More than one-quarter of all under fives in the developing world are underweight . This accounts for about 143 million underweight children in developing countries . Of these 143 million underweight children, nearly three-quarters live in just 10 countries . In Sub-Saharan Africa more than one-quarter of children under five are underweight. Nigeria and Ethiopia alone account for more than one-third of all underweight children in Sub-Saharan Africa . Undernutrition, conversely, has been estimated to be an underlying cause for around half of all child deaths worldwide . According to recent comparative risk assessments, under-nutrition is estimated to be, by far, the largest contributor to the global burden of disease [2, 3]. Undernourished children have lowered resistance to infection and are more likely to die from common childhood ailments like diarrhoeal disease and respiratory infection. Frequent illness saps the nutritional status of those who survive, locking them into a vicious cycle of recurring sickness and faltering growth. Their plight is largely invisible: Three quarters of the children who die from causes related to malnutrition were only mildly or moderately undernourished, showing no outward sign of their vulnerability .
The Millennium Development Goals (MDGs) state as the first goal "to halve between 1990 and 2015 the proportion of people who suffer from hunger." One indicator to monitor progress for this target is the proportion of children who are underweight – i.e. low weight compared with that expected for a well-nourished child of that age and sex. Child malnutrition is one of the measures of health status that the World Health Organization (WHO) recommends for equity in health . From the existing evidence it is clear that childhood malnutrition is associated with a number of socioeconomic and environmental characteristics such as poverty, parent's education/occupation, sanitation, rural/urban residence and access to health care services. Also demographic factors such as the child's age and sex, birth interval and mother's age at birth have been linked with malnutrition [5–8]. In addition, previous studies have drawn attention to the disproportional burden of malnutrition among children from poor households [4, 5]. There seems to be a broad agreement that many socioeconomic inequalities are unfair , because they are result of a division of labour in society that puts certain groups of people at a disadvantage, not only economically, socially, and politically but also in terms of their possibilities to be healthy . Inequalities in health arise, in part, because of inequalities in society . There is no society without inequalities . It is a major challenge to reduce the magnitude of social inequalities in health. To do so requires commitment and concerted action across many sectors of society.
In the biomedical field, linear and logistic regression analyses are the classical approaches to studying the association between socioeconomic position (SEP) and childhood malnutrition . Usually, odds ratios (OR) or beta coefficients are reported to indicate the magnitude and direction of the association [13, 14]. These methods are straightforward, but suffer from several limitations. First, although traditional regression analysis can help examine whether there is an association between SEP and childhood malnutrition, it is not powerful enough to measure the disparity quantitatively, i.e., to tell how severe the inequality is. Second, comparing inequality across studies or over time using traditional regression analysis is difficult, since the validity of regression analysis is based on the assumption of multi-normality and independence between study variables over time . Third, from a statistical perspective, linear regression analysis assesses the relationship between the outcome and explanatory variables on average but ignores the possibility that the effect of explanatory variables may vary across the distribution. To solve similar problems, economists have developed summary indices such as the Gini coefficient and the concentration index to quantitatively measure the degree of income-related inequality . Unlike Gini coefficient, the concentration index meets all three important criteria that a good measure of inequality is expected to fulfill : (1) it takes account of the socio-economic dimension of inequality in health; (2) 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 (3) it is sensitive to changes in the population across socio-economic groups. The concentration index has proven as a useful tool for measuring inequalities in the health sector  and have been used extensively in public health to studies socioeconomic inequality in self-rated health [19, 17], child injury , ownership of insecticide net [21–23], measles immunization coverage , childhood malnutrition [4, 25–27], overweight , obesity , mental health , and infant mortality [29, 30].
Despite these strengths, it does however have limitations . First, like the Gini coefficient, it has implicit in it a particular set of value judgments about aversion to inequality. However, the "extended" concentration index proposed by Wagstaff's  allows attitudes to inequality to be made explicit, and to see how inequality changes measured as the attitude to inequality changes. The second drawback of the concentration index – and the generalization of it – is that it is just a measure of inequality. Although equity is an important goal of health policy, it is not the only one. It is not just health inequality that matters; the average level of health also matters. Policy makers are likely to be willing to trade one off against the other – a little more inequality might be considered acceptable if the average increases substantially. This point to a second extension of the concentration index : a general measure of health "achievement" that captures inequality in the distribution of health (or some other health sector variable) as well as its mean.
In country like Nigeria with high degree of socioeconomic inequality, the existence of morbidity and mortality differentials related socioeconomic status is not unexpected. However, policies aimed at reducing inequalities, magnitude and determinants of the problem, as policy decisions based on intuition are likely to be misguided [4, 33]. To date, few studies have been done to examine differences in childhood malnutrition rates across socioeconomic groups in Nigeria [25, 26]. The aim of this paper was therefore, to contribute to the efforts to quantify inequalities in health in Nigeria, by assessing the magnitude of inequalities in malnutrition of under-five children that are ascribable to socio-economic status.