Identification Of Positive Specimen Based On Quantitative Measurements Under Group Testing

How to quickly detect individuals carrying the virus from a large number of people are critical to controlling the spread of infection and disease,as well as the survival and development of human beings.In scientific research such as epidemiology,the work of individual testing is time-consuming,and labor-intensive.Until Dorfman proposed group testing,the experimental research process in many fields paid more and more attention to the group testing method.Compared with individual testing of samples,the group testing method reduces the number of tests and reduces the cost of testing,and at the same time effectively screens out diseased samples to control the spread of disease.When using the group detection method,we divide the group into various groups,the number of positive individuals in the group is unknown,and the positive individuals are effectively identified by testing in groups.This article mainly has two parts.First,under the group testing,group observation data is a continuous situation,the number of positive individuals is introduced as a hidden variable,a hybrid model is established.In the process of establishing the hybrid model,we found that this hybrid model is different from the general hybrid model.The general hybrid models with k class sub-models,assuming that the number of parameters of the each sub-model is p,then the degree of freedom of the total parameter is(k+k×p-1),and this article establishes a hybrid model with k class sub-models,the degree of freedom of the total parameter is(2×p+1).The hybrid model parameters are controlled by low dimensional parameter,the degrees of freedom of the parameters are smaller than the degrees of freedom of the general hybrid model parameters.This is a problem with limited parameters,we give parameter-limited EM algorithm to solve the problem.And consider the unknown parameter estimation in the case of three different categories of function distributions: the normal distribution,the gamma distribution,and the normal distribution with additional covariate information.Second,in the retesting process of traditional group testing methods,such as Dorfman,if the group test result is positive,all samples of this group are tested individually.Or Sterrett,randomly test the samples in the group until the first positive sample is detected,reassemble the remaining samples to continue testing.And this article combines the continuous observations of the group and the estimated parameters,the posterior probability of the number of positive individuals is calculated,and the number of positive individuals corresponding to the maximum posterior probability,is estimated as the number of positive samples in the group.We use this information to give a new retest process.