Computational statistical model for group testing with retesting

Abstract

Screening of pooled urine specimen was suggested during the Second World War as a method for reducing the cost of detecting syphilis in U.S. soldiers. Recently, pooling has been used in epidemiological studies for screening of human immunodeficiency virus HIV/AIDS antibody to help curb the spread of the virus. Pooling reduces the cost but also – and more importantly – offers a feasible way to lower the misclassifications associated with labeling specimens when imperfect tests are used. Furthermore, misclassifications can be reduced by employing a re-testing design in a pool testing procedure. In this design a large sample from a population of interest is pooled into n pools each of size k and each pool is subjected to a single test. For pools that test negative further testing are discontinued but those that test positive are given a re-test. Pools that test positive on re-testing, their constituent members are tested individually so as to classify them as either defectives or non-defectives. This study has developed a computational statistical model for classifying a large sample from a population of interest based on the re-testing design described above. This model permits calculation of cost of testing and the number of misclassifications made in this design. Simulated data from a multinomial distribution (specifically a trinomial distribution) has been used to illustrate the computation of cost and the number of misclassifications in the re-testing design. This study has also considered pool testing procedure without re-testing when imperfect tests are used. In this procedure, a sample from the population of interest is pooled into n pools of size k and each pool subjected to a single test. Pools that test negative further testing are discontinued whereas those that test positive their constituent members are tested individually. Simulation from a binomial distribution has been carried out and statistical moments based on this distribution have been computed to illustrate this testing design. The cost of this testing design and the number of misclassifications made has also been computed. Comparison of the two pool testing designs on the basis of cost and misclassifications has been carried out for the purpose of generalization and improvement. From this study, it has been established that re-testing reduces misclassifications significantly and more so, it is stable at high rates of probability of incidences as compared to Dorfman procedure. However, re-testing comes with a cost i.e. increase in the number of tests. Re-testing considered reduces the sensitivity of the testing scheme but at the same time it improves the specificity; making the model viable in blood donation.