Estimating Proportions by Group Retesting with Unequal Group Sizes at Each Stage

Abstract

Group testing is a procedure that splits samples into multiple groups based on some specific grouping criterion and then tests each group. It is usually used in identifying affected individuals or estimating the population proportion of affected individuals. Improving precision of group testing and saving cost of experiment are two crucial tasks for investigators. Cost-efficiency is a ratio of precision to cost; hence improving cost-efficiency is as crucial as improvement of precision and cost saving. In this thesis, retesting will be considered as a method to improve precision and cost-efficiency, and save cost. Retesting is an extension of group testing. It uses two or more group testing stages, and testing original samples in all of the stages. Hepworth and Watson (2015) proposed a two-stage group testing procedure where two stages have equal group sizes, and the number of groups of the second stage is based on the number of positive groups in the first stage. In this thesis, our main goal is estimating a proportion p under the circumstance of unequal group sizes in two stages, and discovering the most cost-efficient experiment design. Analytical solutions of precision will be provided; we will use these analytical solutions with simulations to analyse some experimental designs, and discover whether doing one group testing only is precise enough or not and if it is worth retesting for each design. In the end, we will combine all these analyses and identify the optimal experiment design.