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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Zentralblatt MATH identifier

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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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)].