Purpose: To investigate the feasibility of closed-form analytic solutions of decision analytic models and compare their efficiency and accuracy to cohort and patient-level simulation models.

Background: Long-term cost-effectiveness models require estimates of expected costs and effects accounting for patient variation over time and discounting. This usually involves either patient level simulation or cohort modelling. These are computationally intensive, restricting the application of value-of-information methods and require Monte-Carlo simulation and interpolation.

Methods: Models of rheumatoid arthritis (RA) usually include components representing the initial amelioration of disease when the treatment is started, the progression of disease while on treatment, and the ‘rebound' in symptoms and subsequent progression when treatment is ended. The estimates of cost-effectiveness are sensitive to the assumptions surrounding rebound and hence whether treatment delays the progress of disease. A closed form analytic solution of an RA model was derived by using MAPLE to obtain a definite integral which provided estimates of expected costs and effects as a function of time to treatment failure for an individual. This was then integrated over the variation in time to treatment failure between individuals to obtain expected costs and effects. For the patient level simulation, the outcome pathway for a patient was repeatedly simulated to obtain estimates of expected costs and effects. In the cohort model, the probabilities of a patient following each of a set of outcome pathways were estimated and the expected costs and effects derived. The accuracy and computational efficiency of the three approaches were compared.

Results: The patient level simulation took 600 seconds to evaluate, the cohort model took 40 seconds to evaluate and the closed form analytic model took 0.0004 seconds to evaluate. The results from the cohort and patient-level simulation models converged on the results of the closed form solution as the number of simulations and the number of time-points evaluated increased. The analytic model was the fastest to evaluate and provided an ‘exact' solution.

Conclusion: Closed-form analytic solutions of decision-analytic models, where feasible, have the advantage over simulation methods of being both exact and computationally efficient and should be considered when constructing cost-effectiveness models. The increased speed is potentially of great help in the implementation of value of information methods