Bayesian modeling for monitoring and forecasting in global health

Where are we, and where are we heading?

Where are we, and where are we heading? Bayesian estimates and forecasts of family planning, maternal and child health indicators, used by the UN, WHO and FP2030.

How many women use modern contraception? How many maternal deaths are there in a given country, and is the number going down? The data that go into answering these questions are often sparse, come from different sources, and contain errors. For more than fifteen years my group has built Bayesian models that combine these data to produce estimates and forecasts with uncertainty. We have worked with international agencies, organizations, and countries to put those models to use.

Overview

The table gives an overview of the indicators we have worked on, the methods we developed, and who uses them. Click an indicator to read more.

Indicator Methods and use in global monitoring Examples of what we found
Family planning Bayesian hierarchical time series transition model (FPET). Used by the UN Population Division since 2013 and for FP2020/FP2030 monitoring. Married or in-union women using modern contraception rose from about 420 million in 1990 to 712 million in 2020. In 2020, unmet need in sub-Saharan Africa was 25.7%.
Health coverage indicators Bayesian hierarchical transition models that combine survey and routine data. Used for country modeling by Countdown to 2030. Ongoing, stay tuned!
Maternal mortality Bayesian maternal mortality estimation model (BMat), plus a model for misclassification of maternal deaths in civil registration data (BMis). Used by the UN Maternal Mortality Estimation Inter-Agency Group since 2014. About 295,000 maternal deaths in 2017, 94% of them in low-resource settings.
Child mortality and stillbirths Bayesian B-spline bias-reduction model (B3), models for neonatal mortality and sex differentials in mortality, and a Bayesian sparse regression model for stillbirths. Used by the UN Inter-agency Group for Child Mortality Estimation since 2012. Under-5 mortality fell by almost 60% between 1990 and 2019. There are about 2 million stillbirths a year, roughly one every 16 seconds.
Abortion and unintended pregnancy Bayesian demographic accounting model, plus a model for abortion safety. Used by the Guttmacher Institute and WHO since 2016. In 2015–2019 there were about 121 million unintended pregnancies a year, and about 61% of them ended in abortion (about 73 million abortions a year).
Sex ratio at birth Bayesian hierarchical time series mixture model with scenario-based projections. About 50 million female births were missing worldwide by 2020 because of sex-selective abortion.
Total fertility rate Bayesian three-phase transition model (BayesTFR). Used for the UN World Population Prospects since 2011. Global fertility is projected to be about 1.9 children per woman by the end of the century.

Most findings in the table come from estimates published between 2017 and 2022. For the latest numbers, see the most recent reports from the agencies.

Ongoing work

Family Planning Estimation Tool (FPET)

FPET is used to monitor contraceptive use, unmet need and demand satisfied for the FP2030 initiative and by the United Nations Population Division. The underlying model is a Bayesian hierarchical time series transition model, first developed for the UN Population Division. The new version, FPET2, produces estimates for national and subnational populations and makes use of routine data on family planning service statistics.

  • Key papers: Alkema et al. (2013), The Lancet; Cahill et al. (2018), The Lancet; Cahill et al. (2021), PLOS ONE; Susmann & Alkema (2025), Journal of the Royal Statistical Society Series C; Alkema et al. (2026), Statistics and Public Policy
  • R packages: fpet2, fpemlocal, BayesTransitionModels

Coverage indicators for Countdown to 2030

We extended the FPET approach to other reproductive, maternal, newborn and child health coverage indicators, including vaccination, antenatal care and facility-based deliveries. Country teams use the models through Countdown to 2030. More details about the project can be found on the Bayesian modeling for RMNCH coverage indicators project site.

Other areas

Maternal mortality

The Bayesian maternal mortality estimation model (BMat) and a model for misclassification of maternal deaths in civil registration data (BMis) have been used by the UN Maternal Mortality Estimation Inter-Agency Group since 2014. The models were extended to estimate maternal mortality during the COVID-19 pandemic. The most recent report is Trends in maternal mortality 2000 to 2023 (WHO, UNICEF, UNFPA, World Bank Group and UN DESA/Population Division, 2025).

  • Key papers: Alkema et al. (2016), The Lancet; Alkema et al. (2017), Annals of Applied Statistics; Peterson et al. (2022), Statistics in Medicine; Peterson et al. (2024), Statistics and Public Policy
  • R package: BMat/BMis

Child mortality and stillbirths

We developed Bayesian penalized B-spline regression models for estimating mortality at different ages, hierarchical time series models for sex differences in mortality, and a Bayesian sparse regression model with temporal smoothing for stillbirths. These models are used by the UN Inter-agency Group for Child Mortality Estimation, and I have been on its technical advisory group since 2011.

  • Key papers: Alkema & New (2014), Annals of Applied Statistics; You et al. (2015), The Lancet; Alexander & Alkema (2018), Demographic Research; Hug et al. (2021), The Lancet; Wang et al. (2022), Annals of Applied Statistics

Abortion and unintended pregnancy

A Bayesian demographic accounting model estimates unintended pregnancies and abortions jointly, using the fact that pregnancies, births and abortions have to add up. A separate Bayesian hierarchical model estimates abortion safety. The Guttmacher Institute and WHO have used these models for global reporting since 2016.

  • Key papers: Sedgh et al. (2016), The Lancet; Ganatra et al. (2017), The Lancet; Bearak et al. (2020), The Lancet Global Health; Bearak et al. (2022), BMJ Global Health

Sex ratio at birth and fertility

With Fengqing Chao and colleagues, I developed a Bayesian hierarchical time series mixture model to estimate the sex ratio at birth and the number of missing female births, with scenario-based projections to 2100. Earlier, with Adrian Raftery and the UN Population Division, I developed the Bayesian projection model for the total fertility rate that has been used in the UN World Population Prospects since 2011.

  • Key papers: Alkema et al. (2011), Demography; Gerland et al. (2014), Science; Chao et al. (2019), PNAS; Chao et al. (2021), Annals of Applied Statistics; Chao et al. (2021), BMJ Global Health
  • R package: bayesTFR

Full references are on the Publications page.

NoteGet in touch

Are you working on estimating or forecasting health indicators, or would you like to use FPET or the coverage models for your country or program? Get in touch; I’d love to hear about your work.