A Bayesian Decision-Theoretic Model of Sequential Experimentation with Delayed Response

We propose a Bayesian decision-theoretic model of a fully sequential experiment in which the real-valued primary end point is observed with delay. The goal is to identify the sequential experiment which maximises the expected benefits of technology adoption decisions, minus sampling costs. The solution yields a unified policy defining the optimal 'do not experiment'/'fixed sample size experiment'/'sequential experiment' regions and optimal stopping boundaries for sequential sampling, as a function of the prior mean benefit and the size of the delay. The model can also value the expected benefits accruing to study units and the fixed costs of switching from control to treatment. We apply the model to the field of medical statistics, using data from published clinical trials.