Analysis of a Two-Stage Adaptive Negative Binomial Group Testing Model for Estimating Prevalence of a Rare Trait

Group testing is an efficient method for classifying observations and estimating trait prevalence in a population. However, using appropriate group sizes is crucial for maximizing its benefits. Adaptive schemes have been developed to address improper group size selection issues. Existing adaptive schemes are based on a Binomial sampling model, requiring testing of all groups before recording successes. In certain scenarios, like infectious diseases, immediate reporting of estimates upon detection is necessary. A two-stage adaptive Negative Binomial group testing model for such cases was constructed. This adaptive model adjusted group sizes based on estimates from previous stages thus using optimal sizes to minimize the mean squared error and variance of the prevalence rate estimate. The maximum likelihood estimation method was employed to find the model’s parameter estimate, and its properties were also investigated. The comparative analysis highlighted the superiority of the adaptive model over the non-adaptive model especially under low prevalence emphasizing the importance of incorporating adaptivity in group testing procedures, particularly in disease screening and surveillance, such as for COVID-19.