Sample sizes for identifying the key types of container occupied by dengue-vector pupae: the use of entropy in analyses of compositional data

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Abstract
A method has been developed for estimating the sample sizes needed to identify categories that comprise a large proportion of a compositional data-set. The method is to be used in the design of surveys of mosquito pupae, for identifying the key container types from which the majority of adult dengue vectors emerge. Although a finite-population correction was devised for estimating the mean of a negative binomial distribution, other complications of parametric approaches make them unlikely to yield methods simple enough to be practically applicable. The Shannon-Wiener index was therefore investigated as a more useful alternative, at the cost of theoretical generalizability, in an approach based on re-sampling methods in conjunction with the use of entropy. This index can be used to summarize the degree to which pupae are either concentrated in a few container types, or dispersed among many. An empirical relationship between the index and the repeatability of surveys of differing sample sizes was observed. A step-wise rule, based on the entropy of the cumulative data, was devised for determining the sample size, in terms of the number of houses positive for pupae, at which a pupal survey might reasonably be stopped.