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Group, Re-test, Specificity, Sensitivity, Multinomial, Misclassifications.

Screening of grouped urine sample was suggested during the Second World War as a method for reducing the cost of detecting syphilis in U.S. soldiers. Grouping has been used in epidemiological studies for screening of human immunodeficiency virus HIV/AIDS antibody to help curb the spread of the virus in recent studies. It reduces the cost of testing and more importantly it offers a feasible way to lower the misclassifications associated with labeling samples when imperfect tests are used. Furthermore, misclassifications can be reduced by employing a re-testing design in a group testing procedure. This study has developed a computational statistical model for classifying a large sample of interest based on a proposed design of group testing with re-testing. This model permits computation of moments on the number of tests and misclassification arising in this design. Simulated data from a multinomial distribution (specifically a trinomial distribution) has been used to illustrate these computations. From our 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 although 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.