The Annals of Applied Statistics

Global estimation of child mortality using a Bayesian B-spline Bias-reduction model

Abstract

Estimates of the under-five mortality rate (U5MR) are used to track progress in reducing child mortality and to evaluate countries’ performance related to Millennium Development Goal 4. However, for the great majority of developing countries without well-functioning vital registration systems, estimating the U5MR is challenging due to limited data availability and data quality issues.

We describe a Bayesian penalized B-spline regression model for assessing levels and trends in the U5MR for all countries in the world, whereby biases in data series are estimated through the inclusion of a multilevel model to improve upon the limitations of current methods. B-spline smoothing parameters are also estimated through a multilevel model. Improved spline extrapolations are obtained through logarithmic pooling of the posterior predictive distribution of country-specific changes in spline coefficients with observed changes on the global level.

The proposed model is able to flexibly capture changes in U5MR over time, gives point estimates and credible intervals reflecting potential biases in data series and performs reasonably well in out-of-sample validation exercises. It has been accepted by the United Nations Inter-agency Group for Child Mortality Estimation to generate estimates for all member countries.

Article information

Source
Ann. Appl. Stat., Volume 8, Number 4 (2014), 2122-2149.

Dates
First available in Project Euclid: 19 December 2014

https://projecteuclid.org/euclid.aoas/1419001737

Digital Object Identifier
doi:10.1214/14-AOAS768

Mathematical Reviews number (MathSciNet)
MR3292491

Zentralblatt MATH identifier
06408772

Citation

Alkema, Leontine; New, Jin Rou. Global estimation of child mortality using a Bayesian B-spline Bias-reduction model. Ann. Appl. Stat. 8 (2014), no. 4, 2122--2149. doi:10.1214/14-AOAS768. https://projecteuclid.org/euclid.aoas/1419001737

References

• Alkema, L. and New, J. R. (2012). Progress toward global reduction in under-five mortality: A bootstrap analysis of uncertainty in Millennium Development Goal 4 estimates. PLoS Med. 9 e1001355.
• Alkema, L. and New, J. R. (2013). Global estimation of child mortality using a Bayesian B-spline bias-reduction model. Technical report. Available at http://arxiv.org/abs/1309.1602.
• Alkema, L. and New, J. (2014). Supplement to “Global estimation of child mortality using a Bayesian B-spline Bias-reduction model.” DOI:10.1214/14-AOAS768SUPPA, DOI:10.1214/14-AOAS768SUPPB.
• Alkema, L., Wong, M. B. and Seah, P. R. (2012). Monitoring progress towards Millennium Development Goal 4: A call for improved validation of under-5 mortality rate estimates. Statistics, Politics and Policy 3 Article ID 2.
• Amouzou, A. (2011). Real-time results tracking. Technical report, Institute for International Programs, Johns Hopkins Bloomberg School of Public Healt, Baltimore. Available at http://www.jhsph.edu/departments/international-health/centers-and-institutes/institute-for-international-programs/_documents/RRT_Technical_Note.pdf.
• Brass, W. (1964). Uses of census or survey data for the estimation of vital rates. In African Seminar on Vital Statistics, 1419 December 1964, United Nations, New York.
• Census of India (2011). Sample registration. Available at http://censusindia.gov.in/Vital_Statistics/SRS/Sample_Registration_System.aspx.
• Clark, S. J., Wakefield, J., McCormick, T. and Ross, M. (2012). Hyak mortality monitoring system: Innovative sampling and estimation methods. Working Paper 118. Available at http://www.csss.washington.edu/Papers/wp118.pdf.
• Currie, I. D. and Durban, M. (2002). Flexible smoothing with $P$-splines: A unified approach. Stat. Model. 2 333–349.
• Eilers, P. H. C. (1999). Discussion of “The analysis of designed experiments and longitudinal data using smoothing splines” by A. P. Verbyla, B. R. Cullis, M. G. Kenward and S. J. Welham. J. R. Stat. Soc. Ser. C. Appl. Stat. 48 300–311.
• Eilers, P. H. C. and Marx, B. D. (1996). Flexible smoothing with $B$-splines and penalties. Statist. Sci. 11 89–121.
• Eilers, P. H. C. and Marx, B. D. (2010). Splines, knots, and penalties. Wiley Interdisciplinary Reviews: Computational Statistics 2 637–653.
• Gelman, A. and Rubin, D. (1992). Inference from iterative simulation using multiple sequences. Statist. Sci. 7 457–511.
• Gneiting, T. and Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. J. Amer. Statist. Assoc. 102 359–378.
• Hill, K., You, D., Inoue, M. and Oestergaard, M. Z. (2012). Child mortality estimation: Accelerated progress in reducing global child mortality PLoS Med. 9 e1001303.
• 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. International Journal of Epidemiology 42 645–647.
• Pedersen, J. and Liu, J. (2012). Child mortality estimation: Appropriate time periods for child mortality estimates from full birth histories. PLoS Med. 9 e1001289.
• 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), Vienna. Available at http://mcmc-jags.sourceforge.net/.
• Raftery, A. E. and Lewis, S. M. (1992). How many iterations in the Gibbs sampler? In Bayesian Statistics 4 (J. M. Bernardo et al., eds.) 763–773. Oxford Univ. Press, Oxford.
• Raftery, A. E and Lewis, S. M. (1996). Implementing MCMC. In Markov Chain Monte Carlo in Practice (W. R. Gilks, D. J. Spiegelhalter and S. Richardson, eds.) 115–130. Chapman & Hall, London.
• Rajaratnam, J. K., Marcus, J., Flaxman, A., Wang, H., Levin-Rector, A., Dwyer, L., Costa, M., Lopez, A. and Murray, C. (2010). Neonatal, postneonatal, childhood, and under-5 mortality for 187 countries, 1970–2010: A systematic analysis of progress towards Millennium Development Goal 4. The Lancet 375 1988–2008.
• Sullivan, J. M. (2008). An assessment of the credibility of child mortality declines estimated from DHS mortality rates. Working Paper 1, United Nations Children’s Fund, New York. Available at http://www.childinfo.org/files/Overall_Results_of_Analysis.pdf.
• UN System Task Team on the Post-2015 UN Development Agenda (2012). Addressing inequalities: The heart of the post-2015 agenda and the future we want for all. Available at http://www.un.org/millenniumgoals/pdf/10_inequalities_20July.pdf.
• United Nations (1983). Manual X: Indirect Techniques for Demographic Estimation. United Nations, New York.
• United Nations Children’s Fund and USAID (2012). Real-time child mortality monitoring meeting. United Nations Children’s Fund, New York. Available at http://newsletter.childrenandaids.org/real-time-child-mortality-monitoring-meeting-december-19-2012/.
• United Nations Children’s Fund, Division of Policy and Strategy (2013). Committing to child survival: A promise renewed progress report 2013. United Nations Children’s Fund, New York.
• United Nations, Department of Economic and Social Affairs, Population Division (2011). World population prospects. The 2010 Revision.
• Wang, H., Dwyer-Lindgren, L., Lofgren, K. T., Rajaratnam, J. K., Marcus, J. R., Levin-Rector, A., Levitz, C. E., Lopez, A. D. and Murray, C. J. (2012). Age-specific and sex-specific mortality in 187 countries, 1970–2010: A systematic analysis for the global burden of disease study 2010. The Lancet 380 2071–2094.
• United Nations Inter-Agency Group for Child Mortality Estimation (2012). Levels & trends in child mortality: Report 2012. United Nations Children’s Fund, New York.
• United Nations Inter-Agency Group for Child Mortality Estimation (2013). Levels & trends in child mortality: Report 2013. United Nations Children’s Fund, New York.

Supplemental materials

• Supplementary material A: Figure S1: Illustration of differences in estimates and projections for all 194 countries between the unpooled (country-specific) and pooled B-spline model projection approach. Country-specific graphs to illustrate the effect of the pooling, as in Figure 4, for all 194 countries.
• Supplementary material B: Figure S2: U5MR data series and estimates for all 194 countries. Country-specific graphs, as in Figures 1 and 2, for all 194 countries.