The Optimal Design Of Inverse Binomial Group Testing

With the development of social globalization,infectious diseases are also moving in the direction of globalization.If not well control the spread of infectious diseases,not only endanger the safety of people’s property and life safety,and even cause a devastating blow to the whole society and the state.So the monitoring and control of infectious diseases has always been an important task in the health department of governments.In the monitoring of disease,how to accurately,efficiently and economically test the sample and estimate the prevalence of the disease is a problem that deserves research very much.In the detection of small probability of disease,it is a very cost-effective method to test sample by group testing.Using this method to test sample must choose an appropriate group size,because the choice of group size plays an important role in the efficiency and success of the experiment.In estimating the prevalence of the disease,it is common for people to use a fixed number of samples to test the sample.However,when the prevalence of the disease is small,this method exposes its shortcomings.The samples are tested being positive very few and even none of them in these samples.Aimed at this case,it can effectively solve the problem by using reverse sampling method to test the samples.That is,fixed the number of positive people,until tested the number of positive people stop testing.In this paper,the method of group testing and inverse sampling method are combined to estimate the prevalence of the disease,and the main study is how to select the optimal group size to improve the accuracy of estimation.In the first part,we mainly study the selection of optimal group size for inverse binomial group testing under exact detection.We assume that the results of each group follows i.i.d.Bernoulli distributions and the prevalence of disease follows the beta distribution.Using the method of maximum likelihood estimation,we obtain the mathematical expression of the prevalence and asymptotic variance,and the existence of the optimal group size is proved by theory.In the second part,we mainly study the selection of optimal group size for inverse binomial group testing under inaccurate detection.As the testing instrument measure of precision different,there will be more or less the existence of detection error causing the phenomenon of misclassification,and impact on accuracy of prevalence estimates.Therefore,it is necessary to consider the sensitivity and specificity of the detection instrument.In this part,two cases are considered that the priori information of the prevalence rate is a fixed value and follow the Beta distribution.And also using the method of maximum likelihood estimation,we obtain the mathematical expression of the prevalence and asymptotic variance,and the existence of the optimal group size is proved by theory.In the third part,we mainly study a two-stage adaptive group testing procedure for estimating proportions under inverse sampling.The main idea of this approach is that by a relatively small number of experiments in the first stage estimate a prevalence of disease,and select the optimal group size for the second stage of the experiment.Finally,we estimate the prevalence of the disease by two stages of experimental results.The advantage of this approach is that it doesn’t depend on the priori information of the prevalence,so that the method is very useful when the priori information about the prevalence of the disease is very small.In the fourth part,the correctness of the first three parts has been verified by simulation.In the last part,we propose the conclusion and expectation.