Source of data
The data used in this study is derived from the project for statistics on Living Standards and Development Survey (LSDS). This survey was conducted jointly by the South African Labour and Development Research Unit (SALDRU) and the World Bank in 1993. It was based on a sample of 8,848 households, which consisted of 40,284 individuals. The survey is designed to collect household data that can be used to assess multiple aspects of household welfare and behaviour and to evaluate the effect of various government policies on the living conditions of the population using a multi-topic questionnaire. The section on nutrition, besides questions related to child health, includes anthropometric measurements. For the purpose of this study, data on 3765 under-five children whose records were complete in the required individual and household level variables are included.
The LSDS provides the most recent data set, which includes both anthropometric measures and extensive socio-economic indicators. The more recent Demographic and Health Survey contains extremely limited asset indicators, which are inadequate for detailed socio-economic inequality analysis.
Measurement of nutritional status
There are various ways of assessing the nutritional status of under-five children. It can be assessed using clinical signs, biochemical indicators or anthropometry [13]. The anthropometric approach is the most commonly used tool [14] and is more advantageous compared to the other two [13]. While clinical signs and biochemical abnormalities may only be useful in advanced cases of malnutrition, the anthropometric indicators are sensitive even in incipient ones. Furthermore, anthropometric measures are non-invasive, less costly and easy to obtain compared to the other two techniques.
Anthropometric indicators are constructed using data on the children's age, height and weight. Three key anthropometric measures calculated from the age, height and weight data are weight-for-height, height-for-age and weight-for-age. These measures are expressed in the form of Z-scores, which compare a child's weight and height with those of a similar child from a reference healthy population. For example the height-for-age Z-score of child "i" is given as:
where, H
i
is the height of the child; H
r
is the median height of the reference population; and SD is the standard deviation of height of the same reference population.
The World Health Organization recommends the US National Center for Health Statistics (NCHS) population as a reference for international use [14]. This reference population, which has been in use since 1977 [14], however, has been found to have some technical and biological drawbacks, thus driving the WHO to conduct a multi-country study geared towards developing new reference values [13].
Following conventional cut-off points, malnutrition in its various forms is operationally defined as follows:
i. stunting: height-for-age that is less than the international reference value by more than two standard deviations;
ii. wasting: weight-for-height less than the international reference value by more than two standard deviations; and
iii. underweight: weight-for-age that is more than two standard deviations below the international reference value.
Stunting is regarded as an indicator of long-standing dietary inadequacy. A high prevalence of stunting in the community is associated with poor socio-economic conditions [15]. The WHO recommends stunting as a reliable measure of overall social deprivation [14]. The height-for-age measure is less sensitive to temporary food shortages and thus, is the most reliable indicator of long-standing malnutrition in childhood [7]. Wasting on the other hand reflects acute malnutrition. It has the advantage that it does not require an accurate knowledge of the child's age. This is particularly important in the setting of developing countries, where it may be difficult to get the exact age of the child. Wasting is also useful in evaluating the benefits of nutrition intervention programmes as it is sensitive to short-term changes (unlike stunting which does not respond quickly). Low weight-for-age is difficult to interpret, as it cannot discriminate between temporary and permanent malnutrition. However, in populations were the rate of wasting is low, it can be interpreted in the same way as height-for-age [15]. Stunting and wasting are, thus the preferred measures of child nutritional status, since they can distinguish between long-standing and short-run malnutrition [14].
In this analysis, outliers were removed in line with the exclusion ranges recommended by WHO [10]. Hence, weight-for-height Z-scores less than -4.0 and greater than +5.0, height-for-age Z-scores less than -5.0 and greater than +3 and weight-for-age Z-scores less than -5.0 and greater than +5.0 are excluded from the analysis.
Measurement of socio-economic status
Income is the most commonly used measure of socio-economic status (SES) [16]. Given the difficulties of obtaining accurate income data in household surveys, household expenditure is frequently used as a proxy of household income. Indeed, household expenditure, particularly expenditure on basic needs of life, is the most frequently used measure of SES in nutritional analysis studies [17]. Such expenditure is regarded as accurately representing the household's resource endowment that influences the health status of its members [18].
Measurement of socio-economic inequalities in malnutrition
Inequality in malnutrition is measured using the illness concentration index (C) proposed by Wagstaff et al [19]. It is computed from the illness concentration curve (see Figure 1), which plots the cumulative proportions of children ranked by the household's socio-economic status against the cumulative proportions of malnutrition. It estimates the extent of socio-economic inequality in illness. The concentration index is similar to the relative index of inequality that is frequently used by epidemiologists.
The concentration index meets three important criteria that a good measure of inequality is expected to fulfill [19]:
i. it takes account of the socio-economic dimension of inequality in health (unlike the gini coefficient for example);
ii. it reflects the experience of the entire population rather than two extreme groups on the socio-economic scale (e.g. income quintile 5 versus income quintile 1) as is the case in range measures (e.g. rate-ratios), and
iii. it is sensitive to changes in the population across socio-economic groups.
The concentration index is twice the area between the illness concentration curve (L(S)) and the diagonal with values ranging from +1 to -1. Its value is positive (negative) when it lies below (above) the diagonal. A negative illness concentration inde x indicates the existence of inequalities in health that are pro-rich (i.e. high income groups have less ill-health than low income groups). A positive concentration index implies inequalities in favour of the least advantaged socio-economic groups. If illness is distributed equally, the concentration curve overlaps with the diagonal (line of equality).
On individual level data, the concentration index can be computed as follows [20]:
where,
x
i
(i = 1,...n) is the ill-health score of the ithindividual;
μ is the mean level of ill-health; and
R
i
represents the relative rank of the ithperson. The individuals are ranked according to their socio-economic status beginning with the worst off.
The above computation, however, does not enable statistical inference, that is, it is not possible to know whether or not the calculated concentration index has a statistical significance. To this end, a standard error for C can be calculated using a convenient regression as follows [20]:
In the above equation β1 is equal to the concentration index.
The overall concentration index is calculated (i.e. for all under-five children in the sample), as well as concentration indices for certain disaggregated categories including each 'race' group, area of residence (metropolitan areas, other urban areas and rural areas) and province. Thus, the distribution of malnutrition across per capita household expenditure quintiles is evaluated for each sub-group (e.g. rural areas).