A Bayesian group sequential design for a multiple arm randomized clinical trial

Do we need to adjust for interim analyses in a Bayesian adaptive trial design?

Background

Bayesian adaptive methods are increasingly being used to design clinical trials and offer several advantages over traditional approaches. Decisions at analysis points are usually based on the posterior distribution of the treatment effect. However, there is some confusion as to whether control of type I error is required for Bayesian designs as this is a frequentist concept.

Methods

We discuss the arguments for and against adjusting for multiplicities in Bayesian trials with interim analyses. With two case studies we illustrate the effect of including interim analyses on type I/II error rates in Bayesian clinical trials where no adjustments for multiplicities are made. We propose several approaches to control type I error, and also alternative methods for decision-making in Bayesian clinical trials.

Results

In both case studies we demonstrated that the type I error was inflated in the Bayesian adaptive designs through incorporation of interim analyses that allowed early stopping for efficacy and without adjustments to account for multiplicity. Incorporation of early stopping for efficacy also increased the power in some instances. An increase in the number of interim analyses that only allowed early stopping for futility decreased the type I error, but also decreased power. An increase in the number of interim analyses that allowed for either early stopping for efficacy or futility generally increased type I error and decreased power.

Conclusions

Currently, regulators require demonstration of control of type I error for both frequentist and Bayesian adaptive designs, particularly for late-phase trials. To demonstrate control of type I error in Bayesian adaptive designs, adjustments to the stopping boundaries are usually required for designs that allow for early stopping for efficacy as the number of analyses increase. If the designs only allow for early stopping for futility then adjustments to the stopping boundaries are not needed to control type I error. If one instead uses a strict Bayesian approach, which is currently more accepted in the design and analysis of exploratory trials, then type I errors could be ignored and the designs could instead focus on the posterior probabilities of treatment effects of clinically-relevant values.

Rare ovarian tumours: Epidemiology, treatment challenges in and outside a network setting

PURPOSE OF THE REVIEW

More than 50% of all gynaecological cancers can be classified as rare tumours (defined as an annual incidence of <6 per 100,000) and such tumours represent an important challenge for clinicians.

RECENT FINDINGS

Rare cancers account for more than one fifth of all new cancer diagnoses, more than any of the single common cancers alone. Reviewing the RARECAREnet database, some of the tumours occur infrequently, whilst others because of their natural history have a high prevalence, and therefore appear to be more common, although their incidence is also rare. Harmonization of medical practice, guidelines and novel trials are needed to identify rare tumours and facilitate the development of new treatments. Ovarian tumours are the focus of this review, but we comment on other rare gynaecological tumours, as the diagnosis and treatment challenges faced are similar.

FUTURE

This requires European collaboration, international partnerships, harmonization of treatment and collaboration to overcome the regulatory barriers to conduct international trials. Whilst randomized trials can be done in many tumour types, there are some for which conducting even single arm studies may be challenging. For these tumours alternative study designs, robust collection of data through national registries and audits could lead to improvements in the treatment of rare tumours. In addition, concentring the care of patients with rare tumours into a limited number of centres will help to build expertise, facilitate trials and improve outcomes.

Novel approaches to improve the treatment of rare gynecologic cancers: research opportunities and challenges

More than 50% of all gynecologic cancers can be classified as rare tumors (defined as an incidence of fewer than six per 100,000). Improved understanding of the molecular pathogenesis of tumors increases the proportion of rare tumors and creates challenges in optimizing the design of clinical trials. Novel trial designs are needed to take forward the development of new treatments in rare tumors. This requires international partnerships, harmonization of treatment, and collaboration to overcome the regulatory barriers to conducting international trials. Although randomized trials can be done in many tumor types, there are some for which conducting even single-arm studies may be challenging. For these tumors, robust collection of data through national and/or international registries could lead through audit to improvements in the treatment of rare tumors.

Bayesian sequential meta-analysis design in evaluating cardiovascular risk in a new antidiabetic drug development program

Recently, the Center for Drug Evaluation and Research at the Food and Drug Administration released a guidance that makes recommendations about how to demonstrate that a new antidiabetic therapy to treat type 2 diabetes is not associated with an unacceptable increase in cardiovascular risk. One of the recommendations from the guidance is that phases II and III trials should be appropriately designed and conducted so that a meta-analysis can be performed. In addition, the guidance implies that a sequential meta-analysis strategy could be adopted. That is, the initial meta-analysis could aim at demonstrating the upper bound of a 95% confidence interval (CI) for the estimated hazard ratio to be < 1.8 for the purpose of enabling a new drug application or a biologics license application. Subsequently after the marketing authorization, a final meta-analysis would need to show the upper bound to be < 1.3. In this context, we develop a new Bayesian sequential meta-analysis approach using survival regression models to assess whether the size of a clinical development program is adequate to evaluate a particular safety endpoint. We propose a Bayesian sample size determination methodology for sequential meta-analysis clinical trial design with a focus on controlling the familywise type I error rate and power. We use the partial borrowing power prior to incorporate the historical survival meta-data into the Bayesian design. We examine various properties of the proposed methodology, and simulation-based computational algorithms are developed to generate predictive data at various interim analyses, sample from the posterior distributions, and compute various quantities such as the power and the type I error in the Bayesian sequential meta-analysis trial design. We apply the proposed methodology to the design of a hypothetical antidiabetic drug development program for evaluating cardiovascular risk.

Phase II trial design with Bayesian adaptive randomization and predictive probability

We propose a randomized phase II clinical trial design based on Bayesian adaptive randomization and predictive probability monitoring. Adaptive randomization assigns more patients to a more efficacious treatment arm by comparing the posterior probabilities of efficacy between different arms. We continuously monitor the trial by using the predictive probability. The trial is terminated early when it is shown that one treatment is overwhelmingly superior to others or that all the treatments are equivalent. We develop two methods to compute the predictive probability by considering the uncertainty of the sample size of the future data. We illustrate the proposed Bayesian adaptive randomization and predictive probability design by using a phase II lung cancer clinical trial, and we conduct extensive simulation studies to examine the operating characteristics of the design. By coupling adaptive randomization and predictive probability approaches, the trial can treat more patients with a more efficacious treatment and allow for early stopping whenever sufficient information is obtained to conclude treatment superiority or equivalence. The design proposed also controls both the type I and the type II errors and offers an alternative Bayesian approach to the frequentist group sequential design.

Using short-term response information to facilitate adaptive randomization for survival clinical trials

Increased survival is a common goal of cancer clinical trials. Owing to the long periods of observation and follow-up to assess patient survival outcome, it is difficult to use outcome-adaptive randomization in these trials. In practice, often information about a short-term response is quickly available during or shortly after treatment, and this short-term response is a good predictor for long-term survival. For example, complete remission of leukemia can be achieved and measured after a few cycles of treatment. It is a short-term response that is desirable for prolonging survival. We propose a new design for survival trials when such short-term response information is available. We use the short-term information to 'speed up' the adaptation of the randomization procedure. We establish a connection between the short-term response and the long-term survival through a Bayesian model, first by using prior clinical information, and then by dynamically updating the model according to information accumulated in the ongoing trial. Interim monitoring and final decision making are based upon inference on the primary outcome of survival. The new design uses fewer patients, and can more effectively assign patients to the better treatment arms. We demonstrate these properties through simulation studies.

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.

Sequential methods and group sequential designs for comparative clinical trials

Comparative clinical trials are performed to assess whether a new treatment has superior efficacy than a placebo or a standard treatment (one-sided formulation) or whether two active treatments have different efficacies (two-sided formulation) in a given population. The reference approach is the single-stage design and the statistical test is performed after inclusion and evaluation of a predetermined sample size. In practice, the single-stage design is sometimes difficult to implement because of ethical concerns and/or economic reasons. Thus, specific early termination procedures have been developed to allow repeated statistical analyses to be performed on accumulating data and stop the trial as soon as the information is sufficient to conclude. Two main different approaches can be used. The first one is derived from strictly sequential methods and includes the sequential probability ratio test and the triangular test. The second one is derived from group sequential designs and includes Peto, Pocock, and O'Brien and Fleming methods, alpha and beta spending functions, and one-parameter boundaries. We review all these methods and describe the bases on which they rely as well as their statistical properties. We also compare these methods and comment on their advantages and drawbacks. We present software packages which are available for the planning, monitoring and analysis of comparative clinical trials with these methods and discuss the practical problems encountered when using them. The latest versions of all these methods can offer substantial sample size reductions when compared with the single-stage design not only in the case of clear efficacy but also in the case of complete lack of efficacy of the new treatment. The software packages make their use quite simple. However, it has to be stressed that using these methods requires efficient logistics with real-time data monitoring and, apart from survival studies or long-term clinical trials with censored endpoints, is most appropriate when the endpoint is obtained quickly when compared with the recruitment rate.

Decision theoretic designs for phase II clinical trials with multiple outcomes

In many phase II clinical trials, it is essential to assess both efficacy and safety. Although several phase II designs that accommodate multiple outcomes have been proposed recently, none are derived using decision theory. This paper describes a Bayesian decision theoretic strategy for constructing phase II designs based on both efficacy and adverse events. The gain function includes utilities assigned to patient outcomes, a reward for declaring the new treatment promising, and costs associated with the conduct of the phase II trial and future phase III testing. A method for eliciting gain function parameters from medical collaborators and for evaluating the design's frequentist operating characteristics is described. The strategy is illustrated by application to a clinical trial of peripheral blood stem cell transplantation for multiple myeloma.