Optimal Group Size Based On Individual Information Under Dorfman Algorithm

During the detection of the disease,if each test sample is tested,it will consume a lot of manpower,material resources,and financial resources.Therefore,how to reduce the number of detections,thereby reducing the cost of detection and improving the detection efficiency has become the focus of people's research.During World War II,the group detection idea(also called Dorfman algorithm)proposed by Dorfman can effectively improve the detection efficiency and reduce the detection cost.Scholars at home and abroad have conducted an in-depth study on the optimal grouping size for group detection,but mostly focused on the assumption that the prevalence rate is fixed,combined with less individual differences.This paper considers the differences of the tested populations,that is,considering the regression model of individual prevalence and individual information when the individual prevalence changes with the individual information.According to the Fisher information matrix of the unknown parameters in the model,the binomial distribution sampling and the inverse binomial distribution sampling optimal group size are derived.Fistly,the paper derives the Fisher information matrix of the regression model parameters for the prevalence rate in the case of binomial distribution sampling,and combines the D-optimal criterion to derive the expression of the optimal grouping size.Secondly,the Fisher information matrix of the parameters of the prevalence regression model under inverse binomial sampling is deduced,and the expression of the optimal grouping size is obtained by combining the D-optimal criterion.The two parts consider the individual differences.The Fisher information matrix of the individual prevalence regression model parameters is used to maximize the optimal packet size,and more accurate estimates of prevalence parameters can be obtained.According to the expression of the optimal grouping size and taking into account multiple grouping strategies,the simulation is performed.And the optimal group size is sought in the cases where the prevalence rate is the population mean value and the individual prevalence rate is directly considered,so that the corresponding parameter estimation is performed which has good statistical properties.The data from the case analysis was from an HIV surveillance study conducted in Kenya.The optimal group size was used to find out the optimal group size for Kenyan HIV test samples under different grouping strategies.Finally,some prospects for follow-up research are proposed,and the method of applying the optimal grouping method for group detection to HIV/AIDS testing and social epidemic disease detection in universities is proposed.