To provide a practical approach for calculating uncertainty intervals and variance components associated with initial-condition and dynamic-equation parameters in computationally expensive population-based disease microsimulation models.
In the proposed uncertainty analysis approach, we calculated the required computational time and the number of runs given a user-defined error bound on the variance of the grand mean. The equations for optimal sample sizes were derived by minimizing the variance of the grand mean using initial estimates for variance components. Finally, analysis of variance estimators were used to calculate unbiased variance estimates.
To illustrate the proposed approach, we performed uncertainty analysis to estimate the uncertainty associated with total direct cost of osteoarthritis in Canada from 2010 to 2031 according to a previously published population health microsimulation model of osteoarthritis. We first calculated crude estimates for initial-population sampling and dynamic-equation parameters uncertainty by performing a small number of runs. We then calculated the optimal sample sizes and finally derived 95% uncertainty intervals of the total cost and unbiased estimates for variance components. According to our results, the contribution of dynamic-equation parameter uncertainty to the overall variance was higher than that of initial parameter sampling uncertainty throughout the study period.
The proposed analysis of variance approach provides the uncertainty intervals for the mean outcome in addition to unbiased estimates for each source of uncertainty. The contributions of each source of uncertainty can then be compared with each other for validation purposes so as to improve the model accuracy.