IJE vol.33 no.6 © International Epidemiological Association 2004; all rights reserved.
Advance Access publication 12 November 2004
International Journal of Epidemiology 2004;33:1260–1270
doi:10.1093/ije/dyh202
Methodology for estimating regional and
global trends of child malnutrition
Mercedes de Onis,1 Monika Blössner,1 Elaine Borghi,1 Richard Morris2 and Edward A Frongillo3
Accepted
17 March 2004
Background Child malnutrition is an important indicator for monitoring progress towards the
Millennium Development Goals (MDG). This paper describes the methodology
developed by the World Health Organization (WHO) to derive global and
regional trends of child stunting and underweight, and reports trends in
prevalence and numbers affected for 1990–2005.
National prevalence data from 139 countries were extracted from the WHO
Global Database on Child Growth and Malnutrition. A total of 419 and 388
survey data points were available for underweight and stunting, respectively. To
estimate trends we used linear mixed-effect models allowing for random effects
at country level and for heterogeneous covariance structures. One model was
fitted for each United Nation’s region using the logit transform of the prevalence
and results back-transformed to the original scale. Best models were selected
based on explicit statistical and graphical criteria.
Results
During 1990–2000 global stunting and underweight prevalences declined from
34% to 27% and 27% to 22%, respectively. Large declines were achieved in
Eastern and South-eastern Asia, while South-central Asia continued to suffer
very high levels of malnutrition. Substantial improvements were also made in
Latin America and the Caribbean, whereas in Africa numbers of stunted and
underweight children increased from 40 to 45, and 25 to 31 million, respectively.
Conclusion
Linear mixed-effect models made best use of all available information. Trends are
uneven across regions, with some showing a need for more concerted and
efficient interventions to meet the MDG of reducing levels of child malnutrition
by half between 1990 and 2015.
Keywords
Child, stunting, underweight, malnutrition, trends
Child malnutrition is internationally recognized as an important
public health indicator for monitoring nutritional status and
health in populations. The devastating effects of malnutrition
on human performance, health, and survival are today wellestablished1–6 and a recent global analysis demonstrated that
child malnutrition is the leading cause of the global burden of
disease.7,8 As a result of the increased recognition of the
relevance of nutrition as a basic pillar for social and economic
development, monitoring trends in childhood malnutrition has
gained increasing importance in assessing the progress made by
1 Department of Nutrition, World Health Organization, Geneva, Switzerland.
2 Royal Free and University College Medical School, London, UK.
3 Division of Nutritional Sciences, Cornell University, Ithaca, New York, USA.
Correspondence: Dr Mercedes de Onis, Department of Nutrition, World
Health Organization, 1211 Geneva 27, Switzerland. E-mail:
deonism@who.int
nations in achieving internationally set goals, such as the
Millennium Development Goals.9 The objective of this paper is
to describe the methodology developed and applied by the
World Health Organization (WHO) to calculate regional and
global estimates of childhood underweight and stunting and to
report trends from 1990 to 2005. This analysis is an update of
earlier trend modelling10 using additional data points that have
become available subsequently and new population estimates.
Material and Methods
Data
To estimate regional and global trends in child stunting and
underweight, national prevalence of low height-for-age and
low weight-for-age (2 standard deviation (SD) of the
National Center for Health Statistics/World Health Organization
international reference population) were derived from the
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Methods
TRENDS IN CHILD MALNUTRITION
Statistical analysis
Fitting trends for the sub-regions of developing countries
The methodology of linear mixed-effect models, as described by
Laird and Ware13 was used for modelling the data set at subregional levels with countries’ effect being defined as random.
The model used is part of a more general class of models, the
multilevel models. In the multilevel modelling literature,
notably in Goldstein,14 the same model is called a ‘two-level
model’, counting the levels of variation, i.e. level one the survey
and level two countries. By regarding countries within a subregion as random effects, our analysis was able to exploit the
common influences throughout the sub-region.
One single linear mixed-effect model was considered for each
group of sub-regions belonging to the same region. The basic
model contained the fixed factors sub-region and year, the
interaction between year and the sub-region as fixed effects, and
country as random effect. Consequently we obtained from each
model an intercept and a slope estimate for every sub-region
within the region.
One of the advantages of a mixed-effect model over a fixedeffect model is that the former allows for both correlation
within level (countries) and heterogeneous variances, although
the mixed effect models assume normality for the errors in both
cases.15 We considered three different structures for modelling
the covariance: compound symmetric, unstructured, and autoregressive of order 1. The compound symmetry model for a
region allows the country to have its own intercept (influencing
prevalence estimate) and forces all countries to have a common
slope in prevalence over time. The unstructured model for a
region allows each country to have its own intercept and slope.
The auto-regressive model of order 1 allows for correlations
between observations within the same country to weaken as
the time between them increases (see Appendix 1 for model
details). Year was centred at the year 1995, around which there
was a high concentration of available survey data points.
Restricted maximum likelihood estimation method was used, as
well as robust estimators for estimating the fixed-effect
estimates of standard deviations.16
The fitting was performed on the logistic transform (‘logit’) of the
prevalence. This transformation ensured that all prevalence
estimates and their CI would lie between zero and one. The
inherent properties of the logit transform meant (1) that trend lines
would curve, decreasing at a slower rate, as zero prevalence was
approached, and (2) CI for prevalence estimates close to zero were
asymmetric and narrower than for values close to 50%.17 Because
estimates were calculated on the logit scale, prevalence estimates
and their respective CI were derived by back-transformation.
To account for the different country populations and ensure
that the influence in the regional trend analysis of a country’s
survey estimate was proportional to the country’s population,
we carried out weighted analysis. The population weights were
derived from the UN Population Prospects, revision 2000.12 For
each data point, we obtained the respective under-5 population
estimate for the specific survey year. If a survey was performed
over an extended period, for example 1995–1997, the mean
year, i.e. 1996, was used as the year from which to choose the
respective population estimate. For countries with multiple data
points the weights were calculated by dividing the mean of the
country’s under-5 population (over the observed years) by the
sum of the countries’ mean population in the whole region.
Weights of countries with single data points were derived by
dividing the under-5 population at the time of the survey by the
sum of the countries’ mean population in the whole region.
The decision on how to choose the best model among different
covariance structures was based on the model-fit criterion
Akaike’s Information Criterion (AIC), which is essentially loglikelihood values penalized for the number of parameters
estimated.15 Lower AIC values mean better fit. In parallel, we
examined the graphed display of the fitted trend line against the
survey data points and discarded models which did not present
a reasonable fit with respect to the empirical data.
Analysis of the residuals indicated significant departure from
normality at the 5% level of significance for only two of the
sub-regions of Latin America, one sub-region in Asia, and one
in Africa. The application of a more general class of models, the
generalized mixed-effect models which allows for the errors to
have, for example, a binomial distribution, was considered.
However, the increase in complexity compared with the limited
gain in using this class of models, and in the interest of keeping
a common approach for all the regions, we decided to use the
simpler approach, the linear mixed-effect models with a robust
estimator for the CI.
The linear trend fitting was adequate, and therefore we did not
fit higher-order polynomials. The final models were then used to
project the trend of underweight and stunting in children from
1990 to 2005. Using the resulting prevalence estimates (after
back-transformation), the total numbers of affected were
calculated with a spreadsheet multiplying the prevalence and
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WHO Global Database on Child Growth and Malnutrition
(www.who.int/nutgrowthdb, version January 2003).11
A total of 419 nationally representative surveys giving a
prevalence for underweight were available from 139 countries.
For 98 countries, national survey data were available from at
least 2 surveys and 61 countries had at least 3 surveys. For
stunting, 388 national representative survey data points were
available from 138 countries. For 96 countries, at least 2 survey
data points were available, and for 56 countries at least 3 data
survey points were included in this analysis.
Countries providing data were regarded as a representative
sample of all countries within their sub-region. Several subregions constitute a region. For example within the region of
Asia there are four sub-regions: Eastern, South-central, Southeastern, and Western Asia. Hence the data present different
hierarchical levels, i.e. at the bottom the countries, then subregions, then regions, then the group of all developing regions,
and finally global which includes all the regions of developing
countries (i.e. Africa, Asia, Latin America and the Caribbean,
and Oceania) plus the group of developed countries. Regions
and sub-regions were defined according to the UN country
classification system.12
A data file was constructed consisting of the variables: region,
sub-region, country, survey year, sample size, minimum and maximum
age surveyed, prevalence of stunting, prevalence of underweight,
and country population of under 5 year olds at the respective
survey year. The methodology followed to obtain standardized
country prevalence of underweight and stunting has been
described elsewhere.11 The comprehensive list of national
prevalence data and their sources included in this analysis are
available from authors on request.
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INTERNATIONAL JOURNAL OF EPIDEMIOLOGY
lower and upper limits of the CI by the sub-regional population
derived from the UN population estimates.12
Fitting trends for the group of developed countries
Twenty-one observations were for the developed countries.
Given that we had few data points and considering the relative
homogeneity of the group, we fitted a linear mixed-effects
model in the same way as described above for the trend in subregions, having as fixed effects only year, and keeping country as
random effect. There was some departure from normality for
the residuals, but we considered that there were too few data
points to justify moving to a more complex class of models, like
the generalized linear mixed-effect models.
Global prevalence estimates and CI
The global prevalence estimates and respective CI were
calculated using the same methodology as described for the
regional estimates, but adding up regional estimated numbers of
affected plus the number of affected for the developed countries
group and the number of affected for Oceania.
For the region of Oceania, there were only six data points and,
therefore, we estimated the overall prevalence trend using a simple
linear regression. The resultant prevalence estimate, the standard
error and corresponding numbers of affected were used only to add
up the total global number of affected children in order to obtain
the global prevalence estimate and respective standard error.
The first step in the process of deciding on the covariance model
was to check the AIC fit statistics, being the smaller the better.
Table 1 presents the comparison of AIC fit statistics for stunting
and underweight by UN regions.
As a second step we produced graphs of the data to inspect
the fit of the empirical data points to the modelled trend line.
Figures 1–6 show the plots of the individual survey estimates
(circles) against the estimated model trend line for the final
selected models; the sizes of the circles indicating the weighted
contribution according to the population size in the country
within the region. The size of country populations influences
the trend. For example, for underweight in Eastern and
Western Africa (Figure 4), two of the worst regions in terms of
trend, there seems to be a ‘large country’ effect in that the larger
countries have the highest prevalence. This also works through
to a ‘large sub-region’ effect with Eastern and Western Africa
being the largest two sub-regions in Africa and their prevalence
being the worst and third worst in this region.
For stunting, discrepancies between fitted and empirical values
were noticed for Africa (Northern Africa) and Asia (Eastern Asia),
when considering the covariance model with the lowest AIC. We
thus rejected that model and selected the next best AIC value
(Figures 1 and 2). For underweight, model decision was based on
AIC value for Africa and Latin America & the Caribbean while in
the case of Asia we took a final decision on the basis of the plot.
For the latter, the graphs based on the unstructured covariance
model (which had the smallest AIC value) did not fit the
empirical data points for South-central and Eastern Asia (too low
and not giving appropriate weight to the India survey data; too
low and not giving appropriate weight to the China data). As with
stunting, we rejected that model and selected the next best AIC
value, i.e. compound symmetry (Figure 5). Tables 2 and 3 present
the prevalence and number of stunted and underweight children,
respectively, from 1990 to 2005.
Discussion
The methodology that we have developed was primarily
intended to produce precise and accurate estimates of progress
made in reducing child malnutrition at the sub-regional,
Table 1 Fitted models’ AICa statistics for stunting and underweight by UN regions (✓ indicating selected models)
Regions
Unstructured
Compound symmetry
Autoregressive
Africa
200.3b
249.9✓
256.8
Asia
187.7c
207.5✓
Did not converge
192.8✓
244.3
Did not converge
Stunting
Latin America & Caribbean
Underweight
Africa
204.5✓
245.0
260.9
Asia
165.2d
187.2✓
Did not converge
Latin America & Caribbean
195.7✓
208.0
Did not converge
a Akaike’s Information Criterion.
b Did not reflect empirical trend in Northern Africa.
c Did not reflect empirical trend in Eastern Asia.
d Did not reflect empirical trends in Eastern Asia and South-central Asia.
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Prevalence estimates and CI for the regions of developing
countries
For the regional level, an attempt was made to fit an overall
model considering all the countries within the region, including
a model with random effects for the sub-region trends. For some
regions there was a significant interaction between year and subregion, because different sub-regions presented different trends
on the logistic scale. This resulted (after back-transformation) in
numbers of malnourished children at the regional level that did
not match the sum of the sub-regional totals. We therefore
adopted the approach of estimating the prevalence for the region
using the sum of the estimated numbers of affected in the subregions divided by the total under-5 population of that region.
This overall regional estimate is thus the weighted average of the
sub-region prevalence estimates (weighted by the respective
under-5 population proportions). The CI were estimated using
the delta method (Appendix 2 for formulae).
Results
TRENDS IN CHILD MALNUTRITION
1263
Figure 2 Empirical stunting prevalence (circles) plotted against estimated model trend (line) using compound symmetry covariance
structure: Asia
regional, and global levels. The basic elements of the
methodology are: (1) estimation for each sub-region, using
country-level population weights and assuming linear trend, (2)
aggregation from sub-region to region to global using
population weights, (3) estimation using random intercept and
slope models where data allow and give reasonable results, with
simplification to random intercept only models where data do
not allow or do not give reasonable results, (4) use of all
available country data (i.e. use of all countries that have data
and use of all quality data for each country), including countries
with only one survey, (5) use of an explicit, multilevel statistical
model, (6) use of the delta method to calculate approximate
standard errors and CI when an exact formula does not exist.
There are a number of advantages of this methodology. First,
multilevel modelling has become a standard approach for this
type of task, since software to fit these models became widely
available in the past decade. The model specifies the structure
across levels through the random effects, the relations among
the fixed effects, and the form of the dependency among the
residuals (i.e. covariance structure). The use of an explicit
statistical model means that assumptions and postulated
features of the model (e.g. relations among variables) can be
clearly stated and examined.
Second, all available country data points are used, including
countries with one data point. This is important for getting the
best (i.e. most precise and accurate) estimates of prevalence. A
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Figure 1 Empirical stunting prevalence (circles) plotted against estimated model trend (line) using compound symmetry covariance
structure: Africa
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INTERNATIONAL JOURNAL OF EPIDEMIOLOGY
Figure 4 Empirical underweight prevalence (circles) plotted against estimated model trend (line) using unstructured covariance with random
intercepts and slopes: Africa
country with only one survey contributes to the prevalence
estimate for its sub-region, even though it does not contribute
to the estimate of progress over time. The methodology uses all
surveys that are available for a country, and does not require
that the survey years for each country are the same.
Furthermore, as is desirable, countries with data throughout the
interval of interest will have more influence on the trend than
countries with data from only a part of the interval of interest.
Third, although we assumed for our analyses a linear (i.e.
straight-line) trend among variables, the methodology can
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Figure 3 Empirical stunting prevalence (circles) plotted against estimated model trend (line) using unstructured covariance with random
intercepts and slopes: Latin America & Caribbean
TRENDS IN CHILD MALNUTRITION
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Figure 6 Empirical underweight prevalence (circles) plotted against estimated model trend (line) using unstructured covariance with random
intercepts and slopes: Latin America & Caribbean
easily incorporate deviations from the linear trend. This can be
done by specifying second-degree and higher polynomial terms.
In this analysis we examined this and no evidence of non-linear
relationships was found for any region.
Fourth, the fact that not all the countries have available
underweight and/or stunting prevalence data has to be
considered and incorporated in the model. The best way to do
this is to include countries as random effects in the model, under
the assumption that the countries without data are missing at
random.19,20 This also allows exploitation of common influences
operating on the prevalence of underweight and stunting for
countries when making estimates for the sub-region.
Fifth, specifying random intercept and slope models means
that the trend in each country with multiple surveys is captured
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Figure 5 Empirical underweight prevalence (circles) plotted against estimated model trend (line) using compound symmetry covariance
structure: Asia
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INTERNATIONAL JOURNAL OF EPIDEMIOLOGY
Table 2 Estimated prevalence and numbers of stunted preschool children 1990–2005 with 95% CI
UN regions and
sub-regions
% Stunting
No. stunted (in millions)
1995
2000
2005
1990
1995
2000
2005
36.9
33.3–40.5
36.1
33.0–39.1
35.2
32.5–38.0
34.5
31.7–37.4
39.6
35.7–43.5
41.9
38.4–45.5
45.1
41.6–48.7
48.5
44.5–52.6
Eastern
44.4
36.6–52.4
44.4
37.3–51.8
44.4
37.6–51.4
44.4
37.6–51.4
15.8
13.0–18.7
17.3
14.5–20.2
19.4
16.5–22.5
21.6
18.3–25.0
Middle
42.2
34.2–50.5
40.0
34.0–46.2
37.8
33.7–42.1
35.8
33.0–38.6
5.6
4.5–6.7
6.3
5.4–7.3
6.8
6.0–7.6
7.4
6.9–8.0
Northern
27.4
21.1–34.7
24.4
18.7–31.2
21.7
16.1–28.6
19.1
13.5–26.5
5.8
4.5–7.4
5.1
3.9–6.5
4.6
3.4–6.1
4.2
2.9–5.8
Southern
25.4
23.7–27.1
25.0
22.6–27.6
24.6
21.5–28.1
24.3
20.4–28.6
1.5
1.4–1.6
1.4
1.3–1.6
1.5
1.3–1.7
1.4
1.2–1.7
Western
34.7
28.7–41.2
33.8
29.9–37.9
32.9
30.2–35.7
32.0
28.4–35.7
10.9
9.0–13.0
11.8
10.4–13.2
12.7
11.7–13.8
13.9
12.4–15.5
41.1
38.6–43.6
35.4
32.6–38.2
30.1
27.1–33.1
25.7
154.6
130.8
22.5–28.9 145.1–164.1 120.5–141.0
109.4
98.6–120.2
92.4
80.9–103.8
Eastern
30.0
28.7–31.3
21.5
20.4–22.6
14.8
13.9–15.8
10.0
9.3–10.7
37.5
35.9–39.1
23.5
22.3–24.7
15.2
14.3–16.1
9.5
8.8–10.2
South-central
50.8
46.1–55.4
45.2
40.2–50.3
39.7
34.4–45.3
34.5
29.0–40.5
88.0
79.9–96.0
81.0
72.0–90.2
71.5
62.0–81.6
63.5
53.3–74.4
South-eastern
41.8
33.6–50.4
36.8
29.3–44.9
32.1
25.2–39.7
27.7
21.3–35.1
23.9
19.2–28.8
21.3
17.0–26.0
18.1
14.3–22.5
15.3
11.8–19.4
Western
25.0
20.2–30.4
21.7
15.1–30.1
18.7
10.9–30.1
16.1
7.8–30.3
5.2
4.2–6.3
5.0
3.5–6.9
4.5
2.7–7.3
4.1
2.0–7.8
18.3
13.6–23.0
15.9
11.3–20.5
13.7
9.1–18.4
11.8
7.0–16.5
10.0
7.4–12.6
8.8
6.2–11.3
7.6
5.0–10.2
6.5
3.9–9.2
12.4
6.8–21.5
9.6
5.1–17.3
7.4
3.8–14.1
5.7
2.7–11.5
0.5
0.3–0.9
0.4
0.2–0.7
0.3
0.1–0.5
0.2
0.1–0.4
Central America
25.9
16.3–38.4
23.0
14.4–34.8
20.4
12.5–31.5
18.0
10.8–28.4
4.0
2.5–5.9
3.7
2.3–5.6
3.3
2.0–5.1
2.9
1.8–4.6
South America
15.7
10.8–22.2
13.3
8.6–20.0
11.3
6.5–18.9
9.6
4.9–18.2
5.5
3.8–7.8
4.7
3.0–7.1
4.0
2.3–6.7
3.4
1.7–6.5
n/aa
n/a
n/a
n/a
n/a
37.9
35.9–39.8
33.5
31.4–35.6
29.3
7.9–66.7
29.6
27.5–31.7
2.8
0.8–9.1
2.8
0.8–8.9
2.7
0.8–8.7
2.6
0.8–8.4
2.2
0.7–7.1
2.0
0.6–6.4
33.5
29.5–44.9
29.9
23.0–40.0
26.7
17.4–35.5
Africa
Asia
Latin America & Caribbean
Caribbean
Oceania
All developing countries
Developed Countries
Global
0.32
n/a
0.09–0.72
26.5
204.3
181.5
162.1
147.5
24.2–28.7 193.7–214.9 170.4–192.7 150.4–173.8 135.0–159.9
1.8
0.5–5.7
1.6
0.5–5.2
24.1
206.5
183.5
163.9
149.1
12.9–31.4 195.7–217.2 172.2–194.8 152.1–175.7 136.6–161.6
a Not available due to insufficient data.
well by the model. This results in a more precise model than if
only random intercepts are used, and is more realistic than
assuming that all countries in a sub-region progress similarly.
Furthermore, constructing overall regional and global
prevalence estimates by using the sub-regional estimates is
preferred, considering the relative homogeneity within subregions, except for the case of South-central Asia. The
heterogeneity found in this sub-region would have justified
splitting it into two distinct groups; however, we chose not to do
so to maintain this UN sub-region as an entity and to be
consistent with the country grouping used in earlier reports.
Sixth, the methodology yields explicit estimates of
uncertainty in the form of CI. When needed, the delta method
was used to estimate standard errors by using a Taylor series
expansion to obtain the asymptotic distribution, a standard
technique for this purpose. The delta method produces an
estimator of the standard error that is straightforward and
intuitive.
Seventh, the methodology can theoretically provide countrylevel estimates that are statistically most efficient by using
principles of shrinkage (i.e. empirical Bayes in this case)
estimation that borrow information from neighbouring
countries when a given country has limited data.18 This
approach has been highly successful in small-area estimation,
for example. Whether this theoretical advantage can be realized
in this case, however, is not clear. Most countries may not
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1990
TRENDS IN CHILD MALNUTRITION
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Table 3 Estimated prevalence and numbers of underweight preschool children 1990–2005 with 95% CI by UN regions and sub-regions
UN regions and
sub-regions
% Underweight
No. underweight (in millions)
1995
2000
2005
1990
1995
2000
2005
23.6
21.0–26.2
23.9
21.5–26.3
24.2
21.9–26.4
24.5
22.1,26.8
25.3
22.6–28.1
27.8
25.0–30.6
30.9
28.0–33.8
34.5
31.1–37.8
Eastern
26.7
22.0–32.0
27.9
23.3–33.0
29.2
24.6–34.3
30.6
25.7–35.8
9.5
7.8–11.4
10.9
9.1–12.9
12.8
10.8–15.0
14.8
12.5–17.4
Middle
27.8
19.8–37.5
26.9
21.0–33.8
26.1
21.8–30.8
25.3
21.6–29.3
3.7
2.6–5.0
4.2
3.3–5.3
4.7
3.9–5.5
5.3
4.5–6.1
Northern
12.3
7.4–19.6
10.9
5.9–19.4
9.7
4.6–19.4
8.6
3.6–19.5
2.6
1.6–4.1
2.3
1.2–4.1
2.1
1.0–4.2
1.9
0.8–4.3
Southern
14.0
9.9–19.5
13.9
9.8–19.2
13.7
9.7–19.0
13.6
9.6–18.8
0.8
0.6–1.1
0.8
0.6–1.1
0.8
0.6–1.2
0.8
0.6–1.1
Western
27.8
23.6–32.4
27.5
24.2–31.0
27.1
24.2–30.3
26.8
23.6–30.3
8.8
7.4–10.2
9.6
8.4–10.8
10.5
9.4–11.7
11.7
10.3–13.2
35.1
31.7–38.5
31.5
27.8–35.1
27.9
24.0–31.7
24.8
20.8–28.8
131.9
119.2–144.7
116.3
102.7–129.8
101.2
87.3–115.0
89.2
74.9–103.5
Eastern
18.5
17.6–19.4
13.2
12.5–13.9
9.3
8.8–9.9
6.5
6.1–6.9
23.1
22.0–24.2
14.5
13.7–15.3
9.5
9.0–10.1
6.1
5.7–6.5
South-central
49.6
42.4–56.8
45.2
37.9–52.6
40.8
33.5–48.5
36.5
29.3–44.4
86.0
73.5–98.5
80.9
67.9–94.3
73.4
60.3–87.3
67.1
53.9–81.5
South-eastern
35.2
30.8–40.0
31.2
27.1–35.6
27.4
23.4–31.8
23.9
19.9–28.5
20.2
17.6–22.9
18.1
15.7–20.7
15.5
13.2–18.0
13.2
11.0–15.7
12.9
9.9–16.7
12.1
7.3–19.4
11.3
5.0–23.7
10.6
3.3–28.9
2.7
2.1–3.5
2.8
1.7–4.5
2.8
1.2–5.8
2.7
0.9–7.5
8.7
6.1–11.3
7.3
5.0–9.6
6.1
4.0–8.1
5.0
3.2–6.8
4.8
3.4–6.2
4.0
2.8–5.3
3.4
2.2–4.5
2.8
1.8–3.8
Caribbean
10.0
5.9–16.4
7.8
4.5–13.3
6.1
3.3–10.8
4.7
2.5–8.7
0.4
0.2–0.7
0.3
0.2–0.5
0.2
0.1–0.4
0.2
0.1–0.3
Central America
12.4
7.5–19.9
10.7
6.3–17.6
9.2
5.2–15.7
7.9
4.3–14.0
1.9
1.2–3.1
1.7
1.0–2.8
1.5
0.9–2.6
1.3
0.7–2.3
South America
7.0
4.5–10.8
5.7
3.6–8.9
4.6
2.9–7.4
3.7
2.3–6.1
2.5
1.6–3.8
2.0
1.3–3.1
1.6
1.0–2.6
1.3
0.8–2.2
n/a
n/a
n/a
Africa
Asia
Western
Latin America & Caribbean
Oceania
All developing countries
Developed Countries
Global
n/aa
n/a
n/a
n/a
n/a
30.1
27.6–32.5
27.3
24.8–29.9
24.8
22.2–27.3
22.7
20.1–25.4
162.2
149.1–175.3
1.6
0.8–3.0
1.4
0.6–3.2
1.3
0.5–3.5
1.1
0.3–3.7
1.2
0.6–2.4
26.5
24.3–28.6
24.3
22.1–26.6
22.2
19.9–24.5
20.6
18.2–22.9
163.4
150.3–176.6
148.2
135.5
126.5
134.4–162.0 121.3–149.7 111.8–141.2
1.0
0.4–2.3
0.8
0.3–2.3
0.7
0.2–2.3
149.2
136.4
127.2
135.3–163.1 122.2–150.6 112.5–141.9
a Not available due to insufficient data
accept an estimate for their country that is statistically adjusted
with data borrowed from other countries.
As shown in Table 1, in all three regions, for both stunting
and underweight, the unstructured covariance model with
random intercepts and slopes presented lower AIC than did the
compound symmetry covariance model with random intercepts
only (the auto-regressive structure performed worst in all
cases). However, in three out of six cases the model with the
lowest AIC was rejected in favour of the model with fixed effect
for the slope (i.e. compound symmetry) because the estimated
trend line did not reflect the empirical trend (footnotes to
Table 1). The fact that models with random slopes fitted better
than models with fixed slopes indicates that there is
heterogeneity between trends in prevalence at the country
level. As can be seen in Figure 5, there appear to be some
outliers which have lower levels of prevalence of underweight
in South-central Asia in surveys conducted from 1995 to 2000.
If these countries had earlier surveys, the sub-regional trend
line might have been steeper. There also appear to be outliers in
the graphs for stunting in Northern Africa and Eastern Asia that
would also might have impact the sub-regional trends if they
had earlier surveys (Figures 1 and 2). For these sub-regions we
therefore decided to use the model with fixed effect for the
slope, that is less affected by outliers and fitted better the
empirical data.
While the methodology described above presents various
strengths, there are also some inherent weaknesses. One
potential drawback is its complexity. Although it has become a
standard approach for many applications—and software is
included in most of the statistical packages—mixed-effect
model fitting requires understanding and caution to ensure
appropriate use. In this analysis, both sound knowledge of the
Downloaded from http://ije.oxfordjournals.org/ by guest on June 15, 2015
1990
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INTERNATIONAL JOURNAL OF EPIDEMIOLOGY
estimated 333 000 children below 5 years of age died in 1999
with HIV infection21 and 11 million are estimated to be
orphaned because of AIDS.22 The predictions of stunting and
underweight made for 2005 might be underestimates if the
HIV/AIDS epidemic worsens in Africa or other regions.
The overall reduction in the prevalence of underweight is
consistent with the increasing rates in childhood overweight
observed in many developing countries. A recent global analysis
reported that 16 of the 38 developing countries with more than
one national survey available, showed a rising trend in
childhood overweight.23 The comparison of both ends of the
weight-for-height distribution suggest a population-wide shift,
with overweight replacing wasting as countries undergo the
nutrition transition.23 Because of this transition, indicators
of malnutrition based on weight will be more complex to
interpret, and stunting will increasingly provide a more
accurate indication of undernutrition than will underweight.
Overall, our analyses show that progress in reducing child
malnutrition has been uneven in distinct regions of the world
and some areas even show an aggravating situation. To achieve
the Millennium Development target for reduction of hunger,9
more concerted efforts are needed in those regions with
stagnating and increasing trends of malnutrition, but without
diminishing support to those which show progress, given that
this is where the majority of children are still to be found.
Well-nourished children have a better chance of surviving, of
learning more easily, and of growing into healthy adults who in
turn can give their children a better start in life. The three pillars
for improving nutritional status are: adequate and safe food
intake, freedom from illness, and appropriate family care. Key
strategies for achieving the latter include improved
breastfeeding and complementary feeding practices. To reduce
malnutrition in a sustained manner, there is also a need for
micro-nutrient supplementation and fortification, the provision of medical services to help reduce infectious diseases,
improvements in access to clean water and sanitation, and
increased education.24 Above all, to set the stage for enabling
progress along these lines, all populations need peace as well as
good governance and equitable distribution of national and
international resources. Only when optimal child growth is
ensured for the majority will governments be successful in their
efforts to accelerate economic development in a sustained way.
KEY MESSAGES
•
During the 1990s, rates of child malnutrition improved, as measured by declines in the prevalence of both stunting
(34–27%) and underweight (27–22%).
•
Large improvements were achieved in Eastern and South-eastern Asia, while South-central Asia continues to suffer
very high levels of malnutrition. Substantial progress was also made in Latin America and the Caribbean.
•
In Africa numbers of stunted and underweight children increased from 40 to 45 and 25 to 31 million, respectively.
•
More concerted and efficient interventions are needed to meet the Millennium Development Goal of reducing levels of
child malnutrition by half between 1990 and 2015.
•
Linear mixed-effects models have several strengths which make them advantageous to other approaches in deriving
trends of child malnutrition.
Downloaded from http://ije.oxfordjournals.org/ by guest on June 15, 2015
nutritional situation in countries and the expertise in developing
models were needed to derive valid estimates. Alternatively, the
use of individual simple regression models at country level
would be conceptually more straightforward, but would lack the
ability to deal with the complexities of the data that are available
for global, regional, and sub-regional monitoring.
Another limitation of this methodology is a by-product of one
of its biggest advantages. The fact that the model enables
inclusion and achieves best use of all the available information for a region, assuming relative homogeneity within subregions, makes it highly dependent on the country grouping.
Consequently, overall estimates can be different depending on
what regional classification is applied. To overcome this
problem, it is recommended to present trends always using the
same regional classification.
There has been global progress in the reduction of child
malnutrition during the 1990s, with stunting and underweight
prevalence declining from 34% to 27% and 27% to 22%,
respectively (Tables 2 and 3). The largest decline was achieved
in Eastern Asia where stunting and underweight levels
decreased by one-half between 1990 and 2000. South-eastern
Asia also experienced substantial improvements with stunting
rates declining from 42% to 32% and underweight from 35%
to 27%. South-central Asia continues to suffer from
staggeringly high levels of child malnutrition but rates are
showing significant declines in stunting, from 51% to 40% and
underweight from 50% to 41% during this period. Substantial
improvements were also made in Latin America and the
Caribbean where a relative decrease of 25% in stunting (from
18% to 14%) and one-third in underweight (from 9% to 6%)
occurred over the last 10 years. In Africa, however, there has
been little or no change in the last decade, and 35% and 24%
of all under 5s remain stunted and underweight, respectively.
The actual number of malnourished children in Africa has
actually increased between 1990 and 2000, from 40 to 45
million stunted and 25 to 31 million underweight. The lack of
progress observed in Africa is likely to be partly due to the effect
of the human immunodeficiency virus (HIV)/AIDS epidemic.
The disease has both a direct and indirect effect: infected
children are more likely to be underweight, but also AIDS
orphans or children of parents affected by AIDS are at increased
risk of becoming malnourished. In sub-Saharan Africa, an
TRENDS IN CHILD MALNUTRITION
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Appendix 1
Structures for modelling the covariance
(1) Statistical model for the compound symmetric structure
within countries:
yij = logit(pij) = β0 sub-region + β1 sub-region ⫻ yearj + bi + ij,
bi ⬃ N(0, 2s I)
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11 de Onis M, Blössner M. The WHO Global Database on Child Growth
and Malnutrition: methodology and applications. Int J Epidemiol
2003;32:518–26.
12 United Nations. Department of Economic and Social Affairs, UN
Biometrics 1982;38:963–74.
ij ⬃N(0, R),
with
sub-region representing a class variable associated with the subregions in the region,
β0 and β1 representing, respectively, the intercept and slope
sub-region effects,
bi is the random effect associated with the ith country,
εij is the random error associated with the ith country’s at time j,
bi and εij independent.
The matrix R is block diagonal with Σ being the ith block
diagonal element of R, associated with the vector of
observations for the ith country over time. In the case of
compound symmetry, Σ is such that
Population Division. World Population Prospects, the 2000 Revision. Vol. ii:
the Sex and Age Distribution of the World Population. New York: United
Nations, 2001.
13 Laird NM, Ware JH. Random-effects models for longitudinal data.
and
Var(yij) ⫽ 2s ⫹ 2T
and
Cov(yij, yij) ⫽ 2S .
(2) Statistical model for the unstructured covariance matrix
with random intercept and random slopes:
14 Goldstein H. Multilevel Statistical Models. 2nd Edn. London: Arnold, 1995.
15 Littell RC, Milliken GA, Stroup WW, Wolfinger RD. SAS System for
Mixed Models. Cary: SAS Institute Inc., 1996.
yij = logit(pij) = β0 sub-region + β1 sub-region ⫻ yearj + b0i
+ b1i yearj + ij,
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22 UNICEF. The State of the World’s Children 2004. New York: UNICEF, 2004.
bi ⬃ N(0, 冱)
and
ij ⬃ N(0,T2 I),
with
sub-region representing a class variable associated with the subregions in the region,
β0 and β1 representing, respectively, the intercept and slope
sub-region effects,
bI = (b0i, b1i) is the random effect vector associated with the ith
country’s parameters intercept and slope,
ij is the random error associated with the ith country’s at time j.
This model was used with the unstructured covariance model,
allowing the variances of b0i and b1i and the correlation
between them to be estimated.
Downloaded from http://ije.oxfordjournals.org/ by guest on June 15, 2015
an underlying cause of child deaths associated with diarrhea,
pneumonia, malaria and measles. Am J Clin Nutr 2004;80:193–8.
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INTERNATIONAL JOURNAL OF EPIDEMIOLOGY
and the back-transform function is given by:
Appendix 2
Formulae prevalence estimates and CI for the
regions
For a region with n sub-regions with under-5 populations given
by Ni (i = 1,…,n) and prevalence estimates given by p̂i, the
overall prevalence estimator is given by:
兺
兺
s.e.(p)
ˆ
n
i1 Ni
冢1 p冣
y g(p) ln
p
冥 [s.e.(yˆ )] pˆ (1 pˆ )
h(yˆ i)
ŷi
2
i
i
i
s.e.(ˆyi),
where p̂i’s are the sub-regional estimates on the logit scale.
Hence, we were able to calculate an approximate standard error
for the regional prevalence estimate p̂, which is given by:
冪冤
兺
n
N2i [s.e(pˆ i)]2
i1
s.e.(p)
ˆ
兺
冥
2
n
i1
Ni
An approximate 95% CI for the overall region prevalence
estimate was then derived by applying a normal range, i.e.:
LowerCL = p̂ 1.96 s.e.(p̂)
and
UpperCL = p̂ 1.96 s.e.(p̂)
Downloaded from http://ije.oxfordjournals.org/ by guest on June 15, 2015
The CI for the sub-regions were derived by back-transforming
the lower and upper limits at the logit scale. For constructing a
confidence interval for the overall region prevalence estimate,
the associated standard error had to be estimated. To do that, we
derived approximated standard errors associated with the subregions’ prevalence estimates p̂i’s using the delta method, which
involves a Taylor series approximation of the logit backtransform function.15,18 The logit function is:
ey
1ey
Applying the delta method, the standard error of the sub-region
prevalence estimates is given by:
冪冤
n
i1Ni p̂i
pˆ
h(y) g1(y)