Flexible design and efficient implementation of adaptive dose-finding studies

A dose-finding study with an adaptive design generates three computational problems: fitting the dose-response curve given the current data, identifying the dose to be given to the next patient that is optimal for learning about the dose-response curve, and pretrial simulation in order to establish operating characteristics of alternative designs. Identifying the 'optimal' dose is the rate-limiting step since conventional methods, estimating the full posterior predictive distribution of some utility function under each of the possible doses, are very slow. We explore a simpler strategy based on importance sampling, whereby the posterior mean of the utility at each candidate dose is estimated by taking its average across an empirical distribution for the model parameters from the current Markov chain Monte Carlo (MCMC) run, weighted according to the likelihood of one or more predicted observations. We identify appropriate settings for this algorithm and illustrate its application in the context of a normal dynamic linear model used in a dose-finding clinical trial of a neutrophil inhibitory factor in acute ischaemic stroke.