September 2021 Global estimation and scenario-based projections of sex ratio at birth and missing female births using a Bayesian hierarchical time series mixture model
Fengqing Chao, Patrick Gerland, Alex R. Cook, Leontine Alkema
Author Affiliations +
Ann. Appl. Stat. 15(3): 1499-1528 (September 2021). DOI: 10.1214/20-AOAS1436


The sex ratio at birth (SRB) is defined as the ratio of male to female live births. The SRB imbalance in parts of the world over the past several decades is a direct consequence of sex-selective abortion, driven by the coexistence of son preference, readily available technology of prenatal sex determination and fertility decline. Estimation and projection of the degree of SRB imbalance is complicated because of variability in SRB reference levels and because of the uncertainty associated with SRB observations.

We develop Bayesian hierarchical time series mixture models for SRB estimation and scenario-based projections for all countries from 1950 to 2100. We model the SRB regional and national reference levels and the fluctuation around national reference levels. We identify countries at risk of SRB imbalances and model both: (i) the absence or presence of sex ratio transitions in such countries and, if present, (ii) the transition process. The transition model of SRB imbalance captures three stages (increase, stagnation and convergence back to SRB baselines). The model identifies countries with statistical evidence of SRB inflation in a fully Bayesian approach. The scenario-based SRB projections are based on the sex ratio transition model with varying assumptions regarding the occurrence of a sex ratio transition in at-risk countries. Projections are used to quantify the future burden of missing female births due to sex-selective abortions under different scenarios.

Funding Statement

This work was supported by a research grant from the National University of Singapore.


The authors would like to thank the anonymous referees, the Associate Editor and the Editor for their insightful and constructive comments that improved the quality of this paper. The study described is solely the responsibility of the authors and does not necessarily represent the official views of the United Nations.


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Fengqing Chao. Patrick Gerland. Alex R. Cook. Leontine Alkema. "Global estimation and scenario-based projections of sex ratio at birth and missing female births using a Bayesian hierarchical time series mixture model." Ann. Appl. Stat. 15 (3) 1499 - 1528, September 2021.


Received: 1 June 2020; Revised: 1 November 2020; Published: September 2021
First available in Project Euclid: 23 September 2021

MathSciNet: MR4316659
zbMATH: 1478.62322
Digital Object Identifier: 10.1214/20-AOAS1436

Keywords: Bayesian hierarchical model , missing female births , probabilistic scenario-based projection , sex ratio transition , sex-selective abortion , time series analysis

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.15 • No. 3 • September 2021
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