Input-output reduced order modeling for public health intervention evaluation

TL;DR

The paper addresses the challenge of high-dimensional input spaces in public health intervention modeling by introducing an input-output reduced-order modeling framework. It reduces the model's outputs to a $p$-dimensional representation using PCA on a snapshot matrix and builds a gPCE surrogate mapping inputs to the reduced outputs, then derives a $p$-dimensional input space via the gradient of the surrogate and the Moore-Penrose pseudoinverse to obtain directions $\boldsymbol{\tau}_j$. The HOPE HIV prevention model serves as a proof-of-concept, showing that distinct intervention mixes achieving specified targets can be identified with reduced computational cost and without iterative optimization. The method demonstrates interpretability of reduced directions and the ability to adapt intervention planning to targets that involve both health outcomes and spending, with potential broad applicability beyond HIV to other high-dimensional parameterized models.

Abstract

In recent years, mathematical models have become an indispensable tool in the planning, evaluation, and implementation of public health interventions. Models must often provide detailed information for many levels of population stratification. Such detail comes at a price: in addition to the computational costs, the number of considered input parameters can be large, making effective study design difficult. To address these difficulties, we propose a novel technique to reduce the dimension of the model input space to simplify model-informed intervention planning. The method works by first applying a dimension reduction technique on the model output space. We then develop a method which allows us to map each reduced output to a corresponding vector in the input space, thereby reducing its dimension. We apply the method to the HIV Optimization and Prevention Economics (HOPE) model, to validate the approach and establish proof of concept.

Figures (3)

• Figure 1: The four identified reduced-order outputs for the HIV prevention test case.
• Figure 2: Reduced-order inputs corresponding to each reduced-order output.
• Figure 3: Distinct interventions identified through input-output ROM procedure.