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Background Child health interventions were drastically scaled up in the period leading up to 2015 as countries aimed at meeting the 2015 target of the Millennium Development Goals (MDGs). MDGs were defined in terms of achieving improvements in average health. Significant improvements in average child health are documented, but evidence also points to rising inequality. It is important to investigate factors that drive the increasing disparities in order to inform the post-2015 development agenda of reducing inequality, as captured in the Sustainable Development Goals (SDGs). We investigated changes in socioeconomic inequality in stunting and fever in Zambia in 2007 and 2014. Unlike the huge literature that seeks to quantify the contribution of different determinants on the observed inequality at any given time, we quantify determinants of changes in inequality. Methods Data from the 2007 and 2014 waves of the Zambia Demographic and Health Survey (DHS) were utilized. Our sample consisted of children aged 0-5 years (n = 5,616 in 2007 and n = 12,714 in 2014). We employed multilevel models to assess the determinants of stunting and fever, which are two important child health indicators. The concentration index (CI) was used to measure the magnitude of inequality. Changes in inequality of stunting and fever were investigated using Oaxaca-type decomposition of the CI. In this approach, the change in the CI for stunting/fever is decomposed into changes in CI for each determinant and changes in the effect-measured as an elasticity-of each determinant on stunting/fever. Results While average rates of stunting reduced in 2014 socioeconomic inequality in stunting increased significantly. Inequality in fever incidence also increased significantly, but average rates of fever did not reduce.The increase in the inequality (CI) of determinants accounted for the largest part (42.5%) of the increase in inequality of stunting, while the increase in the effect of determinants explained 35% of the increase. The determinants with the greatest total contribution (change in CI plus change in effect) to the increase in inequality of stunting were mother’s height and weight, wealth, birth order, facility delivery, duration of breastfeeding, and maternal education. For fever, almost all (86%) the increase in inequality was accounted for by the increase in the effect of determinants of fever, while the distribution of determinants mattered less. The determinants with the greatest total contribution to the increase in inequality of fever were wealth, maternal education, birth order and breastfeeding duration. In the multilevel model, we found that the likelihood of a child being stunted or experiencing fever depends on the community in which they live. Conclusions To curb the increase in inequality of stunting and fever, policy may focus on improving levels of, and reducing inequality in, access to facility deliveries, maternal nutrition (which may be related to maternal weight and height), complementary feeding (for breastfed children), wealth, maternal education, and child care (related to birth order effects). Improving overall levels of these determinants contribute to the persistence of inequality if these determinants are unequally concentrated on the well off to begin with.
For each survey year and each outcome, we fit a two level random intercept (multilevel) regression model. The first level is for the individual (child) while the second level is the community (enumeration area or cluster) where the child lives. The model takes the form: where yijt is a binary variable equal to one if the outcome (fever or stunting) for child i residing in community j in year t is true. αjt, is the random effect for community j in year t, with δj being the time average random effect for community j. xijt is a vector of determinants of yijt while β is a vector of regression coefficients which show the effect of xijt on yijt. The variable εijt represents all other individual level determinants of yit that we are not able to observe. It is normally distributed with mean zero and variance, σεijt2. Similarly, μjt represents all other community level unobservable determinants of child i’s outcome. It has mean zero and variance, σμjt2. If variation at the community level, σμjt2, is sufficiently small—approaching zero—then multilevel modelling is not necessary. We test the hypothesis that community level factors are not important determinants of childhood ill-health by assessing the size and significance of the intra-cluster correlation (ICC). The ICC is given as: This paper does not aim to conduct a full multilevel analysis. Our only interest is to see whether or not, broadly viewed, the community in which a child lives matters for their health. As such, no covariates are included at the second level. We are only interested in the ICC and the coefficients in β. The above regression model can be estimated using multilevel logistic regression since yijt is binary. Our interest is to also use the coefficients in β in the decomposition of the concentration index. However, since logistic regression is nonlinear while the decomposition of the concentration index requires linearity, we can either compute partial effects (probabilities) from the log odds, β, or use the log odds themselves in the decomposition. Partial effects have the advantage of being easily understood. However, generating them from the vector β in multilevel logistic regression is complicated. Since we are interested in partial effects, and for ease of interpretation as well as computation simplicity, we used the multilevel linear regression which yields direct estimates of partial effects. Linear regression as a method of modelling binary variables, formally termed linear probability models (LPM), has seen widespread use in the literature lately and yields partial effects that are not different from probit or logistic regression partial effects [30–32]. It has been shown that if interest is not in prediction but simply the coefficients vector, β, then the LPM is very appropriate [33]. We use the concentration index to quantify the extent of socio-economic inequality in the prevalence of stunting and incidence of fever in 2007 and 2014. The concentration index summarizes the extent to which good or bad health is dependent on income or wealth and it may be explained using the concentration curve concept. The concentration curve plots the cumulative share of health (on the y-axis) against the cumulative proportion of the population, ranked by wealth, from poor to richest (on the x-axis). For example, the concentration curve may show the cumulative percentage of stunting accruing to the poorest 25% of the population. To be complete, suppose that we want to look at inequality in ill-health. If the concentration curve lies on the 45-degree line, then the cumulative share of ill-health is equally shared between the rich and the poor and there is no socioeconomic inequality in health. However, if the concentration curve lies on the left of the 45-degree line, then the poor carry a disproportionately high share of ill-health. The standard concentration index is twice the area between the concentration curve and the 45-degree line and in any given year, t, it can be written as: where yt¯ is the average rate of fever or stunting in year t. Rijt is the rank of child i’s household in the wealth distribution, in our case measured by the wealth index from principal component analysis. The concentration index ranges from -1 to 1. It is zero if there is no socioeconomic inequality in health, -1 if all the ill-health is borne by the poor, and +1 if the richest have all the ill-health. It has been shown however that the concentration index may not be bounded between -1 and +1 if the health variable is binary [34], as it is in our case. This may lead to misleading conclusions. In particular, the bounds of the concentration index for a binary variable depend on average health and this can cause problems if one is comparing inequalities for two different areas or time periods that have substantially different average levels. This is important in our case since we compare inequality between 2007 and 2014. Two alternative normalizations of the standard CI have been proposed by Wagstaff [34] and Erreygers [35]. The standard CI is a measure of relative inequality, which is also the emphasis of the Wagstaff normalization. On the other hand, the Erreygers normalization is an absolute measure. It has been shown that neither of the two normalizations is superior to the other but each of them embodies different value judgements [36]. We used the Wagstaff normalization in this paper. The normalization involves dividing the standard concentration index in Eq 4 by (1−yt¯) which give: For each outcome, we computed this index in 2007 and 2014 to assess the extent of inequality in each year. For each outcome, y, we computed the change in the concentration index as follows; The computation of the normalized CI based on Eq 5 and the change in the index as specified in Eq 6 involves a four stage computation process, which raises the issue of how to appropriately compute confidence intervals. In estimating the normalized CI for each year, the first stage involves the computation of the mean of the outcome and weighted fractional wealth rank for each year. In the second stage, these estimates are combined to estimate the standard CI. The third stage involves dividing the standard CI by (1−yt¯) to obtain the normalized CI. The change in the concentration index adds a fourth step to these computations; subtracting the 2007 normalized CI from that of 2014. Our challenge is that since each estimate in these stages is computed from survey data, it has uncertainties which have to be taken into account when computing standard errors. Using analytical standard errors (from the last stage only) would make confidence intervals appear narrower than they actually are. To guard against this problem, we employ a bootstrap procedure with 1,000 replications. This involves repeating the above four step procedure 1,000 times, each time collecting the estimates, and then using these estimates to compute confidence intervals—which are then called bootstrap confidences intervals. To decompose the changes in the overall concentration index, we make use of the estimated partial effects of determinants of fever/stunting, β, from Eq 1. The concentration index for outcome y in year t can then be written as a sum of the weighted concentration indices for all the determinants of y plus the generalized concentration index for the error term: where CIkt is the concentration index for determinant k at time t computed as in Eq 5, that is, yijt in Eq 5 is replaced with xijt to get CIkt. The weight, (β^ktx¯kty¯t) is the elasticity of the kth variable with respect to the health variable yijt at time t and GCεt is the generalized concentration index for the error term. GCεt is obtained by multiplying the concentration index for the error term by the mean of the outcome, y¯t. Thus, GCεty¯t, is the concentration index for the error term. At any given time, t, Eq 7 says that the concentration index of yt can be written as a weighted sum of the concentration indices of the K determinants plus the concentration index of the unobserved determinants of yt. The weight for each concentration index of the determinant, CIkt, is the elasticity of yt with respect to that determinant (note that the elasticity is a nonlinear combination of β^kt, x¯kt and y¯t). Eq 7 is the most commonly used method of decomposing inequalities in child health. Clearly this decomposition only allows one to examine the relative contribution of various determinants in explaining inequality at any given time, but it does not allow one to see which determinants are driving changes in inequality at any two given periods. To examining the drivers of changes in the childhood ill-health inequality specified in Eq 6 we apply the Oaxaca decomposition to Eq 7 [26]. This leads to the following: where ηkt is the elasticity of y with respect to determinant k in year t. Since ηkt=(β^ktx¯kty¯t), the elasticity of determinant k, ηkt, can change due to changes in any of its component, namely, y¯t, β^kt, and x¯kt. Eq 8 says that changes in the concentration index of health outcome y can be written as a sum of three components, namely, the weighted sum of the changes in the inequality of the K determinants, the weighted sum of the changes in the elasticities of y with respect to the K determinants, and the change in inequality of unobservable determinants. The change in inequality of each determinant is weighted by the elasticity of y with respect to this determinant in 2014 while the change in elasticity is weighted by the inequality of the determinant in 2007. In other words, apart from the contribution of unexplained factors, Δ(GCεty¯t), the contribution of the kth determinant to the change in inequality in y, ΔCIy, can be brought about by the change in the concentration index of the kth determinant, (CIk2014 − CIk2007), or the change in it’s the elasticity, (ηk2014 − ηk2007), or both. An increase in the concentration index of the kth determinant in 2014 increases its contribution to inequality. On the other hand, the increase in its elasticity in 2014—resulting from a change in y¯t, β^kt, x¯kt or any other combination of these—can also contribute to the increase in inequality of childhood ill-health. For example, consider a case where the kth determinant is concentrated on the well-off (CIkt > 0) and it has a protective effect (β^kt is negative). In this case, a reduction in the prevalence of y, the mean y¯t, will increase inequality in y. Similarly, an increase in the mean of the kth determinant, x¯kt will increase inequality. Holding y¯t and x¯kt constant, an increase in β^kt will also increase inequality.
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