Simulation-based approaches to disease progression allow us to make counterfactual predictions about the effects of an untried series of treatment choices. However, building accurate simulators of disease progression is challenging, limiting the utility of these approaches for real world treatment planning. In this work, we present a novel simulation-based reinforcement learning approach that mixes between models and kernel-based approaches to make its forward predictions. On two real world tasks, managing sepsis and treating HIV, we demonstrate that our approach both learns state-of-the-art treatment policies and can make accurate forward predictions about the effects of treatments on unseen patients.