Reporting Bayesian analyses of clinical trials

Many clinicians wrongly interpret p-values as probabilities that treatment has an adverse effect and confidence intervals as probability intervals. Such inferences can be validly drawn from Bayesian analyses of trial results. These analyses use the data to update the prior (or pre-trial) beliefs to give posterior (or post-trial) beliefs about the magnitude of a treatment effect. However, for these methods to gain acceptance in the medical literature, understanding between statisticians and clinicians of the issues involved in choosing appropriate prior distributions for trial reporting needs to be reached. I focus on two types of prior that deserve consideration. The first is the non-informative prior giving standardized likelihood distributions as post-trial probability distributions. Their use is unlikely to be controversial among statisticians whilst being intuitively appealing to clinicians. The second type of prior has a spike of probability mass at the point of no treatment effect. Varying the magnitude of the spike illustrates the sensitivity of the conclusions drawn to the degree of prior scepticism in a treatment effect. With both, graphical displays provide clinical readers with the opportunity to explore the results more fully. An example of how a clinical trial might be reported in the medical literature using these methods is given.     

Practical Bayesian guidelines for phase IIB clinical trials

A Phase IIB clinical trial typically is a single-arm study aimed at deciding whether a new treatment E is sufficiently promising, relative to a standard therapy, S, to include in a large-scale randomized trial. Thus, Phase IIB trials are inherently comparative even though a standard therapy arm usually is not included. Uncertainty regarding the response rate theta s of S is rarely made explicit, either in planning the trial or interpreting its results. We propose practical Bayesian guidelines for deciding whether E is promising relative to S in settings where patient response is binary and the data are monitored continuously. The design requires specification of an informative prior for theta s, a targeted improvement for E, and bounds on the allowed sample size. No explicit specification of a loss function is required. Sampling continues until E is shown to be either promising or not promising relative to S with high posterior probability, or the maximum sample size is reached. The design provides decision boundaries, a probability distribution for the sample size at termination, and operating characteristics under fixed response probabilities with E.     

Some comments on frequently used multiple endpoint adjustment methods in clinical trials

Confirmatory clinical trials often classify clinical response variables into primary and secondary endpoints. The presence of two or more primary endpoints in a clinical trial usually means that some adjustments of the observed p-values for multiplicity of tests may be required for the control of the type I error rate. In this paper, we discuss statistical concerns associated with some commonly used multiple endpoint adjustment procedures. We also present limited Monte Carlo simulation results to demonstrate the performance of selected p-value-based methods in protecting the type I error rate.     

Evoked potentials in clinical trials for multiple sclerosis

BACKGROUND: Idiopathic restrictive cardiomyopathy is a rare disease characterized by diastolic dysfunction, and the pathogenesis of the stiff heart remains unclear. The purpose of this study was to analyze the subpopulation of collagen fibers and determine the expression of matrix metalloproteinase in restrictive cardiomyopathy. METHODS AND RESULTS: In endomyocardial biopsy specimens obtained from seven patients with restrictive cardiomyopathy, collagen fiber types I, III, and IV, and matrix metalloproteinase- and two were observed by light and electron microscopy, using monoclonal antibodies. Type I collagen was less prominent in the interstitium, whereas the immunoreactivity for type III collagen was marked. The immunoreactivity against matrix metalloproteinase-1 was observed along with types I and III collagen fibers and in the cytoplasm of some fibrocytes/fibroblasts. The matrix metalloproteinase-1 tended to increase when the reactivity against types I and III collagen was prominent. Both type IV collagen and matrix metalloproteinase-2 were observed along arterial walls and the basement membrane of cardiocytes. CONCLUSIONS: Increased type III collagen may play an important role as the cause of left ventricular stiffness in restrictive cardiomyopathy. The matrix metalloproteinase appeared to be involved in a cascade of collagen synthesis and the remodeling of the heart in patients with restrictive cardiomyopathy.     

Issues in extrapolating from clinical trials to clinical practice and outcomes

Extrapolation of clinical trial results to clinical practice requires consideration of whether the trial patients were representative of clinical practice, whether the trial therapy studied was optimal, whether the sample size was adequate, and the impact of adjunctive treatments. In thrombolytic trials in particular, regional variations in attitudes to coronary angiography may have affected outcomes. Clinical trial results need to be interpreted in the light of the cost effectiveness of the application. The assessment of clinical outcomes depends on interplay between the structure and process of care, patient factors and chance. Large standardised databases are necessary to assess clinical practice and outcomes.     

A multiple decision procedure in clinical trials

In some multiple treatment arm clinical trials there is an order of preference for the treatments based on secondary considerations like toxicity or cost. In this paper, we consider the case where two or more treatments could have equal prior preference. This formulation includes the problem of comparing several equally preferred experimental treatments to one control, or the comparison of a combination with its components. Our decision procedures will guarantee a high selection probability for the correct treatment(s) when that selection is appropriate. We establish sample size requirements for our decision procedures which can be applied to clinical trials with normal, binomial, or right censored exponential endpoints.     

Bayesian interim analysis of phase II cancer clinical trials

Many popular sequential phase II clinical trial designs optimize some criterion subject to constraints on the error probabilities at null and alternative values of the response rate. Such designs may forfeit optimality if one fails to conduct analyses strictly according to plan. Moreover, a decision, say, to accept the experimental therapy at one interim analysis does not necessarily imply the same degree of evidence as the same decision when made at another analysis. I propose an alternative design that bases decisions on the ability of the data to persuade either a sceptic or an enthusiast. My standard of evidence, called the persuasion probability, is based on the Bayesian posterior probability that the experimental treatment is superior to the standard. The design calls for termination at any interim analysis at which an observed persuasion probability exceeds its critical value. I investigate the standards of evidence implied by some frequentist procedures and calculate frequentist properties of persuasion-probability designs.     

Statistical applications for in vitro diagnostic tests and other medical device clinical trials

Some statistical methods applied to in vitro diagnostic tests for the three primary indications (screening, diagnosis, and monitoring) are discussed. Various examples with practical statistical applications are presented, including test for k by k ordered categorical matched-pair data for screening of cervical cancer, receiver operating characteristic (ROC) curve for diagnosis or screening, and the Cox time-to-event model to estimate relative risk of first cancer progression by monitoring carcinoembryonic (CEA) levels for stage IV breast cancer patients.     

Decision analysis: theory and methods in clinical development and monitoring of clinical trials

Decision analysis has been widely used in business, first in operational research, later in economic studies. It is now spreading to medical training. We review methodology of decision analysis which is simple, rational and based on the environmental conditions. When clinical judgments are uncertain, the most appropriate strategy is helped by the use of standard/bayesian probabilities quantifying the risks of each strategy, and the design of decision trees visualizing each outcome. If the probabilities are not suitable, other mathematical concepts such as Markov process are interesting but are still being worked on. Multicriteria analysis, a branch of graph theory, is also a flexible and reliable tool allowing differentiation and ordering strategies. It also takes into account the psychological characteristic of the decision makers. We then illustrate decision analysis by describing computerized systems for monitoring clinical trials, fitted to control the trial data able to estimate the different strategies.     

Early stopping of prevention trials when multiple outcomes are of interest: a discussion

In large prevention and screening trials, we want to answer multiple questions simultaneously. When monitoring prevention trials with multiple disease outcomes, composite measures may be useful, such as a count of important events, or a comparison of expected mortality. There are advantages to investigating multiple interventions in the same prevention or screening trial, using all-versus-none, factorial, or reciprocal control designs. In these situations it may be important to answer some questions early while others are still being investigated.     

Sample size determination for phase II clinical trials based on Bayesian decision theory

This paper describes an application of Bayesian decision theory to the determination of sample size for phase II clinical studies. The approach uses the method of backward induction to obtain group sequential designs that are optimal with respect to some specified gain function. A gain function is proposed focussing on the financial costs of, and potential profits from, the drug development programme. On the basis of this gain function, the optimal procedure is also compared with an alternative Bayesian procedure proposed by Thall and Simon. The latter method, which tightly controls type I error rate, is shown to lead to an expected gain considerably smaller than that from the optimal test. Gain functions with respect to which Thall and Simon's boundary is optimal are sought and it is shown that these can only be of the form considered, that is, with constant cost for phase III study and cost of the phase II study proportional to the sample size, if potential profit increases over time.     

An overview of statistical methods for multiple failure time data in clinical trials

In a long term clinical trial to evaluate a new treatment, quite often each study subject may experience a number of 'failures' that correspond to repeated occurrences of the same type of event or events of entirely different natures during his/her follow-up period. To obtain efficient inference procedures for the therapeutic effect over time, it is desirable to utilize those multiple event times in the analysis. In this article, we review some useful procedures for analysing different kinds of multivariate failure time data. Specifically, we discuss the two-sample problems and the general regression problems with various survival models. We also give some recommendations of appropriate procedures for each type of multiple event data structure for practical usage.     

Clinical trials with multiple outcomes: a statistical perspective on their design, analysis, and interpretation

This article tackles both practical and statistical issues in the handling of multiple outcomes in clinical trials, with relevance to trial design, analysis, and reporting. Specific topics illustrated by examples include: the advantage of prespecifying priorities amongst outcomes and analyses, corrections for multiple significance testing and their limited value, problems with adverse event data, the use of a single global test of significance for clinically related outcomes, the use of a combined outcome for clinical event data, and the value of exploring interrelationships amongst outcomes. The problems in handling multiple outcomes are enhanced by trials being too small, dichotomous attitudes (is the trial "positive" or not?), obsession with p-values, and the manipulative instincts of human nature. While predeclarations of priorities in analysis and reporting of multiple outcomes are important in suppressing distortive claims, it would be unfortunate if too inflexible an approach suppressed unpredictable findings from being seriously considered.     

Interferon beta treatment in multiple sclerosis: the European clinical trials

Studies have demonstrated the failure of gut barrier function in all cases of experimental acute diffuse peritonitis. Histobacterioscopy and electron microscopy showed the occurrence of bacteria under the basal membrane, in lymphatic and blood capillaries of the small intestinal villi. Experimental and clinical trials with blood sampling from different regions of the circulation have demonstrated the gut origin polymicrobial bacteremia in 66% of patients and in 75% of experimental animals with acute diffuse peritonitis.     

Testing simultaneous hypotheses in pharmaceutical trials: a Bayesian approach

The purpose of this paper is to compare the Bayes factor and the likelihood ratio test in a pharmaceutical trial where the two treatments are a new drug and a control (a positive control or a placebo). The goal is to jointly answer the questions (1) is the new drug or the control toxic? (2) Is the new drug more effective and safer than the control? We consider a bivariate model where each treatment is characterized by a target effect (a continuous primary response y) and by a side effect (a continuous supplementary response xi). Using a Bayesian approach, we account for the uncertainty resulting from prediction of the side effect, by making use of the physician's prior inputs about the target-toxicity relationship and the maximum tolerated target effects that are considered to be safe. Finally, we consider an example about a sleeplessness drug, and we show that the Bayes factor provides a more flexible and informative tool than the likelihood ratio test in simultaneous testing. Advantages are greater when the number of experimental subjects is small.     

A strategy to use soft data effectively in randomized controlled clinical trials.

Soft data are defined as measures having substantial intrasubject variability due to errors of measurement or to the inconsistency of subjects' responses. Such data are often important measures of response in randomized clinical trials. In this context, we show that using an intensive design and the slope of response on time as the outcome measure (a) maximizes sample retention and (b) decreases within-group variability, thus (c) maximizing the power of test procedures without requiring increased sample sizes. (PsycINFO Database Record (c) 2010 APA, all rights reserved)