A type of sample size design in cancer clinical trials for response rate estimation

During the early stage of cancer clinical trials, when it is not convenient to construct an explicit hypothesis testing, a study on a new therapy often calls for a response rate (p) estimation concurrently with or right before a typical phase II study. We consider a two-stage process, where the acquired information from Stage I (with a small sample size (m)) would be utilized for sample size (n) recommendation for Stage II study aiming for a more accurate estimation. Once a sample size design and a parameter estimation protocol are applied, we study the overall utility (cost-effectiveness) in connection with the cost due to patient recruitment and treatment as well as the loss due to mean squared error from parameter estimation. Two approaches will be investigated including the posterior mixture method (a Bayesian approach) and the empirical variance method (a frequentist approach). We also discuss response rate estimation under truncated parameter space using maximum likelihood estimation with regard to sample size and mean squared error. The profiles of p-specific expected sample size, mean squared error and risk under different approaches motivate us to introduce the concept of "admissible sample size (design)".