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Risk of poor development in young children in low-income and middle-income countries: an estimation and analysis at the global, regional, and country level

Summary Background A 2007 study published in The Lancet estimated that approximately 219 million children aged younger than 5 years were exposed to stunting or extreme poverty in 2004. We updated the 2004 estimates with the use of improved data and methods and generated estimates for 2010. Methods We used country-level prevalence of stunting in children younger than 5 years based on the 2006 Growth Standards proposed by WHO and poverty ratios from the World Bank to estimate children who were either stunted or lived in extreme poverty for 141 low-income and middle-income countries in 2004 and 2010. To avoid counting the same children twice, we excluded children jointly exposed to stunting and extreme poverty from children living in extreme poverty. To examine the robustness of estimates, we also used moderate poverty measures. Findings The 2007 study underestimated children at risk of poor development. The estimated number of children exposed to the two risk factors in low-income and middle-income countries decreased from 279·1 million (95% CI 250·4 million–307·4 million) in 2004 to 249·4 million (209·3 million–292·6 million) in 2010; prevalence of children at risk fell from 51% (95% CI 46–56) to 43% (36–51). The decline occurred in all income groups and regions with south Asia experiencing the largest drop. Sub-Saharan Africa had the highest prevalence in both years. These findings were robust to variations in poverty measures. Interpretation Progress has been made in reducing the number of children exposed to stunting or poverty between 2004 and 2010, but this is still not enough. Scaling up of effective interventions targeting the most vulnerable children is urgently needed. Funding National Institutes of Health, Bill & Melinda Gates Foundation, Hilton Foundation, and WHO.


Chapter 1 Imputing missing data
(1) Imputing missing child population data for 6 countries We obtained country-level under-five populations from the United Nations Population Division (see data sources in Table A2). Six countries do not have estimates for under-five populations (American Samoa, Dominica, Kosovo, Marshall Islands, Palau, and Tuvalu), and their total population was about 0.03% of the total population in the 141 countries in 2004 and 2010. We did imputation by calculating the average proportion of under-five children in total populations by income groups. Data of a country's total population were obtained from the World Bank (see data sources in Table A2). We obtained the population of under-five children in the six countries by multiplying the average proportion of their income groups to their total populations.
(2) Imputing missing stunting prevalence data for 15 countries Child stunting in this study was defined as height-for-age below minus two standard deviations from the median of the international reference population recommended by the World Health Organization in 2006. 1 The WHO growth standards were developed from the WHO Multicentre Growth Reference Study by monitoring the growth of 8,500 healthy breastfed children in six diverse countries: Ghana, India, Norway, Brazil, Oman, and the United States. 1,2,3 By 2011, over 140 countries and most researchers had adopted these standards. 3 We gathered country-level estimates of stunting prevalence among under-five children from three sources): WHO, UNICEF, and the estimates published in The Lancet ( Table A2 in the webappendix). Stunting estimates from these three sources were constructed based on the 2006 WHO child growth standards. Estimates from the WHO and UNICEF were available for fewer than 30 countries in 2004 and 2010. The Lancet estimates provided the largest available estimates on stunting prevalence (and the 95% confidence intervals) for 126 countries in our sample in the two years. The Lancet estimates used Bayesian hierarchical mixture model to estimate the distribution of z-score by country and year when the micro-level data were not available for generating the stunting prevalence. 4 We chose to use The Lancet estimates in our study.
For the remaining 15 countries without The Lancet estimates (most were upper-middle income countries and their under-five children population was approximate 2% of the total in the 141 countries in the two years), we replaced their missing values in 2004 and 2010 with the average stunting prevalence of their income groups: our Ordinary Least Squares (OLS) regression analysis showed that country-level stunting prevalence was significantly inversely associated with the Gross Domestic Product (GDP) per capita (see Table A3 in the webappendix), suggesting that a country's prevalence of child stunting was likely to be driven by factors such as its income level, rather than regional location.  There were 32 countries (22 middle-income countries) without any poverty data between 2000 and 2012. Their under-five populations accounted for about 4.6% of total under-five population (from 141 countries) in 2004/2010 respectively. We replaced their missing values in the two years with the average poverty ratios by income groups in the respective year. We examined the relationship between poverty ratios and GDP per capita using OLS regression and found a significant inverse association between them (Table A3). We used the GDP per capita to predict the missing values. We compared the root-mean-square error (RMSE) between these two methods and found that the income average method yielded smaller RMSE than the regression method (see next section). We validated the linear trend assumption and compared our estimates to the ones generated from the method used in Grantham-McGregor et al. study (see next section). 3 We found that our imputed values have smaller root-mean-square error than the imputed values from the method of the

Validating linear interpolation/extrapolation for imputing missing poverty data
For countries with two or more estimates of poverty ratios between 2000 and 2012 but not in 2004 or 2010, we followed previous practices 1,2 and used linear interpolation or extrapolation to impute country missing values of poverty in 2004 and 2010. Linear interpolation or extrapolation could be most appropriate for variables with approximately linear trends, or slowly changing conditions in a relative short time frame. 3 To examine this assumption, we graphed the trends of poverty ratios for each country with 3 data points or more between 2000 and 2012 and found that most of the countries in most years followed approximately linear trends (see Figure  A1 in the webappendix). One limitation of this assumption is that we assumed no change in distribution of poverty.
The formula of linear interpolation or extrapolation is given as below. If t m < t x < t n , Y m < Y x < Y n , where t is the year, Y x is missing on poverty, and Y m and Y n are observed poverty ratios, then Y x could be interpolated as Y x = Y m + (t x -t m )*( Y n -Y m )/ (t n -t m ).
We also generated a set of estimates followed the Grantham-McGregor et al. study: using a generalized linear model with a logit link and binomial distribution, a commonly used model for regression with dependent variable as proportion data (values between zero and one), 4 and we generated predicted poverty estimates for each country in each year by regressing poverty estimates on stunting prevalence.
To compare the imputed value of missing poverty data generated from these two methods, we applied the rootmean-square error (RMSE) method. The RMSE measures the difference between imputed values and the observed values and is calculated as the square root of the mean of the squares of the deviations between predicted values and observed values. The smaller the RMSE is, the closer is the imputed value to the actual value, and the more accurate of the imputed value.
To perform the calculation on the RMSE, we first split the existing data into two groups: data used in regression (80% of the existing data), and data used for validation (20% of the existing data). We then conducted predictions with the 80% of the existing data using the two methods and obtained predicted values for the 20% of the validation data. We then calculated the difference between the predicted value obtained from each of the methods and actual value for the observations in the 20% validation data (see procedures in Figure A2). Finally, we obtained the RMSE for each method as shown in Table A4. For example, for extreme poverty measure, the RMSE is 0.025 from the linear interpolation/extrapolation and 0.077 from regression, suggesting that our method generated more accurate predicted values than the one in the Grantham-McGregor et al. study.
We provided Kernel Density plots to illustrate the distribution of actual values and two predicted values. As we can see, estimates derived from the linear extrapolation did well in all range of actual values, while estimates derived from regressions did not work well for actual value of extreme poverty ratio less than 0.2 ( Figure A3a), and moderate poverty ratio less than 0.4 ( Figure A3b).
We also calculated the correlation between actual values and the two predicted values: for extreme poverty ratios, the correlation is 0.987 between the actual values and the predicted values from our method and 0.861 between the actual values and the predicted values from the 2007 method. For moderate poverty, the correlation is 0.984 between the actual values and the predicted values from our method and 0.843 between the actual values and the predicted values from the 2007 method.

Validating methods for countries without any poverty data: income average vs. regression prediction
For countries without any poverty data (32 countries, 4.6% of total under-five population in 2004/2010 respectively), we used two methods to impute the missing data: (1) replacing the missing data with average poverty ratios of a country's income group, and (2) using a generalized linear model to predict the missing values with GDP per capita as a predictor. Using the same validation method as above, we calculated the RMSE from the two methods and found that the RMSE from the first method is smaller than the second method (Table  A5 ). In the analysis, we used imputed values from the average poverty ratios by income group.

Chapter 2 Estimating percentage of under-five children living in extreme or moderate poverty in a subset of countries using micro-level data
We used the World Bank's estimates of the percentage of total population living in extreme or moderate poverty and micro-level data to estimate country-level percentages of under-five children exposed to extreme or moderate poverty for a subset of countries.
We gathered nationally-representative household surveys which have variables on both child stunting and household wealth index scores between 2000 and 2012. The data includes 114 Demographic and Health Surveys (DHS) 1  We estimated the percentages of under-five children living in extreme or moderate poverty in the subset of countries with the following steps. First, we ranked the wealth index score of sampled household members with household weights. Second, we applied a country's poverty headcount ratio to the ranked wealth scores and located the cutoff point of extreme or moderate poverty in the ranked wealth index. For example, according to the World Bank, the 2004 extreme poverty headcount ratio in Bangladesh is 0.52. We used the Bangladesh DHS 2004 and ranked its household members' wealth index score with household weights. We then located the 52 th percentile of the ranked scores as the cutoff point for the extreme poverty. Third, all under-five children below the 52 th percentile were considered to be living in extreme poverty, and we found that 57% of under-five children lived in extreme poverty in 2004 in Bangladesh.
To impute missing values in 2004 and 2010, we conducted linear interpolation or extrapolation for countries with two or more surveys. For countries with only one survey before or after 2004 or 2010, we replaced the missing values with the estimates in these years. To validate estimation for child-level poverty ratios, we examined the correlation of poverty estimates between the total population and under-five population and the coefficient was 0.98, statistically significant at the 0.001 level. The summary of percentages of under-five children/total population living in poverty is presented in Table A7 in the webappendix. We did not observe a significant difference in the means of poverty ratios between the under-five populations and the total populations for the same group of countries. This may be due to the fact that more than half of the countries were not in the low-income group.   Number of children exposed to stunting or extreme poverty could be generated in two ways: (1) children stunted + children living in poverty but not stunted, or (2) children in poverty + children stunted but not in poverty. Both will yield the same numbers, but the components are different. We followed the 2007 study and took the first way: we estimated the number of children stunted and number of children exposed to poverty but not stunting.
With two dichotomous variables on stunting and poverty, we used the micro-level data gathered from 86 countries (as described above) to estimate percentage of under-five children living in extreme/moderate poverty but not stunted in 2004 and 2010.
For countries without surveys in 2004 and 2010, we used the estimate in the year that was closest to 2004 or 2010. We checked estimates of percentage of children living in extreme/moderate poverty but not stunted in countries with more than 5 percent of under-five children living in extreme or moderate poverty. For children living in extreme poverty, among 43 countries, 9 (highlighted) had significantly different estimates across years (21%) ( Table A8a). For children living in moderate poverty, among 50 countries, 16 (highlighted) had significant different estimates across countries (32%) ( Table A8b). There are non-significant differences in this estimate over time in most countries.
For the 53 countries without micro-level data (approximately 23% of the total child population), we replaced their missing values in the two years with the average percentage of children living in poverty but not stunted by their income groups. We also used the generalized linear model (GLM) to predict the missing value with the percentage of children in poverty but not stunted as the dependent variable and GDP per capita as a predictor. We compared the RSME derived from these two methods and found that the income average has smaller RSME than the GLM predictions (0.223 vs. 0.224 for extreme poverty, and 0.207 vs. 0.212). We used the imputed values derived from income average values.
The final estimates of the percentage of children living in extreme poverty but not stunted have a median of 58%/57% with inter-quartile range between 47%/39% and 64%/63% in 2004/2010. For the percentage of children living in moderate poverty but not stunted, the median was 63%/61% with an inter-quartile range between 57%/59% and 67%/68% in 2004/2010.

Chapter 4 Differences in 2004 estimates in the Grantham-McGregor et al. study and the present study
The The difference is likely attributable to improved data availability and quality in both stunting and poverty and imputation method as described in Table A9 . Stunting prevalence used in the present study was estimated with the WHO growth standards, rather than the National Center for

Missing data esti mates for poverty and stunting
Average prevalence of the region Linear ext rapolation or the average prevalence of the income group % of children li ving in poverty but not stunted Global estimate: 50% Country-level estimates with median 57% and inter-quartile range between 47% and 63% Figure A5 Number of children at risk by income when using moderate poverty measure