A recent article by Tan and Machin focuses on sample size calculations, which they determine by specifying a diffuse prior distribution and then calculating a posterior probability that the true response will exceed a prespecified target. In this article, we extend these sample size calculations to include informative prior distributions using various strategies that allow researchers with both optimistic and pessimistic priors direct involvement in the sample size decision making. We select the informative priors via multiple methods determined by the mean, median or mode of the conjugate prior. These cases can result in varying sample sizes.

Considerations when designing a clinical trial of haematopoietic stem cell transplantation for autoimmune disease

The design and conduct of clinical trials of haematopoietic stem cell transplantation (HSCT) for autoimmune diseases requires investigators to address issues unique to this therapeutic approach and patient population. The proper composition of the protocol team is central to success. It is important to recognize that transplant physicians are no longer also the disease experts when transplanting patients with autoimmune diseases, and a close collaborative relationship between these groups early in the design stage must continue through the care of patients on trial to the assessment of toxicity and response. The early involvement of statisticians expert in clinical trial design and patient representatives are also vital to developing the optimal protocol. Each step in design and implementation requires particular consideration of the unique aspects of applying HSCT to autoimmune diseases. Some areas discussed are the role of disease and transplant databases in designing and analysing clinical trials, design options for early-phase trials, maintaining clinical equipoise, eligibility criteria, blinding, outcome measures and statistical analysis, and the composition and role of the data safety and monitoring boards. Although no blueprint for designing and conducting a trial of HSCT for autoimmune diseases can be laid out, the process should take into consideration the issues highlighted herein.

Practical model-based dose-finding in phase I clinical trials: methods based on toxicity

We describe two practical, outcome-adaptive statistical methods for dose-finding in phase I clinical trials. One is the continual reassessment method and the other is based on a logistic regression model. Both methods use Bayesian probability models as a basis for learning from the accruing data during the trial, choosing doses for successive patient cohorts, and selecting a maximum tolerable dose (MTD). These methods are illustrated and compared to the conventional 3+3 algorithm by application to a particular trial in renal cell carcinoma. We also compare their average behavior by computer simulation under each of several hypothetical dose-toxicity curves. The comparisons show that the Bayesian methods are much more reliable than the conventional algorithm for selecting an MTD, and that they have a low risk of treating patients at unacceptably toxic doses.

Are we doing any good by doing really well? (Where's the Bacon?)

Francis Bacon, who with Rene Decartes laid the intellectual foundations for Western science in the seventeenth century, asserted that the purpose of all knowledge is "action in the production of works for ... the relief of man's estate." We assess briefly several aspects of a few of the current efforts directed to the production of such "works" with respect to such "relief" as they may provide: cancer mortality, the medical literature, evidence-based medicine, clinical trials, observational databases and criteria for the promotion and tenure of the medical faculty. We suggest why each of these efforts appears to have failed to some degree and then propose some measures that may possibly serve as correctives.

A Bayesian analysis of pharmacoeconomic data from a clinical trial on schizophrenia

Pharmacoeconomic studies are performed in a higher frequency to assess the economic interest of new drugs. However, a standard methodology does not still completely exist. We present here the principles and results of a cost-effectiveness Bayesian analysis on data from 146 patients (interim analysis) collected during a clinical trial. This trial was originally planned to enrol 245 patients with predominantly negative schizophrenia symptoms and involved four treatment groups (a new treatment given at low dose and high dose, a comparator and a placebo). First, some prior distributions of the cost-effectiveness ratio were numerically deduced from the effectiveness parameter clinical priors (based on investigators' opinions and questionnaires before going to blind breaking) and from cost function priors. The costs taken into account were hospitalizations, sick leave days, treatments, visits to the doctor, laboratory exams and suicide attempts. The effectiveness parameter was the change from baseline on SANS (scale for the assessment of negative symptoms). Posterior distributions were elaborated for the cost-effectiveness ratio by combining the cost-effectiveness ratio priors and likelihood together using the Bayes theorem. Results lead to a conclusion in favour of the new treatment given at high dose.

Further statistics in dentistry. Part 9: Bayesian statistics

Statistics can be defined as the methods used to assimilate data, so that guidance can be given, and conclusions drawn, in situations which involve uncertainty. In particular, statistical inference is concerned with drawing conclusions about particular aspects of a population when that population cannot be studied in full. Uncertainty arises here because the totality of the information is not available. Instead, to make inferences about the population, it is necessary to rely on a sample of data which is selected from the population; this sample data may be augmented, in certain circumstances, by auxiliary information which is obtained independently of the sample data. Clearly, uncertainty lies at the heart of statistics and statistical inference. This uncertainty is measured by a probability which therefore forms the crux of statistics and must be properly understood in order to interpret a statistical analysis.

Seamlessly expanding a randomized phase II trial to phase III

A sequential Bayesian phase II/III design is proposed for comparative clinical trials. The design is based on both survival time and discrete early events that may be related to survival and assumes a parametric mixture model. Phase II involves a small number of centers. Patients are randomized between treatments throughout, and sequential decisions are based on predictive probabilities of concluding superiority of the experimental treatment. Whether to stop early, continue, or shift into phase III is assessed repeatedly in phase II. Phase III begins when additional institutions are incorporated into the ongoing phase II trial. Simulation studies in the context of a non-small-cell lung cancer trial indicate that the proposed method maintains overall size and power while usually requiring substantially smaller sample size and shorter trial duration when compared with conventional group-sequential phase III designs.

Bayeswatch: an overview of Bayesian statistics

Increasingly, clinical research is evaluated on the quality of its statistical analysis. Traditionally, statistical analyses in clinical research have been carried out from a 'frequentist' perspective. The presence of an alternative paradigm - the Bayesian paradigm - has been relatively unknown in clinical research until recently. There is currently a growing interest in the use of Bayesian statistics in health care research. This is due both to a growing realization of the limitations of frequentist methods and to the ability of Bayesian methods explicitly to incorporate prior expert knowledge and belief into the analyses. This is in contrast to frequentist methods, where prior experience and beliefs tend to be incorporated into the analyses in an ad hoc fashion. This paper outlines the frequentist and Bayesian paradigms. Acute myocardial infarction mortality data are then analysed from both a Bayesian and a frequentist perspective. In some analyses, the two methods are seen to produce comparable results; in others, they produce different results. It is noted that in this example, there are clinically relevant questions that are more easily addressed from a Bayesian perspective. Finally, areas in clinical research where Bayesian ideas are increasingly common are highlighted.

The impact of foot massage and guided relaxation following cardiac surgery: a randomized controlled trial

BACKGROUND

Because of the widely presumed association between heart disease and psychological wellbeing, the use of so-called 'complementary' therapies as adjuncts to conventional treatment modalities have been the subject of considerable debate. The present study arose from an attempt to identify a safe and effective therapeutic intervention to promote wellbe ing, which could be practicably delivered by nurses to patients in the postoperative recovery period following coronary artery bypass graft (CABG) surgery. Aim. To investigate the impact of foot massage and guided relaxation on the wellbeing of patients who had undergone CABG surgery.

METHOD

Twenty-five subjects were randomly assigned to either a control or one of two intervention groups. Psychological and physical variables were measured immediately before and after the intervention. A discharge questionnaire was also administered.

RESULTS

No significant differences between physiological parameters were found. There was a significant effect of the intervention on the calm scores (ANOVA, P=0.014). Dunnett's multiple comparison showed that this was attributable to increased calm among the massage group. Although not significant the guided relaxation group also reported substantially higher levels of calm than control. There was a clear (nonsignificant) trend across all psychological variables for both foot massage and, to a lesser extent, guided relaxation to improve psychological wellbeing. Both interventions were well received by the subjects.

CONCLUSIONS

These interventions appear to be effective, noninvasive techniques for promoting psychological wellbeing in this patient group. Further investigation is indicated.

Quantifying and documenting prior beliefs in clinical trials

Collecting and documenting subjective prior beliefs from knowledgeable clinicians about the potential results of a clinical trial has many advantages. Two large trials of prophylactic treatments in an HIV-positive population are used as examples. The trials recruited patients of primary care physicians and compared treatments which were in use in clinical practice. Opinions about these trials were elicited from 58 practising HIV clinicians. It is shown how the documented opinions can be used to augment the monitoring process; the prior opinions are updated with interim data using approximate Bayesian methods to give posterior opinions incorporating interim results. These posterior opinions can be used by the monitoring board to anticipate the clinicians' reaction to the results. Eliciting prior beliefs is also ethically important for documenting the nature of the uncertainty or equipoise. Important information is provided for the informed consent process and Institutional Review Board (IRB).

A new statistical method for dose-finding based on efficacy and toxicity in early phase clinical trials

Most statistical methods for dose-finding in phase I clinical trials determine a maximum tolerable dose based on toxicity while ignoring efficacy. Most phase II designs assume that an acceptable dose has been determined and aim to estimate treatment efficacy, possibly with early stopping rules for safety monitoring. The purpose of this paper is to describe a new statistical strategy for dose-finding in single-arm clinical trials where patient outcome is characterized in terms of both response and toxicity. The strategy, which may be considered a phase I/II hybrid, was first proposed by Thall and Russell [1] and subsequently modified by Thall [2]. The underlying mathematical model expresses the probabilities of response and toxicity as interdependent functions of dose. The method is based on fixed standards for the minimum probability of response and the maximum probability of toxicity appropriate for the particular trial. The best acceptable dose is chosen for each successive patient cohort adaptively, based on the fixed standards and the dose-outcome data from patients treated previously in the trial. The scientific goals are to select one best acceptable dose for future patients and to estimate the response and toxicity probabilities at that dose, or to stop the trial early if it becomes sufficiently unlikely that any dose is both safe and efficacious. An application of the method to a trial of donor lymphocyte infusion as salvage therapy for chemo-refractory AML/MDS patients is described. To illustrate the method's flexibility and potential breadth of application, two additional examples are provided, including a hypothetical trial in which a 5% response rate is of interest.

Bayesian communication: a clinically significant paradigm for electronic publication

OBJECTIVE

To develop a model for Bayesian communication to enable readers to make reported data more relevant by including their prior knowledge and values.

BACKGROUND

To change their practice, clinicians need good evidence, yet they also need to make new technology applicable to their local knowledge and circumstances. Availability of the Web has the potential for greatly affecting the scientific communication process between research and clinician. Going beyond format changes and hyperlinking, Bayesian communication enables readers to make reported data more relevant by including their prior knowledge and values. This paper addresses the needs and implications for Bayesian communication. FORMULATION: Literature review and development of specifications from readers', authors', publishers', and computers' perspectives consistent with formal requirements for Bayesian reasoning.

RESULTS

Seventeen specifications were developed, which included eight for readers (express prior knowledge, view effect size and variability, express threshold, make inferences, view explanation, evaluate study and statistical quality, synthesize multiple studies, and view prior beliefs of the community), three for authors (protect the author's investment, publish enough information, make authoring easy), three for publishers (limit liability, scale up, and establish a business model), and two for computers (incorporate into reading process, use familiar interface metaphors). A sample client-only prototype is available at http://omie.med.jhmi.edu/bayes.

CONCLUSION

Bayesian communication has formal justification consistent with the needs of readers and can best be implemented in an online environment. Much research must be done to establish whether the formalism and the reality of readers' needs can meet.

Early stopping of clinical trials in lupus and other uncommon rheumatologic diseases

Use of statistical methods for early stopping of clinical trials allows more efficient and ethical utilization of subjects. In uncommon diseases, where the pool of potential subjects is limited, these methods provide a way to maximize the information gathered from trials. For trials in lupus, methods for early stopping should be more widely utilized. We discuss the ethics, practical aspects, pros and cons, and statistical foundations of some established methods for early stopping, with an emphasis on those that have available implementation in computer software. An example of the design and analysis of a treatment trial in systemic lupus erythematosus with the triangular test method of early stopping is also given.

Cross-study hierarchical modeling of stratified clinical trial data

Hierarchical random-effects models can be used to estimate treatment or other covariate effects in single-study analyses coordinated over multiple clinical units and can also be extended to a wide variety of cross-study applications. After reviewing the single-study case, we use data from five trial protocols to look for units that tend to have treatment effects consistently above or below the study-specific grand mean across several studies. As a first step, we summarize the patient-level data as study-specific and unit-specific estimated treatment effects and standard errors using independent Cox regression models. We then compare the results of a hierarchical model using these data summaries as input to those produced by a more fully Bayesian method that uses the actual patient-level survival data. We also compare various different models using a deviance information criterion, a recent extension of the Akaike information criterion designed for hierarchical models. Our procedure appears to be effective at answering the question whether certain clinical units of the Terry Beirn Community Programs for Clinical Research on AIDS are better than others at identifying treatment effects where they exist.

A strategic view of randomized trial design in low-incidence paediatric cancer

We use a statistical model to examine the relationship between alpha level, sample size, trial duration, patient accrual rate and therapeutic innovation rate on the increase in treatment efficacy achieved after a series of two-treatment randomized phase III trials. In a setting where the trials include most of the patients in the target population for inference, as in some paediatric cancers, we show that the traditional criteria by which one determines trial size are difficult to justify and apply. In particular, using as a measure of evidence type I error levels larger than the typical 5 per cent for judging treatment differences, and performing smaller trials than one would usually consider feasible, yields on average, over a 25-year research course, larger gains in cure rate. Judicious choice of type I error rate and trial size keeps the chance of worsening treatment efficacy at a low level, even while increasing the chance of making large improvements in cure rate. We propose that a more appropriate view of trial design in low-incidence cancer settings is in the overall context of the research setting and long-term goals rather than in the narrow context of the current single trial. From this viewpoint, insistence on large trials and stringent evidence for accepting new treatments can be counter-productive, in that likely gains in efficacy of treatment will be smaller over the long term.

From practice to research: the case for criticism in an age of evidence

The growth in research and in health care costs has made it important for clinicians to use and critically appraise published evidence for their medical decisions. The evidence-based medicine movement is an example of the present effort to teach clinicians to evaluate research evidence by methodologic standards. Though this effort can only improve the clinical decisions of practitioners, it suggests that when assessing evidence there are no reasons to critically evaluate the standards of research and evidence themselves. A precedent for assessing standards of research and evidence exists in the broad tradition known as "criticism". Using contextual, cultural and other forms of analysis, writers have used criticism to show that the meaning and validity of scientific evidence is influenced as much by the sociocultural characteristics of readers and users as it is by the meticulous use of research methods. Scholars outside of medicine have suggested, for example, that data become evidence only in the context of specific beliefs and disagreements and that there are interesting pragmatic reasons why we see some forms of evidence and not others in the medical literature. Social critical studies of research and evidence would reveal the many influences similar to these that are relevant to clinical medicine. The effort would be practically useful to physicians, who with a broader understanding of research could critically appraise published evidence from both scientific and sociocultural perspectives. It would also help correct an imbalance in contemporary medicine in which clinicians are being trained to maintain high standards of critical consciousness in methodological domains but not in the broader historical and sociocultural domains which subsume them.

A cost-benefit analysis of a cardiovascular disease prevention trial, using folate supplementation as an example

OBJECTIVES

This study illustrates a cost-benefit analysis of clinical trial design, using as an example a trial of folate supplementation to prevent cardiovascular disease.

METHODS

Bayesian statistical and decision-analytic techniques were used to estimate the cost-benefit and sample size of a placebo-controlled trial of folate targeted to US citizens, aged 35 to 84 years, with elevated serum homocysteine levels. The main end point is event-free survival (i.e., survival without new ischemic heart disease or stroke) at 5 years.

RESULTS

Because the screening cost and annual cost and inconvenience of taking folate is small compared with the consequences of stroke, ischemic heart disease, or death, the increase in 5-year event-free survival with folate that should compel the use of folate is just 1.1%. The sample size per group needed to establish this level of folate's medical effectiveness is estimated to be 17310. Such a trial would provide an expected societal cost-benefit savings exceeding $11 billion within 15 years.

CONCLUSIONS

This study illustrates how Bayesian methods may help in assessing the societal cost-benefit consequences of proposed disease prevention trials, deciding which trials are worth sponsoring, and designing cost-effective trials.

Clinical trials and rare diseases: a way out of a conundrum

Currently, clinical trials tend to be individually funded and applicants must include a power calculation in their grant request. However, conventional levels of statistical precision are unlikely to be obtainable prospectively if the trial is required to evaluate treatment of a rare disease. This means that clinicians treating such diseases remain in ignorance and must form their judgments solely on the basis of (potentially biased) observational studies experience, and anecdote. Since some unbiased evidence is clearly better than none, this state of affairs should not continue. However, conventional (frequentist) confidence limits are unlikely to exclude a null result, even when treatments differ substantially. Bayesian methods utilise all available data to calculate probabilities that may be extrapolated directly to clinical practice. Funding bodies should therefore fund a repertoire of small trials, which need have no predetermined end, alongside standard larger studies.

Prime time for Bayes

This paper reviews what Bayesian statistics is and gives pointers to the literature. The need for a subjectively determined prior distribution, likelihood, and loss function is often taken to be the principal disadvantage of Bayesian statistics. This paper argues that the requirement that these be explicitly stated is a distinct Bayesian advantage. Advances in Bayesian technology make it ready now to be the main inferential tool for clinical trials.

Adaptive assignment versus balanced randomization in clinical trials: a decision analysis

We compare balanced randomization with four adaptive treatment allocation procedures in a clinical trial involving two treatments. The objective is to treat as many patients in and out of the trial as effectively as possible. Randomization is a satisfactory solution to the decision problem when the disease in question is at least moderately common. Adaptive procedures are more difficult to use, but might play a role in clinical research when a substantial proportion of all patients with the disease are included in the trial.