Bayesian sample size determination using commensurate priors to leverage preexperimental data.

This paper develops Bayesian sample size formulae for experiments comparing two groups, where relevant preexperimental information from multiple sources can be incorporated in a robust prior to support both the design and analysis. We use commensurate predictive priors for borrowing of information and further place Gamma mixture priors on the precisions to account for preliminary belief about the pairwise (in)commensurability between parameters that underpin the historical and new experiments. Averaged over the probability space of the new experimental data, appropriate sample sizes are found according to criteria that control certain aspects of the posterior distribution, such as the coverage probability or length of a defined density region. Our Bayesian methodology can be applied to circumstances that compare two normal means, proportions, or event times. When nuisance parameters (such as variance) in the new experiment are unknown, a prior distribution can further be specified based on preexperimental data. Exact solutions are available based on most of the criteria considered for Bayesian sample size determination, while a search procedure is described in cases for which there are no closed-form expressions. We illustrate the application of our sample size formulae in the design of clinical trials, where pretrial information is available to be leveraged. Hypothetical data examples, motivated by a rare-disease trial with an elicited expert prior opinion, and a comprehensive performance evaluation of the proposed methodology are presented.

Bayesian sample size determination using commensurate priors to leverage pre-experimental data.

This paper develops Bayesian sample size formulae for experiments comparing two groups, where relevant pre-experimental information from multiple sources can be incorporated in a robust prior to support both the design and analysis. We use commensurate predictive priors for borrowing of information, and further place Gamma mixture priors on the precisions to account for preliminary belief about the pairwise (in)commensurability between parameters that underpin the historical and new experiments. Averaged over the probability space of the new experimental data, appropriate sample sizes are found according to criteria that control certain aspects of the posterior distribution, such as the coverage probability or length of a defined density region. Our Bayesian methodology can be applied to circumstances that compare two normal means, proportions or event times. When nuisance parameters (such as variance) in the new experiment are unknown, a prior distribution can further be specified based on pre-experimental data. Exact solutions are available based on most of the criteria considered for Bayesian sample size determination, while a search procedure is described in cases for which there are no closed-form expressions. We illustrate the application of our sample size formulae in the design of clinical trials, where pre-trial information is available to be leveraged. Hypothetical data examples, motivated by a rare-disease trial with elicited expert prior opinion, and a comprehensive performance evaluation of the proposed methodology are presented.

Comparison of chronic kidney disease trial designs and analysis strategies.

BACKGROUND: Despite the large burden of chronic kidney disease (CKD), it is challenging to conduct adequately powered clinical trials in this setting. Sound and efficient trials are needed to advance treatment. Various analysis strategies can be used to compare the efficacy of a parallel trial design with that of three two period trial designs. METHODS: The type 1 error rates and powers of various trial designs were calculated using simulated data from models fit to two recent CKD trials. In addition, we assessed the influences of a variety of analysis strategies and of the presence of a carryover effect. RESULTS: The parallel and crossover designs (with analysis of change from baseline to the off treatment value) maintained the target type 1 error rate in all scenarios. In some scenarios, an open label design yielded inflated type 1 error rates. In many scenarios, the open label and delayed start designs had unacceptably low power and high type 1 error rates. Overall, the crossover design had the highest power by far, and always controlled the type 1 error rate. CONCLUSION: The recommended approach to a CKD trial is a two period design with an endpoint that is the rate of change in estimated glomerular filtration rate from pretreatment to off treatment. As compared to a parallel trial, a crossover study involves a considerably smaller sample size and shorter total follow-up duration. A crossover design may also be preferable for patients, and facilitates recruitment of a sufficient number of subjects.

Response-adaptive trial designs with accelerated Thompson sampling.

In a clinical trial, sometimes it is desirable to allocate as many patients as possible to the best treatment, in particular, when a trial for a rare disease may contain a considerable portion of the whole target population. The Gittins index rule is a powerful tool for sequentially allocating patients to the best treatment based on the responses of patients already treated. However, its application in clinical trials is limited due to technical complexity and lack of randomness. Thompson sampling is an appealing approach, since it makes a compromise between optimal treatment allocation and randomness with some desirable optimal properties in the machine learning context. However, in clinical trial settings, multiple simulation studies have shown disappointing results with Thompson samplers. We consider how to improve short-run performance of Thompson sampling and propose a novel acceleration approach. This approach can also be applied to situations when patients can only be allocated by batch and is very easy to implement without using complex algorithms. A simulation study showed that this approach could improve the performance of Thompson sampling in terms of average total response rate. An application to a redesign of a preference trial to maximize patient's satisfaction is also presented.

Methodology of clinical trials for rare diseases.

Evidence from clinical trials, ideally using randomisation and allocation concealment, is essential for informing clinical decisions regarding the benefits and harms of treatments for patients. Where diseases are rare, such as in paediatric rheumatic diseases, patient recruitment into clinical trials can be a major obstacle, leading to an absence of evidence and patients receiving treatments based on anecdotal evidence. There are numerous trial designs and modifications that can be made to improve efficiency and maximise what little data may be available in a rare disease clinical trial. These are discussed and illustrated with examples from paediatric rheumatology. Regulatory incentives and support from research networks have helped to deliver these trials, but more can be done to continue this important research.