Abstract: Estimating the prevalence of an infectious disease in a big population typically requires testing a specimen (e.g., blood, urine, or swab) for the disease. When the disease spreads quickly, time constraints and limited resources often restrict the number of tests that can be performed. In such cases, if the prevalence is not too high, the group testing procedure can be employed to save time, money, and resources. The procedure tests pooled specimens of groups of individuals, rather than testing each individual for the disease. This technique is also used in other contexts, for example, to detect abnormalities or contamination in animals, plants, food, or water. Although methods exist for estimating a prevalence conditional on the explanatory variables from the group testing data, they require the specimen to be available for all individuals, which is not always possible. Therefore, we construct new nonparametric estimators that are consistent when some of the specimens are missing. We demonstrate the numerical performance of our methods using simulations and a hepatitis B example.

Key words and phrases: Cost saving, disease monitoring, limited resources, pooling, time saving.