Fast approximate Bayesian inference of HIV indicators using PCA adaptive Gauss-Hermite quadrature

TL;DR

This paper introduces a fast, accurate Bayesian inference method for HIV indicators in sub-Saharan Africa, extending adaptive Gauss-Hermite quadrature to handle numerous hyperparameters efficiently.

Contribution

It develops a novel inference approach based on extended adaptive Gauss-Hermite quadrature, improving speed and accuracy over previous methods for complex spatial HIV models.

Findings

Enhanced inference accuracy for HIV model parameters.

Significantly faster than Hamiltonian Monte Carlo methods.

Compatible with existing TMB C++ templates.

Abstract

Naomi is a spatial evidence synthesis model used to produce district-level HIV epidemic indicators in sub-Saharan Africa. Multiple outcomes of policy interest, including HIV prevalence, HIV incidence, and antiretroviral therapy treatment coverage are jointly modelled using both household survey data and routinely reported health system data. The model is provided as a tool for countries to input their data to and generate estimates with during a yearly process supported by UNAIDS. Previously, inference has been conducted using empirical Bayes and a Gaussian approximation, implemented via the TMB R package. We propose a new inference method based on an extension of adaptive Gauss-Hermite quadrature to deal with more than 20 hyperparameters. Using data from Malawi, our method improves the accuracy of inferences for model parameters, while being substantially faster to run than Hamiltonian Monte Carlo with the No-U-Turn sampler. Our implementation leverages the existing TMB C++ template for the model's log-posterior, and is compatible with any model with such a template.