Training in Bayesian modeling

Overview

Background

Why would we want to introduce Bayesian statistical models to produce estimates and forecasts for Countdown coverage indicators?

• Link to slides

• Link to recording

Training content

The training is divided into modules:

1. Introduction to Bayesian inference and Bayesian modeling in global health

2. How to exchange information between populations: Hierarchical models (also called multilevel models)

3. Introduction to Bayesian modeling of coverage indicators and the Family Planning Estimation Tool (FPET)

In each module, topics include conceptual understanding as well as hands-on analysis and modeling exercises.

Module 1: Introduction to Bayesian inference

Unit 1: Let’s think like a Bayesian!

Material:

• link to slides

• link to recording

Unit 2: Bayesian inference for a population proportion

Material:

• link to slides

• link to recording, note that the start of the recording has an issue with the screen capture of the title slide but that resolves itself on the 2nd slide.

Unit 3: More details on Bayesian inference and Bayes’ rule for estimating a population proportion

Material:

• link to slides

• link to recording

• link to R notebook to do Bayesian inference for a population proportion is saved in our github repo in the folder module1, direct link here.

Unit 4: Why Bayesians like sampling so much

Material: simulation-based inference, Monte Carlo approximation

• link to slides

• link to recording

Unit 5: Introduction to MCMC

Material:

• link to slides

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Unit 6: Let’s Stan!

The slides and recording start with a summary of units 4 and 5, followed by unit 6. The recording ends with a demo of how to get started with brms using the notebook:

• link to slides

• link to recording

• R notebook to get started with brms (saved in our github repo in the folder module1, direct link here)

Once you can run the brm-function, use this notebook to check out more examples of fitting Bayesian regression models using brm:

• Link to R notebook in repo and the corresponding knitted pdf

Module 2: Hierarchical (or multilevel) models

In this module, we’re going to discuss how to exchange information between populations using hierarchical models, which are also called multilevel models, and fit such models using the brm function.

To introduce the topic, we are using material from a different course:

• Unit 1 (referred to as module 7 in the course): slides and recording

• Unit 2 (referred to as module 8 in the course): slides and recording

The example used in this material is the estimation and prediction of radon levels in counties in the US. Radon is a naturally occurring radioactive gas. Its decay products are also radioactive; in high concentrations, they can cause lung cancer (several 1000 deaths/year in the USA). Radon levels vary greatly across US homes. The data we work with contains radon measurements from different counties in the US. One final goal in the two units is to predict radon levels for a specific country or in a non-sampled house using a Bayesian hierarchical regression model. The application was originally taken from the book Gelman and Hill (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.(A great book but outdated now wrt computation; remind me to post a list of references with more recent books!)

Note that in this material, the second unit gets a little more technical and may be beyond what some of you are looking for in this training. Please do go through the material, focusing on trying to understand the main points (i.e, what type of models and predictions are discussed). As usual, feel free to post any questions or comments on slack. We can have more technical discussions if there is an interest, during our meetings or over slack.

In our group meetings, we will do hands-on exercises that focus on estimating modern contraceptive use (mCPR). For our first meeting, the exercise concerns the estimation of country-specific mCPR for a given time period using the hierarchical model from unit 1. For the second meeting, we will fit hierarchical regression models to estimate country-year specific mCPR, applying the different types of models introduced in unit 8.

Module 3: Introduction to Bayesian modeling of coverage indicators and the Family Planning Estimation Tool (FPET)

Now that we are familiar with Bayesian inference and hierarchical models, we can start to consider model classes and model building blocks that are needed to develop a Bayesian model to estimate and forecast a coverage indicator for a population and time period of interest. We consider a general class of Bayesian hierarchical temporal models that includes the Family Planning Estimation Tool (FPET), a model that is used for estimating and forecasting family planning indicators such as modern contraceptive use, based on survey and routine data. 

To introduce FPET, this module discusses the following topics:

1. A general model class referred to as Temporal Models for Multiple Populations (TMMPs). The class makes a distinction between the process model, which describes latent trends in the indicator interest, and the data model, which describes the data generating process of the observed data. To start with a general introduction to this class, please consider reading paper 1 below.

2. What assumptions to make about indicators and how they change with time: Time series process models, focused on transition models, as described in papers 2 and 3 below.  

3. How to best use data to inform estimates: Data models for survey and routine surveillance data, as described in papers 3 and 4 below.   

Readings

1. Introduction to TMMPs [focus on the general class as introduced in section 3, consider case studies based on your interest]: Susmann, Herbert, Monica Alexander, and Leontine Alkema. “Temporal Models for Demographic and Global Health Outcomes in Multiple Populations: Introducing a New Framework to Review and Standardise Documentation of Model Assumptions and Facilitate Model Comparison.” International Statistical Review 90, no. 3 (2022): 437–67. https://doi.org/10.1111/insr.12491.

2. Introduction to transition models [focus on the general set up]: Susmann, Herbert, and Leontine Alkema. “Flexible Modeling of Demographic Transition Processes with a Bayesian Hierarchical Penalized B-Splines Model.” arXiv, 2023. https://doi.org/10.48550/arXiv.2301.09694.

3. FPET overview paper, it discusses the process model and data models for survey data and routine data: Alkema, Leontine, Herbert Susmann, Evan Ray, Shauna Mooney, Niamh Cahill, Kristin Bietsch, A. A. Jayachandran, et al. “Statistical Demography Meets Ministry of Health: The Case of the Family Planning Estimation Tool.” arXiv, 2024. https://doi.org/10.48550/arXiv.2501.00007.

4. Details on how survey data are used in FPET: Alkema, Leontine, Herbert Susmann, and Evan Ray. “Temporal Models for Demographic and Global Health Outcomes in Multiple Populations: Introducing the Normal-with-Optional-Shrinkage Data Model Class.” arXiv, 2024. https://doi.org/10.48550/arXiv.2411.18646.