Optimal Bayesian Learning of Dose-Response Parameters from a Cohort

There has been a surge of clinical interest in the idea of response-guided dosing (RGD). The goal in RGD is to tailor drug-doses to the stochastic evolution of each individual patient's disease condition over the treatment course. The hope is that this form of individualized therapy will deliver the right dose to the right patient at the right time. Several expert panels have observed that despite the excitement surrounding RGD, quantitative, data-driven decision-making approaches that learn patients' dose-response and incorporate this information into adaptive dosing strategies are lagging behind. This situation is particularly exacerbated in clinical trials. For instance, fixed design clinical studies for estimating the key parameter of a dose-response function might not treat trial patients optimally. Similarly, the dosing strategies employed in clinical trials for RGD often appear ad-hoc. In this paper, we study the problem of finding optimal RGD policies while learning the distribution of a dose-response parameter from a cohort of patients. We provide a Bayesian stochastic dynamic programming (DP) formulation of this problem. Exact solution of Bellman's equations for this problem is computationally intractable. We therefore present two approximate control schemes and mathematically analyze the monotonicity, stationarity, and separability structures of the resulting dosing strategies. These structures are then exploited in efficient, approximate solution of the optimal learning problem. Computer simulations using the Michaelis-Menten dose-response function are included as an example wherein we study the effect of cohort size and prior misspecification on learning, and also compare the performance of various dosing policies