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Height-for-age (HAZ), weight-for-age (WAZ), and weight-for-height (WHZ) scores for under-5 children are based on a transformation of height, weight, and age into three pairs of bivariate relationships. The WHO 2006 transformation uses formulas to describe the pairwise relationships and coefficients estimated in a population of healthy, well-nourished children, from six settings around the world. The Z scores in that reference population are normally distributed with mean 0 and standard deviation 1. The tails of the Z distributions provide widely used estimates of the percentages of children in a population who are stunted, underweight, overweight, or wasted.
In order to provide estimates of the prevalence of these outcomes, many household surveys conducted by The Demographic and Health Surveys (DHS) Program and the Multiple Indicator Cluster Surveys (MICS) program include measurements of height and weight. A child’s age is important for many indicators and is always obtained, even in surveys without anthropometry. Recent surveys have emphasized the training and supervision of the fieldworkers who measure height and weight. Nevertheless, measurement errors do occur, especially for height. In many countries the birthdates of children and their exact ages, measured in days, are often inaccurate.
Over-dispersion of the Z scores is an important indicator of measurement error. When the standard deviations are too large, it is challenging to identify the source or magnitude of the measurement error. The true values of the standard deviations are unknown and are unlikely to be exactly 1. Each measurement affects two Z scores. The impact of error depends on whether the input is in the numerator or the denominator of the Z score.
This report describes the potential impact of measurement error on the Z scores, under a larger perspective of examining the sensitivity of the means and standard deviations of the Z scores, and the estimates of the four problematic outcomes, to specified displacements in the inputs. For illustrative purposes, two DHS surveys with different nutritional profiles and evidence of good data quality are employed: the Peru 2012 and Nepal 2016 surveys. We used three strategies: analysis, macro-simulation, and micro-simulation. With the analytical approach, the formulas and coefficients are used to calculate the Z scores for pairs of hypothetical children, who differ by specified amounts of height, weight, or age. The amounts were arbitrarily set at maximum differences of 5 cm of height, 2 kg of weight, and 90 days of age, because these are approximately 5% of the full range of height, weight, and age, respectively.
A macro-simulation approach describes the sensitivity of the percentage of children who are stunted to changes in the mean and standard deviation of the HAZ. Those results extend to the sensitivity of the other outcomes to the mean and standard deviation of the relevant Z score. Micro-simulation is used to describe the effect of random and normally distributed bidirectional displacements in height, weight, and age on the means and standard deviations of the Z scores and the prevalence of the problematic outcomes. We also describe how population heterogeneity tends to increase the standard deviations and should not always be interpreted as evidence of measurement error, and discuss the potential role of bias, or systematic error, in the measurement of height, weight, and age.