Bayesian sample size determination in basket trials borrowing information between subsets.

Basket trials are increasingly used for the simultaneous evaluation of a new treatment in various patient subgroups under one overarching protocol. We propose a Bayesian approach to sample size determination in basket trials that permit borrowing of information between commensurate subsets. Specifically, we consider a randomized basket trial design where patients are randomly assigned to the new treatment or control within each trial subset ("subtrial" for short). Closed-form sample size formulae are derived to ensure that each subtrial has a specified chance of correctly deciding whether the new treatment is superior to or not better than the control by some clinically relevant difference. Given prespecified levels of pairwise (in)commensurability, the subtrial sample sizes are solved simultaneously. The proposed Bayesian approach resembles the frequentist formulation of the problem in yielding comparable sample sizes for circumstances of no borrowing. When borrowing is enabled between commensurate subtrials, a considerably smaller trial sample size is required compared to the widely implemented approach of no borrowing. We illustrate the use of our sample size formulae with two examples based on real basket trials. A comprehensive simulation study further shows that the proposed methodology can maintain the true positive and false positive rates at desired levels.

Bayesian design of clinical trials using the scale transformed power prior.

There are many Bayesian design methods allowing for the incorporation of historical data for sample size determination (SSD) in situations where the outcome in the historical data is the same as the outcome of a new study. However, there is a dearth of methods supporting the incorporation of data from a previously completed clinical trial that investigated the same or similar treatment as the new trial but had a primary outcome that is different. We propose a simulation-based Bayesian SSD framework using the partial-borrowing scale transformed power prior (straPP). The partial-borrowing straPP is developed by applying a novel scale transformation to a traditional power prior on the parameters from the historical data model to make the information better align with the new data model. The scale transformation is based on the assumption that the standardized parameters (i.e., parameters multiplied by the square roots of their respective Fisher information matrices) are equal. To illustrate the method, we present results from simulation studies that use real data from a previously completed clinical trial to design a new clinical trial with a primary time-to-event endpoint.

Bayesian sample size determination for a Phase III clinical trial with diluted treatment effect.

When Phase III treatment effect is diluted from what was observed from Phase II results, we propose to determine the Bayesian sample size for a Phase III clinical trial based on the normal, uniform, and truncated normal prior distributions of the treatment effects on an interval, which starts from an acceptable treatment effect to the observed treatment effect from Phase II. After incorporating the prior information of the treatment effects, the Bayesian sample size is the number of patients of the Phase III trial for a given Bayesian Predictive Power (BPP) or Bayesian Historical Predictive Power (BHPP). After that, the numerical simulations are carried out to determine the Bayesian sample size for the Phase III clinical trial. In particular, there exists a hook phenomenon for the BHPP when the number of patients of the Phase II trial equals 70 assuming the normal, uniform, or truncated normal treatment effect. Moreover, we add some sensitivity analysis of the Bayesian sample size about the parameters in the simulations. Finally, we determine the Bayesian sample size (number of events or deaths) of the Phase III trial for a fixed power, Bayesian Historical Power (BHP), and BHPP in the axitinib example.