Quasi-Monte Carlo Simulation and Variance Reduction Techniques Substantially Reduce Computational Requirements of Patient-Level Simulation Models: an Application to a Discrete Event Simulation Model.

Abstract

Objectives: Patient-level simulation models provide increased flexibility to overcome the limitations of cohort-based approaches in health-economic analysis. However, computational requirements of reaching convergence is a notorious barrier. The objective was to assess the impact of using quasi-monte carlo simulation (QMCS) and variance reduction techniques (VRTs) on computational requirements. Methods: A recently published discrete event simulation model assessing the cost-effectiveness of an adjunctive antipsychotic treatment for depression was used. The following VRTs were implemented: antithetic variables, common random numbers (CRN) and the combination (Anti-CRN). In addition, QMCS was conducted using the Sobol low discrepancy sequence. The minimal number of patients required to reach equal precision as the reference situation of 1,000,000 simple monte carlo simulations (MCS) was recorded. Precision was defined by the standard error (SE) of the incremental net monetary benefit (INMB) at a willingness to pay of € 20,000 per quality adjusted life year gained. VRT simulations were replicated 100 times. INMB estimates were compared with the reference situation using mean squared error (MSE), mean absolute error (MAE) and percentage of under- and overestimations. Results: Reference INMB (SE) was € 1,413 (76). The average number of patients required to reach reference precision were 929,628, 35,692, 41,683 and 36,803 for antithetic variables, CRN, Anti-CRN and Sobol respectively. This implied a computation time reduction ranging between 7% and 96% compared to simple MCS. MSE was 346,036, 16,314, 155,950 and 7,475 respectively. MAE was 588, 105, 387 and 86 respectively. Antithetic variables and Anti-CRN structurally underestimated INMB (99% and 100%). CRN marginally overestimated INMB in 76 replications. Conclusions: QMCS and VRT reduce computational requirements in terms of simulated patients and computational time up to 96%, enhancing the practical feasibility of patient-level simulation models. This particularly applies to Sobol and CRN. Antithetic variables should be used with caution and its structural bias warrants further research.