Sizing a phase II trial to find a nearly optimal personalized treatment strategy
A personalized treatment strategy formalizes evidence-based treatment selection by mapping patient information to a recommended treatment. Personalized treatment strategies can lead to better patient outcomes while simultaneously reducing cost and treatment burden. Thus, there is a growing interest among clinical and intervention scientists in conducting randomized clinical trials with the primary aim of estimating a personalized treatment strategy. However, at present there are no appropriate sample size formulae to assist in the design of such a trial. Furthermore, because the asymptotic distribution of the estimated outcome under an estimated optimal treatment strategy can be highly sensitive to small perturbations in the underlying generative model, sample size calculations based on standard (uncorrected) asymptotic approximations or computer simulations may not be reliable. We offer a simple and robust method for powering a two-armed randomized clinical trial when the primary aim is estimating the optimal personalized treatment strategy. The proposed method is based on inverting a plugin projection confidence interval and is thereby regular and robust to small perturbations of the underlying generative model. The method performs well in simulated experiments and is illustrated using data from a pilot study of time to conception and fertility awareness.