Annals of Applied Statistics

Space–time smoothing of complex survey data: Small area estimation for child mortality

Laina D. Mercer, Jon Wakefield, Athena Pantazis, Angelina M. Lutambi, Honorati Masanja, and Samuel Clark

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Many people living in low- and middle-income countries are not covered by civil registration and vital statistics systems. Consequently, a wide variety of other types of data, including many household sample surveys, are used to estimate health and population indicators. In this paper we combine data from sample surveys and demographic surveillance systems to produce small area estimates of child mortality through time. Small area estimates are necessary to understand geographical heterogeneity in health indicators when full-coverage vital statistics are not available. For this endeavor spatio-temporal smoothing is beneficial to alleviate problems of data sparsity. The use of conventional hierarchical models requires careful thought since the survey weights may need to be considered to alleviate bias due to nonrandom sampling and nonresponse. The application that motivated this work is an estimation of child mortality rates in five-year time intervals in regions of Tanzania. Data come from Demographic and Health Surveys conducted over the period 1991–2010 and two demographic surveillance system sites. We derive a variance estimator of under five years child mortality that accounts for the complex survey weighting. For our application, the hierarchical models we consider include random effects for area, time and survey and we compare models using a variety of measures including the conditional predictive ordinate (CPO). The method we propose is implemented via the fast and accurate integrated nested Laplace approximation (INLA).

Article information

Ann. Appl. Stat., Volume 9, Number 4 (2015), 1889-1905.

Received: November 2014
Revised: September 2015
First available in Project Euclid: 28 January 2016

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Zentralblatt MATH identifier

Bayesian smoothing infant mortality small area estimation survey sampling


Mercer, Laina D.; Wakefield, Jon; Pantazis, Athena; Lutambi, Angelina M.; Masanja, Honorati; Clark, Samuel. Space–time smoothing of complex survey data: Small area estimation for child mortality. Ann. Appl. Stat. 9 (2015), no. 4, 1889--1905. doi:10.1214/15-AOAS872.

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Supplemental materials

  • Supplement to “Space–time smoothing models for complex survey data: Small area estimation for child mortality”. The organization of the supplementary material is as follows. In Section 1 we provide the details of the discrete survival model. In Section 2 we provide the derivation of the standard error for U5M. Section 3 describes a simulation study aimed to test the coverage performance of the derived standard error against the jackknife standard error used by DHS. In Section 4 we describe the hyperprior specifications for the Bayesian hierarchical model. Section 5 provides a summary of the posterior distribution of the random effects. In Section 6 we provide a comparison of weighted and unweighted direct estimates of U5M. In Section 7 we have included some exploratory analysis looking at the rates and magnitude of regional decreases in U5M and how they relate to the fourth millennium development goal of two thirds reduction in child mortality by 2015. The results of our model validation are presented in Section 8. Lastly, Section 9 includes example R code for the analyses.