Sample size formulae for the Bayesian continual reassessment method

BACKGROUND In the planning of a dose finding study, a primary design objective is to maintain high accuracy in terms of the probability of selecting the maximum tolerated dose. While numerous dose finding methods have been proposed in the literature, concrete guidance on sample size determination is lacking. PURPOSE With a motivation to provide quick and easy calculations during trial planning, we present closed form formulae for sample size determination associated with the use of the Bayesian continual reassessment method (CRM). METHODS We examine the sampling distribution of a nonparametric optimal design and exploit it as a proxy to empirically derive an accuracy index of the CRM using linear regression. RESULTS We apply the formulae to determine the sample size of a phase I trial of PTEN-long in pancreatic cancer patients and demonstrate that the formulae give results very similar to simulation. The formulae are implemented by an R function 'getn' in the package 'dfcrm'. LIMITATIONS The results are developed for the Bayesian CRM and should be validated by simulation when used for other dose finding methods. CONCLUSIONS The analytical formulae we propose give quick and accurate approximation of the required sample size for the CRM. The approach used to derive the formulae can be applied to obtain sample size formulae for other dose finding methods.