naomi-aghq

Code for the manuscript Howes, Stringer, Flaxman and Eaton "Fast approximate Bayesian inference of HIV indicators using PCA adaptive Gauss-Hermite quadrature" (in preparation).

Naomi (Eaton et al, 2021) is a spatial evidence synthesis model used to produce district-level HIV epidemic indicators in sub-Saharan Africa. Multiple outcomes of interest, including HIV prevalence, HIV incidence and 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 during a yearly process supported by UNAIDS. Currently, inference is conducted using empirical Bayes and a Gaussian approximation via the TMB R package. We propose a new inference method extending adaptive Gauss-Hermite quadrature to deal with >20 hyperparameters, enabling fast and accurate inference for Naomi and other extended latent Gaussian models. Using data from Malawi, our method improves the accuracy of inferences across a range of metrics, while being substantially faster to run than Hamiltonian Monte Carlo with the No-U-Turn sampler. Our implementation is based on the existing TMB C++ template for the model's log-posterior, and is compatible with any model with such a template.

C++ template for the log-posterior

The TMB template for the simplified Naomi model is available here.

File structure

The directories of this repository are:

Directory	Contains
docs	Hosted files at https://athowes.github.io/naomi-aghq/
make	Scripts used to run the reports. _make.R runs everything in order
misc	Ideas for further work and other documents that don't need to be in src
src	All orderly reports
utils	Helper scripts for common development tasks

orderly

We use the orderly package (RESIDE, 2020) to simplify the process of doing reproducible research. After installing orderly (from either CRAN or Github) a report, example, may be run by:

orderly::orderly_run(name = "src/example")

The results of this run will appear in the draft/ folder (ignored on Github). To commit the draft (with associated id) to the archive/ folder (also ignored on Github, and treated as "read only") use:

orderly::orderly_commit(id)

Any outputs of this report will then be available to use as dependencies within other reports. Reports can be pushed to the HIV inference group sharepoint (the remote) using:

orderly::orderly_push_archive("example")

Or can be pulled (alongside any dependencies) from the remote using:

orderly_pull_archive("example")

Alternatively, just the dependencies can be pulled using orderly::orderly_pull_dependencies("example").

R package dependencies

This repository is supported by the inf.utils package, which can be installed from Github via:

devtools::install_github("athowes/inf.utils")

We also use the aghq package for inference, which is available from CRAN, though the latest development version can be installed from Github via:

devtools::install_github("athowes/aghq", ref = "adam-dev")

Session information

The sessionInfo() used to run this analysis is:

R version 4.2.0 (2022-04-22)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS 13.3.1

Matrix products: default
LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] patchwork_1.1.2 stringr_1.5.0   purrr_1.0.1     readr_2.1.3     tidyr_1.2.1     tibble_3.2.1    tidyverse_1.3.1 forcats_0.5.2   ggplot2_3.4.0  
[10] dplyr_1.0.10    rmarkdown_2.18 

Reports

The reports within src are as follows:

Report	Description
astro	Analysis of an astronomy example
check_hyper-marginals	Visualise hyperparameter posteriors fitted with NUTS for simplified Naomi, as well as positions of PCA-AGHQ nodes
check_pca-aghq	Unit tests for the PCA-AGHQ procedure working as expected
check_sd-estimation	Analysing odd behaviour for simplified Naomi whereby joint Gaussian approximation better estimates the standard deviation than conditionals
check_tmb-aghq-k1	Assessment that TMB and aghq run with k = 1 produce essentially the same inferences for simplified Naomi, in contrast to inferences from aghq with any grid
check_tmb-output	Checking the the TMB output for simplified Naomi looks Gaussian, as it should be
dev_hyper-sampling	Method development for sampling from the hyperparameters within TMB or AGHQ
dev_scale-grid	Method development for hyperparameter grids over many dimensional spaces
dev_sinla	Method development for Laplace and reduced cost Laplace marginals
docs_01-04-20-mini	Presentation for StatML CDT
docs_01-07-21-stats-epi-group	Presentation for Flaxman, Bhatt groups
docs_15-11-22-seminar	Presentation for Waterloo SAS
docs_18-04-23-lab-group	Presentation for HIV Inference Group
docs_19-05-23-turing	Presentation for Alan Turing Institute
docs_21-06-23-mlgh	Presentation for Machine Learning and Global Health Network
docs_bayescomp-poster	Poster for BayesComp 2023
docs_bioinference-poster	Poster for BioInference 2023
docs_model-structure	Analysis of inputs to simplified Naomi outputs
docs_paper	Paper and appendix
epil	Analysis of epilepsy example
example_inla-grid	Demonstration of grid construction method used in R-INLA
example_inla-replication	Step-by-step version of INLA method in R and TMB
example_naomi	Follow the naomi package vignette
explore_aghq	Walkthrough various aghq package functions
explore_posterior-comparison	Explore methods for comparing the accuracy of computed posterior distributions
naomi-simple_contraction	Comparison of prior and posterior standard deviations across inference methods
naomi-simple_exceedance	Case-study on computation of exceedance probabilities for second 90 target and high incidence
naomi-simple_fit	Fit the simplified Naomi model using a range of inference methods
naomi-simple_increase-s-k	Is the log normalising constant better estimated as $s$ and $k$ are increased in PCA-AGHQ?
naomi-simple_ks	Comparison of inference methods using Kolmogorov-Smirnov tests on marginals
naomi-simple_mcmc	Diagnostics for MCMC convergence
naomi-simple_mmd	Comparison of inference methods using maximum mean discrepancy on joint distributions
naomi-simple_model-checks	Checking the model fit to data
naomi-simple_point-estimates	Comparison of inference methods for estimating the mean and standard deviation
naomi-simple_psis	Comparison of inference methods using Pareto-smoothed importance sampling on joint distributions
plot-tikz_algorithm-flowchart	TikZ diagram of proposed algorithm
plot-tikz_simplified-naomi	TikZ diagram of the simplified Naomi directed acyclic graph
prev-anc-art_model0	Fit prevalence, ANC, ART model version 0
prev-anc-art_model1	Fit prevalence, ANC, ART model version 1
prev-anc-art_model2	Fit prevalence, ANC, ART model version 2
prev-anc-art_model3	Fit prevalence, ANC, ART model version 3
prev-anc-art_model4	Fit prevalence, ANC, ART model version 4
prev-anc-art_results	Analyse results of prevalence, ANC, ART model
prev-anc-art_sim	Simulate prevalence, ANC, ART data