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A key and challenging step toward personalized/precision medicine is the ability to redesign dose-finding clinical trials. This work studies a problem of fully response-adaptive Bayesian design of phase II dose-finding clinical trials with patient information, where the decision maker seeks to identify the right dose for each patient type (often defined as an effective target dose for each group of patients) by minimizing the expected (over patient types) variance of the right dose. We formulate this problem by a stochastic dynamic program and exploit a few properties of this class of learning problems. Because the optimal solution is intractable, we propose an approximate policy by an adaptation of a one-step look-ahead framework. We show the optimality of the proposed policy for a setting with homogeneous patients and two doses and find its asymptotic rate of sampling. We adapt a number of commonly applied allocation policies in dose-finding clinical trials, such as posterior adaptive sampling, and test their performance against our proposed policy via extensive simulations with synthetic and real data. Our numerical analyses provide insights regarding the connection between the structure of the dose-response curve for each patient type and the performance of allocation policies. This paper provides a practical framework for the Food and Drug Administration and pharmaceutical companies to transition from the current phase II procedures to the era of personalized dose-finding clinical trials. Funding: This research is supported by the National Science Foundation [Grant 1651912]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/serv.2022.0306 . 

Abstract We study the classical ranking and selection problem, where the ultimate goal is to find the unknown best alternative in terms of the probability of correct selection or expected opportunity cost. However, this paper adopts an alternative sampling approach to achieve this goal, where sampling decisions are made with the objective of maximizing information about the unknown best alternative, or equivalently, minimizing its Shannon entropy. This adaptive learning is formulated via a Bayesian stochastic dynamic programming problem, by which several properties of the learning problem are presented, including the monotonicity of the optimal value function in an information‐seeking setting. Since the state space of the stochastic dynamic program is unbounded in the Gaussian setting, a one‐step look‐ahead approach is used to develop a policy. The proposed policy seeks to maximize the one‐step information gain about the unknown best alternative, and therefore, it is called information gradient (IG). It is also proved that the IG policy is consistent, that is, as the sampling budget grows to infinity, the IG policy finds the true best alternative almost surely. Later, a computationally efficient estimate of the proposed policy, called approximated information gradient (AIG), is introduced and in the numerical experiments its performance is tested against recent benchmarks alongside several sensitivity analyses. Results show that AIG performs competitively against other algorithms from the literature.