The Distribution of Sample Egg-Count and its Effect on the Sensitivity of Schistosomiasis Tests PDF

Keywords

eggs, schistosomiasis, probability

Abstract

Let D be the total number of Schistosomiasis eggs produced by an individual in a day, counting only those eggs which leave the body, and let S denote the number of eggs observed on a slide under the microscope and p the probability that a given egg ends up in a given slide. Assuming that D follows a negative binomial distribution, the distribution of S and that of D given S are studied. Explicit expressions for the coordinated mean and variance of D given S and for the probability of a false negative slide are obtained. Two different cases are considered. In the first case, p is assumed to be constant, and in the second, more general case p is assumed to follow a beta distribution. In either case, the probability of a false negative slide, which is a measure of the insensitivity of the laboratory test, is shown to ultimately decrease with the degree of clumping of the daily egg excretion D.