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

We solve a Bayesian decision-theoretic model of a sequential experiment in which the real-valued primary end point is observed with delay. The solution yields a unified policy defining the optimal 'do notexperiment'/'fixed sample size experiment'/'sequential experiment' regions as a function of the prior mean. The model can value the expected benefits accruing to study units, the fixed costs of switching from control to treatment, and allows the number of study units to benefit from a stopping decision to fall as the number of study units recruited to the experiment rises. We apply the model to the field of medical statistics, using data from a published trial investigating the clinical- and cost-effectiveness of drug-eluting stents versus bare metal stents. We demonstrate the model’s superiority over alternative trial designs when judged according to the maximisation of the net benefits of the trial, minus sampling costs, and we investigate how the size of the delay determines the optimal choice of trial design. The optimal policy also performs well when judged according to the probability of making the correct selection of health technology.