Date Published: November 07, 2012
Publisher: The American Society of Tropical Medicine and Hygiene
Author(s): Shira Mitchell, Marcello Pagano.
Rapid and accurate identification of the prevalence of schistosomiasis is key for control and eradication of this devastating disease. The current screening standard for intestinal schistosomiasis is the Katz-Kato method, which look for eggs on slides of fecal matter. Although work has been done to estimate prevalence using the number of eggs on a slide, the procedure is much faster if the laboratory only reports the presence or absence of eggs on each slide. To further help reduce screening costs while maintaining accuracy, we propose a pooled method for estimating prevalence. We compare it to the standard individualed method, investigating differences in efficiency, measured by the number of slides read, and accuracy, measured by mean square error of estimation. Complication is introduced by the unknown and varying sensitivity of the procedure with population prevalence. The DeVlas model for the worm and egg distributions in the population describes how test sensitivity increases with age of the epidemic, as prevalence and intensity of infection increase, making the problem fundamentally different from earlier work in pooling. Previous literature discusses varying sensitivity with the number of positive samples within a pool, known as the “dilution effect.” We model both the dilution effect and varying sensitivity with population prevalence. For model parameter values suited to younger age groups, the pooled method has less than half the mean square error of the individualed method. Thus, we can use half as many slides while maintaining accuracy. Such savings might encourage more frequent measurements in regions where schistosomiasis is a serious but neglected problem.
Schistosomiasis (also known as Bilharzia) is a chronic disease caused by parasitic worms. Its intestinal form is responsible for severe liver and intestinal damage, physical growth retardation, and cognition and memory problems. The World Health Organization (WHO) reports that more than 200 million people are infected worldwide and an estimated 700 million people are at risk of infection because of their residence in tropical and subtropical areas, and in poor communities without access to safe drinking water and adequate sanitation. Young children are especially vulnerable to infection because of their hygiene and play habits, and the symptoms are quite harmful to them, impairing learning ability and physical development, and even sometimes causing death.
In this section we discuss the estimator of prevalence using the individualed method. Let P1 be the probability of a positive slide, which is a function of the prevalence p. Let m be the number of slides tested and W the number of positive slides, with . Letting sens4 = Pr[Y1 + Y2 + Y3 + Y4 > 0∣X > 0] be the sensitivity of the test using the individualed method with four smears from one person, we see that P1(p) is
because we assume no “eggs” will be spotted in a smear coming from a person with no worm-pairs, and thus take the specificity of the measurements to be one—i.e.,
Now consider the estimator of prevalence using the pooled method. Define W as before, with the probability of a positive slide in the pooled case (the subscript “c” denotes that the slide consists of smears from c separate individuals). Again, we maximize the likelihood to get . Letting sens1 = P[Y > 0∣X > 0] = P[Y > 0] / P[X > 0] (the sensitivity for a single smear), and recalling that the specificity is one,
For each plot, we fix three of the four parameters M,k,h0, and r and vary the fourth parameter to study the variance, bias, and mse change for the pooled and individualed estimators. In contrast to the asymptotic analysis, we now allow the true sensitivities to vary with the varying parameter values. In other words, for the individualed method, we pick a random number of worms for the individual (from the Negative Binomial in the DeVlas model above), and given this worm count pick an egg count for a quantity of 47 mg of stool. If this count is nonzero, we say we have a positive test result. Thus, in our simulation we allow each individual in a population to have their own sensitivity, which is a function of their own worm count, in other words: sens(x) = P[Y > 0 ∣ X = x]. Similarly, in the pooled method, we pick four random numbers of worms and for each of these worm counts we pick egg counts for a quantity of 12 mg of stool.
We are trapped in circularity when trying to estimate prevalence, because we need to know the prevalence to know the sensitivity, which is required to estimate the prevalence unbiasedly. Below we suggest a method to arrive at an estimate of prevalence that takes into account the dependence of sensitivity on the prevalence by using an iterative technique.
We used school-level data from schools in Uganda (296 schools, average prevalence of Schistosoma mansoni per school: 28%16), Tanzania (143 schools, average prevalence of S. mansoni per school: 4.4%17), Mali (454 schools, average prevalence of S. mansoni per school: 10%18), and Cameroon (402 schools, average prevalence of S. mansoni per school: 7.3%19).
Previously, we have shown (in Asymptotic mse ratio of the estimators section) that if one assumes constant and known sensitivities (per smear sens1 and per slide, sens4) the mse of the pooled estimator is then roughly half that of the individualed estimator at prevalences below roughly 30%. The pooled estimator has a lower mse than the individualed estimator up to roughly 50% prevalence (and higher as the sensitivities decrease, because that lowers the probability of all positive pools). This is of interest because we can read half as many slides to achieve the same accuracy of prevalence estimation in regions with below 30% prevalence. (It may be most important to monitor the prevalence in these regions below 30%, because above 30% it will be easy to determine that treatment of the region is necessary and that appropriate actions be taken.) We see that as the relative difference between the sensitivity from a single smear sens1 and the sensitivity of an entire slide sens4 becomes smaller, the relative benefits of pooling are increased. The DeVlas model can provide insight into when these sensitivities are closer or farther apart.