Optimality of Group Testing with Differential Misclassification

Group testing is a method that can be used to estimate the prevalence of rare infectious diseases, which can effectively save time and reduce costs compared to the method of random sampling. However, previous literature only demonstrated the optimality of group testing strategy while estimating prevalence under some strong assumptions. This article weakens the assumption of misclassification rate in the previous literature, considers the misclassification rate of the infected samples as a differentiable function of the pool size, and explores some optimal properties of group testing for estimating prevalence in the presence of differential misclassification conforming to this assumption. This article theoretically demonstrates that the group testing strategy performs better than the sample by sample procedure in estimating disease prevalence when the total number of sample pools is given or the size of the test population is determined. Numerical simulation experiments were conducted to evaluate the performance of group tests in estimating prevalence in the presence of dilution effect.