OBJECTIVES: Markov cohort state-transition model has been used extensively to model population trajectories over-time in cost-effectiveness analyses (CEA). We recently showed that a Markov model represents the average of a continuous-time stochastic process on a multidimensional integer lattice governed by a master equation (ME), which represents the time-evolution of the probability function of an integer-valued random vector. From this theoretical connection, this study introduces a novel modeling method, stochastic differential equation (SDE), which captures not only the average behavior but also the variance of a cohort model.

METHODS: We first derive a continuous approximation to an ME by relaxing the integrality constraint of the state space, from integer-valued to real-valued, in the form of Fokker Planck equation (FPE), which represents the time-evolution of the probability function of a real-valued random vector of population counts. Then, we derive the SDE from first principles by formulating the expected changes in the population counts across health states over a small time step. We describe a step-by-step guide to construct and solve an SDE model for use in practice. We show the applications of SDE in two case studies in which we develop SDE models for published decision models.

RESULTS: The first example, a 4-state Markov model, demonstrates that the population trajectories, the mean and the variance of population counts, from the SDE and microsimulation, match. The second example, a breast cancer progression model, shows that users can readily apply the SDE method in their existing works without the need for additional inputs beyond a state-transition diagram and the corresponding transition rates. In both examples, the SDEs are superior to the microsimulation models in terms of computational speed.

CONCLUSIONS: SDE provides an alternative modeling framework which includes information on variance and is computationally less expensive than microsimulation for a typical modeling problem in CEA.