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

Area of Science:

• Epidemiology
• Biostatistics
• Public Health

Background:

• Naomi is a spatial evidence synthesis model for district-level HIV epidemic indicators in sub-Saharan Africa.
• It models HIV prevalence, incidence, and antiretroviral therapy coverage using survey and health system data.
• The model is a UNAIDS-supported tool for national data estimation.

Purpose of the Study:

• To propose and evaluate a new inference method for the Naomi model.
• To improve the accuracy and efficiency of parameter inference for complex spatial models.
• To address challenges with models having over 20 hyperparameters.

Main Methods:

• Developed an extended adaptive Gauss-Hermite quadrature method for inference.
• Applied the new method to the Naomi model using data from Malawi.
• Compared performance against empirical Bayes with Gaussian approximation (TMBR package) and Hamiltonian Monte Carlo (HMC-NUTS).

Main Results:

• The proposed method significantly improved the accuracy of inferences for model parameters.
• The new inference approach was substantially faster than HMC-NUTS.
• The implementation is compatible with existing model templates (TMBC++).

Conclusions:

• The enhanced inference method offers a more accurate and efficient approach for spatial evidence synthesis models like Naomi.
• This advancement can improve the reliability of HIV epidemic indicators for public health decision-making.
• The method is adaptable for other complex statistical models with numerous hyperparameters.