The measurement of population based estimates of malnutrition in children 6 to 59 months is a major component in assessing the nutrition levels in vulnerable populations. Typically, the prevalence of malnutrition is determined by taking a random survey sample of children from a population and indexing each selected child’s weight and height to the standard World Health Organization (WHO) Growth charts . The resulting weight-for-height Z-scores (WHZ) are then compared to malnutrition thresholds; the number of children with WHZ less than the WHZ threshold is then counted and divided by the number of children in the sample. As a measure of precision, a 95% confidence limit around the estimate is calculated based on the sample size and sample design. This is the standard prevalence method of measuring malnutrition .
The 1995 WHO Technical Report 854 described the use of the PROBIT method to measure child anthropometry indicators in nutrition surveys as a more robust alternative to the standard prevalence-based approach . The PROBIT method assumes the true distribution of WHZ comes from a normal distribution, so the distribution can be defined using the mean and the standard deviation (SD). Instead of counting the number of cases below a malnutrition WHZ threshold for a given sample, the PROBIT method estimates the prevalence of malnutrition indirectly by computing the area under the tail of the curve from -∞ to the threshold via the cumulative normal distribution function using the sample mean and standard deviation . Alternatively, to reduce the influence of extreme values for a given survey, robust estimators of the sample mean, such as Winsorized or trimmed means, can be used instead of the standard sample mean . The principal assumption around the PROBIT method when estimating the prevalence of wasting is that the WHZ follow a normal distribution.
The advantage of the PROBIT method is that it will, theoretically, always produce a smaller standard error around a prevalence estimate than the standard prevalence method because it assumes a normal distribution . The other advantage is the method is less vulnerable to field measurement errors of a child’s height and weight versus the standard method which counts cases in the tail of the distribution. The disadvantage of the PROBIT method is that the bias of the PROBIT methodology depends upon the deviation of the true population of WHZ from the assumed normal distribution of WHZ defined by the mean and standard deviation. The prevalence based method on the other hand, assuming no measurement error, will give an unbiased estimate of the true prevalence.
Using a simulation based approach; a recent paper by Dale et al. examined the difference in bias and precision between the PROBIT method and the standard prevalence method for estimating the prevalence of global acute malnutrition (GAM) as well as severe acute (SAM) and moderate acute malnutrition (MAM) . Ignoring clustering, they created simulated true populations by inflating field nutrition surveys and then drawing repeated random samples at different fixed sample sizes to calculate the precision and bias for each method. The results were aggregated across the simulated true populations at each of the fixed sample sizes. The Dale study found that the precision for the PROBIT methodology for GAM based on WHZ was superior to the standard method only for sample sizes <150. The paper also stated that PROBIT method overestimated the prevalence of GAM, MAM and SAM and one can correct for it with the simple subtraction of the bias.
After reviewing the Dale article, the authors had concerns about the generalizability of the reported aggregated results. One concern was that the results of the Dale study contradicted the theoretical model in which the precision from the PROBIT method should always be superior to the standard prevalence method irrespective of the sample size and not solely for sample sizes <150. The other problem was that the aggregation of the bias and precision for multiple simulated populations may have masked individual population differences. We suspected that bias would vary by population depending on WHZ fit to the normal distribution and the magnitude of the prevalence.
Our study investigated the discrepancy between theoretically expected results of precision for the PROBIT method vs. the standard method and the ones reported by Dale. In addition we examined the variation of the bias of the PROBIT method by simulated population. We first examined the difference in precision between the two methods assuming a population with a perfect fit to the normal distribution. Next, using simulated populations from inflated field surveys in a similar manner as Dale, we examined the bias and precision around prevalence of the WHO defined threshold of WHZ < −2 (wasting) instead of GAM which is defined as a WHZ < −2 or the presence of edema. We used wasting as opposed to GAM because we wanted to look at the behavior of the estimates without edema. Instead of aggregating across simulated populations, we looked at the precision and bias from individual simulated populations of different categories of quality and magnitudes of wasting.