Metamodeling for Policy Simulations with Multivariate Outcomes

Metamodels are simplified approximations of more complex models that can be used as surrogates for the original models. Challenges in using metamodels for policy analysis arise when there are multiple correlated outputs of interest. We develop a framework for metamodeling with policy simulations to accommodate multivariate outcomes.

We combine 2 algorithm adaptation methods-multitarget stacking and regression chain with maximum correlation-with different base learners including linear regression (LR), elastic net (EE) with second-order terms, Gaussian process regression (GPR), random forests (RFs), and neural networks. We optimize integrated models using variable selection and hyperparameter tuning. We compare the accuracy, efficiency, and interpretability of different approaches. As an example application, we develop metamodels to emulate a microsimulation model of testing and treatment strategies for hepatitis C in correctional settings.

Output variables from the simulation model were correlated (average ρ = 0.58). Without multioutput algorithm adaptation methods, in-sample fit (measured by R²) ranged from 0.881 for LR to 0.987 for GPR. The multioutput algorithm adaptation method increased R² by an average 0.002 across base learners. Variable selection and hyperparameter tuning increased R² by 0.009. Simpler models such as LR, EE, and RF required minimal training and prediction time. LR and EE had advantages in model interpretability, and we considered methods for improving the interpretability of other models.

In our example application, the choice of base learner had the largest impact on R²; multioutput algorithm adaptation and variable selection and hyperparameter tuning had a modest impact. Although advantages and disadvantages of specific learning algorithms may vary across different modeling applications, our framework for metamodeling in policy analyses with multivariate outcomes has broad applicability to decision analysis in health and medicine.