TWO-STAGE ADAPTIVE NEGATIVE BINOMIAL GROUP TESTING MODEL FOR ESTIMATING THE PREVALENCE OF A RARE TRAIT

Abstract

Group testing has been found to be an efficient and economical way of classifying observations under study as defective or unsatisfactory depending on the test performed as well as estimating the prevalence rate of a trait in a population. However, groups of appropriate sizes should be used to realize these benefits. Adaptive schemes have been developed to counter the problems brought about by inappropriate choice of group sizes. The available adaptive schemes have been constructed using a binomial sampling model where the number of groups to be tested is fixed, implying that all groups must be tested before recording the number of successes. But in some situations, such as the case of infectious diseases, estimates need to be reported as soon as detection is made, and for that case, the Negative Binomial (NB), sampling model is preferred. Under NB model, the testing procedure stops immediately when the desired number of successes, which is fixed prior, is attained. This study constructed a two-stage adaptive NB group testing model for estimating the prevalence of a rare trait. The adaptation adjusts group sizes from one stage to the next based on the estimate obtained from the previous stage. The group size used in each stage was the optimal one that minimizes the variance of the estimate of the prevalence rate in the previous stages. The maximum likelihood estimation method was used to find the point estimate of the parameter of the developed model and its properties investigated. The study further constructed the Wald confidence intervals, and its performance was investigated using mean interval length. The developed model was compared to the non- adaptive group testing model existing in the literature using relative mean squared error (RMSE) and asymptotic relative efficiency (ARE) to identify the best model. R-programming language version 4.1.2 was used for Monte Carlo simulation and analysis to verify the model. The use of the two-stage adaptive NB model combined with MLE provided lower and precise estimates. The comparative analysis highlighted the superiority of the adaptive model over the non-adaptive model emphasizing the importance of incorporating adaptivity in group testing procedures. The study highly recommends leveraging these findings to enhance the efficiency and reliability of group testing methods across diverse applications, including disease screening and surveillance of viral illnesses such as Covid-19. By incorporating these findings, the effectiveness of this testing strategies can greatly be improved, leading to more accurate and timely identification of infections, ultimately contributing to better public health outcomes.