Bayesian design and analysis of active control clinical trials

We consider the design and analysis of active control clinical trials, i.e., clinical trials comparing an experimental treatment E to a control treatment C considered to be effective. Direct comparison of E to placebo P, or no treatment, is sometimes ethically unacceptable. Much discussion of the design and analysis of such clinical trials has focused on whether the comparison of E to C should be based on a test of the null hypothesis of equivalence, on a test of a nonnull hypothesis that the difference is of some minimally medically important size delta, or on one or two-sided confidence intervals. These approaches are essentially the same for study planning. They all suffer from arbitrariness in specifying the size of the difference delta that must be excluded. We propose an alternative Bayesian approach to the design and analysis of active control trials. We derive the posterior probability that E is superior to P or that E is at least k% as good as C and that C is more effective than P. We also derive approximations for use with logistic and proportional hazard models. Selection of prior distributions is discussed, and results are illustrated using data from an active control trial of a drug for the treatment of unstable angina.     

A Bayesian A-optimal and model robust design criterion

Summary . Suppose that the true model underlying a set of data is one of a finite set of candidate models, and that parameter estimation for this model is of primary interest. With this goal, optimal design must depend on a loss function across all possible models. A common method that accounts for model uncertainty is to average the loss over all models; this is the basis of what is known as Läuter's criterion. We generalize Läuter's criterion and show that it can be placed in a Bayesian decision theoretic framework, by extending the definition of Bayesian A‐optimality. We use this generalized A‐optimality to find optimal design points in an environmental safety setting. In estimating the smallest detectable trace limit in a water contamination problem, we obtain optimal designs that are quite different from those suggested by standard A‐optimality.     

Bayesian adaptive trial design for a newly validated surrogate endpoint

The evaluation of surrogate endpoints for primary use in future clinical trials is an increasingly important research area, due to demands for more efficient trials coupled with recent regulatory acceptance of some surrogates as 'valid.' However, little consideration has been given to how a trial that utilizes a newly validated surrogate endpoint as its primary endpoint might be appropriately designed. We propose a novel Bayesian adaptive trial design that allows the new surrogate endpoint to play a dominant role in assessing the effect of an intervention, while remaining realistically cautious about its use. By incorporating multitrial historical information on the validated relationship between the surrogate and clinical endpoints, then subsequently evaluating accumulating data against this relationship as the new trial progresses, we adaptively guard against an erroneous assessment of treatment based upon a truly invalid surrogate. When the joint outcomes in the new trial seem plausible given similar historical trials, we proceed with the surrogate endpoint as the primary endpoint, and do so adaptively-perhaps stopping the trial for early success or inferiority of the experimental treatment, or for futility. Otherwise, we discard the surrogate and switch adaptive determinations to the original primary endpoint. We use simulation to test the operating characteristics of this new design compared to a standard O'Brien-Fleming approach, as well as the ability of our design to discriminate trustworthy from untrustworthy surrogates in hypothetical future trials. Furthermore, we investigate possible benefits using patient-level data from 18 adjuvant therapy trials in colon cancer, where disease-free survival is considered a newly validated surrogate endpoint for overall survival.     

A Bayesian decision approach for sample size determination in phase II trials

Stallard (1998, Biometrics 54, 279-294) recently used Bayesian decision theory for sample-size determination in phase II trials. His design maximizes the expected financial gains in the development of a new treatment. However, it results in a very high probability (0.65) of recommending an ineffective treatment for phase III testing. On the other hand, the expected gain using his design is more than 10 times that of a design that tightly controls the false positive error (Thall and Simon, 1994, Biometrics 50, 337-349). Stallard's design maximizes the expected gain per phase II trial, but it does not maximize the rate of gain or total gain for a fixed length of time because the rate of gain depends on the proportion of treatments forwarding to the phase III study. We suggest maximizing the rate of gain, and the resulting optimal one-stage design becomes twice as efficient as Stallard's one-stage design. Furthermore, the new design has a probability of only 0.12 of passing an ineffective treatment to phase III study.     

Approximate Bayesian evaluation of multiple treatment effects

We propose an approximate Bayesian method for comparing an experimental treatment to a control based on a randomized clinical trial with multivariate patient outcomes. Overall treatment effect is characterized by a vector of parameters corresponding to effects on the individual patient outcomes. We partition the parameter space into four sets where, respectively, the experimental treatment is superior to the control, the control is superior to the experimental, the two treatments are equivalent, and the treatment effects are discordant. We compute posterior probabilities of the parameter sets by treating an estimator of the parameter vector like a random variable in the Bayesian paradigm. The approximation may be used in any setting where a consistent, asymptotically normal estimator of the parameter vector is available. The method is illustrated by application to a breast cancer data set consisting of multiple time-to-event outcomes with covariates and to count data arising from a cross-classification of response, infection, and treatment in an acute leukemia trial.     

Elicitation of a beta prior for Bayesian inference in clinical trials

When making Bayesian inferences we need to elicit an expert's opinion to set up the prior distribution. For applications in clinical trials, we study this problem with binary variables. A critical and often ignored issue in the process of eliciting priors in clinical trials is that medical investigators can seldom specify the prior quantities with precision. In this paper, we discuss several methods of eliciting beta priors from clinical information, and we use simulations to conduct sensitivity analyses of the effect of imprecise assessment of the prior information. These results provide useful guidance for choosing methods of eliciting the prior information in practice.     

A geometric approach to comparing treatments for rapidly fatal diseases

In therapy of rapidly fatal diseases, early treatment efficacy often is characterized by an event, "response," which is observed relatively quickly. Since the risk of death decreases at the time of response, it is desirable not only to achieve a response, but to do so as rapidly as possible. We propose a Bayesian method for comparing treatments in this setting based on a competing risks model for response and death without response. Treatment effect is characterized by a two-dimensional parameter consisting of the probability of response within a specified time and the mean time to response. Several target parameter pairs are elicited from the physician so that, for a reference covariate vector, all elicited pairs embody the same improvement in treatment efficacy compared to a fixed standard. A curve is fit to the elicited pairs and used to determine a two-dimensional parameter set in which a new treatment is considered superior to the standard. Posterior probabilities of this set are used to construct rules for the treatment comparison and safety monitoring. The method is illustrated by a randomized trial comparing two cord blood transplantation methods.     

Blinded and unblinded internal pilot study designs for clinical trials with count data

Internal pilot studies are a popular design feature to address uncertainties in the sample size calculations caused by vague information on nuisance parameters. Despite their popularity, only very recently blinded sample size reestimation procedures for trials with count data were proposed and their properties systematically investigated. Although blinded procedures are favored by regulatory authorities, practical application is somewhat limited by fears that blinded procedures are prone to bias if the treatment effect was misspecified in the planning. Here, we compare unblinded and blinded procedures with respect to bias, error rates, and sample size distribution. We find that both procedures maintain the desired power and that the unblinded procedure is slightly liberal whereas the actual significance level of the blinded procedure is close to the nominal level. Furthermore, we show that in situations where uncertainty about the assumed treatment effect exists, the blinded estimator of the control event rate is biased in contrast to the unblinded estimator, which results in differences in mean sample sizes in favor of the unblinded procedure. However, these differences are rather small compared to the deviations of the mean sample sizes from the sample size required to detect the true, but unknown effect. We demonstrate that the variation of the sample size resulting from the blinded procedure is in many practically relevant situations considerably smaller than the one of the unblinded procedures. The methods are extended to overdispersed counts using a quasi‐likelihood approach and are illustrated by trials in relapsing multiple sclerosis.     

A Bayesian platform trial design to simultaneously evaluate multiple drugs in multiple indications with mixed endpoints

In the era of targeted therapies and immunotherapies, the traditional drug development paradigm of testing one drug at a time in one indication has become increasingly inefficient. Motivated by a real-world application, we propose a master-protocol–based Bayesian platform trial design with mixed endpoints (PDME) to simultaneously evaluate multiple drugs in multiple indications, where different subsets of efficacy measures (eg, objective response and landmark progression-free survival) may be used by different indications as single or multiple endpoints. We propose a Bayesian hierarchical model to accommodate mixed endpoints and reflect the trial structure of indications that are nested within treatments. We develop a two-stage approach that first clusters the indications into homogeneous subgroups and then applies the Bayesian hierarchical model to each subgroup to achieve precision information borrowing. Patients are enrolled in a group-sequential way and adaptively assigned to treatments according to their efficacy estimates. At each interim analysis, the posterior probabilities that the treatment effect exceeds prespecified clinically relevant thresholds are used to drop ineffective treatments and “graduate” effective treatments. Simulations show that the PDME design has desirable operating characteristics compared to existing method.     

Source & Sourceability: Towards a probabilistic framework for dendroprovenance based on hypothesis testing and Bayesian inference

Long-distance procurement of timber was necessary for the construction of Ancestral Pueblo Great Houses in Chaco Canyon, New Mexico. A number of higher-altitude tree sources were available within 30–70 km, though some isolated trees may have been acquired more locally. Highly regional tree ring variations enable matching some construction timbers to their source. Here, a method is developed which 1) develops a rejection criteria for ruling out sources for a tree ring sequence, 2) quantifies the relative spatial representation of a given source sequence, and 3) applies Bayes theorem to calculate posterior probabilities of source attribution. The application of this method in part supports past sourcing work, but indicates that the majority (59–64%) of timbers cannot be ascribed with even low confidence to the most common high-altitude sources. This analysis supports a model of diverse tree acquisition from a number of different sources, though with high uncertainty for a majority of timbers used in the present study.     

Comparison of Bayesian and empirical ranking approaches to visual perception

Much current vision research is predicated on the idea--and a rapidly growing body of evidence--that visual percepts are generated according to the empirical significance of light stimuli rather than their physical characteristics. As a result, an increasing number of investigators have asked how visual perception can be rationalized in these terms. Here, we compare two different theoretical frameworks for predicting what observers actually see in response to visual stimuli: Bayesian decision theory and empirical ranking theory. Deciding which of these approaches has greater merit is likely to determine how the statistical operations that apparently underlie visual perception are eventually understood.     

Methods for the statistical analysis of binary data in split-cluster designs

Split-cluster designs are frequently used in the health sciences when naturally occurring clusters such as multiple sites or organs in the same subject are assigned to different treatments. However, statistical methods for the analysis of binary data arising from such designs are not well developed. The purpose of this article is to propose and evaluate a new procedure for testing the equality of event rates in a design dividing each of k clusters into two segments having multiple sites (e.g., teeth, lesions). The test statistic proposed is a generalization of a previously published procedure based on adjusting the standard Pearson chi-square statistic, but can also be derived as a score test using the approach of generalized estimating equations.