The Annals of Applied Statistics

A Bayesian approach to the global estimation of maternal mortality

Leontine Alkema, Sanqian Zhang, Doris Chou, Alison Gemmill, Ann-Beth Moller, Doris Ma Fat, Lale Say, Colin Mathers, and Daniel Hogan

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The maternal mortality ratio (MMR) is defined as the number of maternal deaths in a population per 100,000 live births. Country-specific MMR estimates are published on a regular basis by the United Nations Maternal Mortality Estimation Inter-agency Group (UN MMEIG) to track progress in reducing maternal deaths and were used to evaluate regional and national performance related to Millennium Development Goal (MDG) 5, which called for a 75% reduction in the MMR between 1990 and 2015.

Until 2014, the UN MMEIG used a multilevel regression model for producing estimates for countries without sufficient data from vital registration systems. While this model worked well in the past to assess MMR levels for countries with limited data, it was deemed unsatisfactory for final MDG 5 reporting for countries where longer time series of observations had become available because, by construction, estimated trends in the MMR were covariate-driven only and did not necessarily track data-driven trends.

We developed a Bayesian maternal mortality estimation model, which extends upon the UN MMEIG multilevel regression model. The new model assesses data-driven trends through the inclusion of an ARIMA time series model that captures accelerations and decelerations in the rate of change in the MMR. Varying reporting and data quality issues are accounted for in source-specific data models. The revised model provides data-driven estimates of MMR levels and trends and was used for MDG 5 reporting for all countries.

Article information

Ann. Appl. Stat. Volume 11, Number 3 (2017), 1245-1274.

Received: August 2015
Revised: November 2016
First available in Project Euclid: 5 October 2017

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ARIMA time series models Bayesian inference multilevel regression model maternal mortality ratio Millennium Development Goal 5 UN Maternal Mortality Estimation Inter-agency Group (UN MMEIG)


Alkema, Leontine; Zhang, Sanqian; Chou, Doris; Gemmill, Alison; Moller, Ann-Beth; Fat, Doris Ma; Say, Lale; Mathers, Colin; Hogan, Daniel. A Bayesian approach to the global estimation of maternal mortality. Ann. Appl. Stat. 11 (2017), no. 3, 1245--1274. doi:10.1214/16-AOAS1014.

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  • Alkema, L. and New, J. R. (2014). Global estimation of child mortality using a Bayesian B-spline Bias-reduction model. Ann. Appl. Stat. 8 2122–2149.
  • Alkema, L., Chou, D., Hogan, D., Zhang, S., Moller, A.-B., Gemmill, A., Fat, D. M., Boerma, T., Temmerman, M., Mathers, C. and Say, L. (2016). Global, regional, and national levels and trends in maternal mortality between 1990 and 2015, with scenario-based projections to 2030: A systematic analysis by the un maternal mortality estimation inter-agency group. The Lancet 387 462–474.
  • Alkema, L., Zhang, S., Chou, D., Gemmill, A., Moller, A.-B., Fat, D. M., Say, L., Mathers, C. and Hogan, D. (2017). Supplement to “A Bayesian approach to the global estimation of maternal mortality.” DOI:10.1214/16-AOAS1014SUPP.
  • Chao, F. and Alkema, L. (2014). How informative are vital registration data for estimating maternal mortality? A Bayesian analysis of WHO adjustment data and parameters. Statistics and Public Policy 1 6–18.
  • Gelman, A. and Rubin, D. (1992). Inference from iterative simulation using multiple sequences. Statist. Sci. 7 457–511.
  • ICF International Inc. (2014). Guidelines for the MEASURE DHS Phase III Main Survey Report. Technical report. Available at
  • Oestergaard, M. Z., Alkema, L. and Lawn, J. E. (2013). Millennium Development Goals national targets are moving targets and the results will not be known until well after the deadline of 2015. Int. J. Epidemiol. 42 645–647.
  • Plummer, M. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003), March 2022, Vienna, Austria. Available at ISSN 1609-395X.
  • UNAIDS (2013). Global Report: UNAIDS Report on the Global AIDS Epidemic $2013$. Geneva: Joint United Nations Programme on HIV/AIDS.
  • United Nations Population Division (2013). World Population Prospects. The $2012$ Revision. United Nations publication.
  • WHO, UNICEF, UNFPA, The World Bank and the United Nations Population Division (2014). Trends in maternal mortality 1990–2013: Estimates developed by WHO, UNICEF, UNFPA, The World Bank and the United Nations Population Division. ISBN 978 92 4 150722 6.
  • WHO, UNICEF, UNFPA, The World Bank and the United Nations Population Division (2015). Trends in maternal mortality 1990–2015: Estimates developed by WHO, UNICEF, UNFPA. The World Bank and the United Nations Population Division.
  • Wilmoth, J. R., Mizoguchi, N., Oestergaard, M. Z., Say, L., Mathers, C. D., Zureick-Brown, S., Inoue, M. and Chou, D. (2012). A new method for deriving global estimates of maternal mortality. Statistics, Politics, and Policy 3.
  • World Health Organization (2010). International Statistical Classification of Diseases and Related Health Problems, Tenth Revision: Instruction Manual. World Health Organization, Geneva.
  • World Health Organization (2014). Life Tables for WHO Member States 1990–2012. World Health Organization, Geneva.
  • World Health Organization (2015). Strategies toward ending preventable maternal mortality (EPMM). Technical report. Available at

Supplemental materials

  • Supplementary figure: Data series and estimates of the PM (proportion of all-cause deaths that are maternal) and the MMR (number of maternal deaths per 100,000 live births) for 183 countries. BMat estimates are illustrated by the solid red lines and 80% CIs are shown by the red shaded areas. Reported (unadjusted) and adjusted observations used for fitting the BMat model are displayed and explained in the legend. The vertical line with each adjusted observation indicates the approximate 80% confidence interval for the PM or MMR associated with that observation, based on point estimates for reporting adjustments and total error variance. The UN MMEIG 2014 estimates are illustrated with the green lines. Adjusted observations that were used in the WHO 2014 regression model are plotted with black crosses. Estimates are shown for the period 1990–2015; data before 1990 were used in model fitting. Note that these estimates are obtained by fitting the model to a 2014 MMEIG database. Therefore, the BMat 2014 estimates presented here differ from the BMat and MMEIG 2015 estimates, which are based on more recent data [WHO et al. (2015)].