Determining optimal sample sizes for multi-stage randomized clinical trials using value of information methods

BACKGROUND: Traditional sample size calculations for randomized clinical trials depend on somewhat arbitrarily chosen factors, such as Type I and II errors. An effectiveness trial (otherwise known as a pragmatic trial or management trial) is essentially an effort to inform decision-making, i.e., should treatment be adopted over standard? Taking a societal perspective and using Bayesian decision theory, Willan and Pinto (Stat. Med. 2005; 24:1791-1806 and Stat. Med. 2006; 25:720) show how to determine the sample size that maximizes the expected net gain, i.e., the difference between the cost of doing the trial and the value of the information gained from the results. METHODS: These methods are extended to include multi-stage adaptive designs, with a solution given for a two-stage design. The methods are applied to two examples. RESULTS: As demonstrated by the two examples, substantial increases in the expected net gain (ENG) can be realized by using multi-stage adaptive designs based on expected value of information methods. In addition, the expected sample size and total cost may be reduced. LIMITATIONS: Exact solutions have been provided for the two-stage design. Solutions for higher-order designs may prove to be prohibitively complex and approximate solutions may be required. CONCLUSIONS: The use of multi-stage adaptive designs for randomized clinical trials based on expected value of sample information methods leads to substantial gains in the ENG and reductions in the expected sample size and total cost.