The Pareto Principle (PP) - that 80% of an attribute are found in 20% of individuals - is one way to characterize heterogeneity in infectious diseases. An alternative is the dispersion parameter (k) of the negative binomial distribution (NBD). The NBD has two parameters, while the PP is a single property which may hold for any distribution family. The objectives of the current work are: a) to obtain a relation between the PP and NBD, i.e. to specify which combinations of NBD parameters comply with the PP; b) for hookworm, a soil-transmitted intestinal parasite of humans, to identify whether the PP or the NBD is a more parsimonious description of heterogeneity of infection load. For objective a), an empirical relation is found in the form of a saw-toothed line on a plot of k against the mean, reaching an asymptote of approximately 0.24. For objective b), we estimate k and the mean from nine studies from a systematic review of hookworm in pregnant women. Seven studies had higher heterogeneity than the PP, ranging from 83:20 to 100:20: we call these super-Pareto. One study was sub-Pareto (74:20), and one was Pareto (80:20). This suggests that at least two parameters, as supplied by the NBD, are necessary to describe the heterogeneity of hookworm. The probability of reaching a target reduction in prevalence is less when there is greater aggregation, which suggests that estimating aggregation via a subsample could be worthwhile, in order to set a target coverage threshold before starting mass drug administration.
Bayesian Estimations on the Exponentiated Distribution Family with Type-II Right Censoring
