Computationally Efficient Estimation of Localized Treatment Effects in High-Dimensional Design Spaces using Gaussian Process Regression

ABSTRACT Population-scale agent-based simulations of the opioid epidemic help evaluate intervention strategies and overdose outcomes in heterogeneous communities and provide estimates of localized treatment effects , which support the design of locally-tailored policies for precision public health . However, it is prohibitively costly to run simulations of all treatment conditions in all communities because the number of possible treatments grows exponentially with the number of interventions and levels at which they are applied. To address this need efficiently, we develop a metamodel framework, whereby treatment outcomes are modeled using a response function whose coefficients are learned through Gaussian process regression (GPR) on locally-contextualized covariates. We apply this framework to efficiently estimate treatment effects on overdose deaths in Pennsylvania counties. In contrast to classical designs such as fractional factorial design or Latin hypercube sampling, our approach leverages spatial correlations and posterior uncertainty to sequentially sample the most informative counties and treatment conditions. Using a calibrated agent-based opioid epidemic model, informed by county-level overdose mortality and baseline dispensing rate data for different treatments, we obtained county-level estimates of treatment effects on overdose deaths per 100,000 population for all treatment conditions in Pennsylvania, achieving approximately 5% average relative error using one-tenth the number of simulation runs required for exhaustive evaluation. Our bi-level framework provides a computationally efficient approach to decision support for policy makers, enabling rapid evaluation of alternative resource-allocation strategies to mitigate the opioid epidemic in local communities. The same analytical framework can be applied to guide precision public health interventions in other epidemic settings.