Bayesian methods for the design and interpretation of clinical trials in very rare diseases.
Bottom Line: For such studies, the sample size needed to meet a conventional frequentist power requirement is clearly infeasible.A systematic elicitation from clinicians of their beliefs concerning treatment efficacy is used to establish Bayesian priors for unknown model parameters.As sample sizes are small, it is possible to compute all possible posterior distributions of the two success rates.
Affiliation: Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K.Show MeSH
Related in: MedlinePlus
Mentions: The frequentist type I error rate does not take into account the prior probability that treatment E is inferior to C. Returning to our Bayesian model, suppose treatment E will be recommended as non-inferior to C if Π > 0.8 with ξ = 0.1. Given this decision criterion and a sample size of n = 40, we seek the E:C allocation ratio that balances the twin objectives of attaining a high Bayesian prior power and a low value of Γ*. Figure 5 compares a range of designs for these criteria, taking as prior distributions pC ∼ Beta(3.6, 2.1) and θ ∼ N( − 0.26,0.25). Curves for both Bayesian prior power and Γ* plateau fairly quickly as nE increases, meaning that there are a number of designs with good operating characteristics from which investigators can choose. For n = 40, Bayesian power is maximised at 0.55 by randomising nE = 25 patients to E and nC = 15 patients to C, for which design Γ* = 0.38, and the frequentist type I error rate is 0.26 under pE = 0.6 and pC = 0.7. This value of Γ* is close to the global minimum of 0.30 achieved by setting nE = 0 and nC = 40, for which design the Bayesian power is 0.14.
Affiliation: Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K.