A behavioural Bayes approach to the determination of sample size for clinical trials considering efficacy and safety: imbalanced sample size in treatment groups

Unequal allocation of sample/event sizes with considerations of sampling cost for testing equality, non-inferiority/superiority, and equivalence of two Poisson rates

For non-inferiority/superiority and equivalence tests of two Poisson rates, the determination of the required number of sample sizes has been studied but the studies for the number of events to be observed are very limited. To fill the gap, the present study first is aimed toward determining the number of events to be observed for testing non-inferiority/superiority and equivalence of two Poisson rates, respectively. Also, considering the cost for each event, the second purpose is to apply an exhaustive search to find the unequal but optimal allocation of events for each group such that the budget is minimal for a user-specified power level, or the statistical power is maximal for a user-specified budget. Four R Shiny apps were developed to obtain the number of events needed for each group. A simulation study showed the proposed approach to be valid in terms of Type I error and statistical power. A comparison of the proposed approach with extant methods from various disciplines was performed, and an illustrative example of comparing the adverse reactions to the COVID-19 vaccines was demonstrated. By applying the proposed approach, researchers also can estimate the most economical number of subjects or time intervals after determining the number of events.

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.

Decision-theoretic designs for small trials and pilot studies: A review

Pilot studies and other small clinical trials are often conducted but serve a variety of purposes and there is little consensus on their design. One paradigm that has been suggested for the design of such studies is Bayesian decision theory. In this article, we review the literature with the aim of summarizing current methodological developments in this area. We find that decision-theoretic methods have been applied to the design of small clinical trials in a number of areas. We divide our discussion of published methods into those for trials conducted in a single stage, those for multi-stage trials in which decisions are made through the course of the trial at a number of interim analyses, and those that attempt to design a series of clinical trials or a drug development programme. In all three cases, a number of methods have been proposed, depending on the decision maker’s perspective being considered and the details of utility functions that are used to construct the optimal design.

Value of information and pricing new healthcare interventions

Previous application of value-of-information methods to optimal clinical trial design have predominantly taken a societal decision-making perspective, implicitly assuming that healthcare costs are covered through public expenditure and trial research is funded by government or donation-based philanthropic agencies. In this paper, we consider the interaction between interrelated perspectives of a societal decision maker (e.g. the National Institute for Health and Clinical Excellence [NICE] in the UK) charged with the responsibility for approving new health interventions for reimbursement and the company that holds the patent for a new intervention. We establish optimal decision making from societal and company perspectives, allowing for trade-offs between the value and cost of research and the price of the new intervention. Given the current level of evidence, there exists a maximum (threshold) price acceptable to the decision maker. Submission for approval with prices above this threshold will be refused. Given the current level of evidence and the decision maker's threshold price, there exists a minimum (threshold) price acceptable to the company. If the decision maker's threshold price exceeds the company's, then current evidence is sufficient since any price between the thresholds is acceptable to both. On the other hand, if the decision maker's threshold price is lower than the company's, then no price is acceptable to both and the company's optimal strategy is to commission additional research. The methods are illustrated using a recent example from the literature.