Approaches for optimal sequential decision analysis in clinical trials

Unlike traditional approaches Bayesian methods enable formal combination of expert opinion and objective information into interim and nal analyses of clinical trials data However most previous Bayesian approaches have based the stopping decision on the posterior probability con tent of one or more regions of the parameter space thus implicitly determining a loss and decision structure In this paper we oer a fully Bayesian approach to this problem specifying not only the likelihood and prior distributions but appropriate loss functions as well At each data moni toring point we enumerate the available decisions and investigate the use of backward induction implemented via Monte Carlo methods to choose the optimal course of action We then present a forward sampling algorithm that substantially eases the analytic and computational burdens associated with backward induction oering the possibility of fully Bayesian optimal sequential monitoring for previously untenable numbers of interim looks We show that forward sampling can always identify the optimal sequential strategy in the case of a oneparameter exponential family with a conjugate prior and monotone loss functions as well as the best member of a certain class of strategies when backward induction is infeasible Finally we illustrate and compare the forward and backward approaches using data from a recent AIDS clinical tria