AbstractStochastic trees are stochastic processes, such as continuous-time Markov chains, which may be represented using tree diagrams. Continuous-risk utility assessment is a methodology that differs from standard assessment protocols by offering choices between alternatives which are not‘sure’things, thus enabling more realistic and familiar assessment scenarios to be posed. In this paper we develop, using information from the medical literature, stochastic tree models of the total hip replacement decision alternatives facing a patient with advanced osteoarthritis of the hip. We describe a decision analytic approach to the problem which uses continuous-risk utility assessment, and present empirical assessment results. We explore the sensitivity of the subjects' treatment recommendations to changes in model parameters and elicited preference values, offering insights into the variety of patient risk attitudes and preferences about functional well-being and the robustness of the total hip replacement decision to them.