Home   >   CSC-OpenAccess Library   >    Manuscript Information
Full Text Available

This is an Open Access publication published under CSC-OpenAccess Policy.
Publications from CSC-OpenAccess Library are being accessed from over 74 countries worldwide.
Computation of Moments in Group Testing with Re-testing and with Errors in Inspection
Cox Lwaka Tamba, Martin Wafula Nandelenga
Pages - 1 - 15     |    Revised - 20-01-2014     |    Published - 11-02-2014
Volume - 3   Issue - 1    |    Publication Date - January / February 2014  Table of Contents
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.
1 CiteSeerX 
2 refSeek 
3 Scribd 
4 SlideShare 
5 PdfSR 
1 C. L. Tamba, K. L. Nyongesa and J. W. Mwangi. “Computational Pool-Testing Strategy”Egerton University Journal, 11: pp 51-56, 2012.
2 E. Litvak, , X. M. Tu, and M. Pagano. “Screening for the presence of a disease by grouping sera samples”. Journal of the America statistical Association, 89, pp 424-434, 1994.
3 F. K. Hwang. “Group testing with a dilution effect”. Biometrika 63, pp 611-613, 1976.
4 F.K. Hwang. “A Generalized Binomial Group Testing Problem”. Journal of the American Statistical Association, 70, pp 923- 926, 1975.
5 G. Hepworth and R. Watson. “Debiased estimation of proportions in group testing”. Royal Statistical Society, 58, pp 105–121, 2008.
6 L. K. Nyongesa. “Dual Estimation of Prevalence and Disease Incidence in Group-Testing Strategy”. Communication in Statistics Theory and Method. Vol. (1): Issue (1), 2010.
7 L. K. Nyongesa. “Hierarchical Screening with Retesting in a low Prevalence Population”. The Indian Journal of Statistics.66, pp 779-790, 2005.
8 L. K. Nyongesa. “Multistage group testing procedure (Group screening)”. Communication in Statistics-Simulation and computation, 33, pp 621-637, 2004.
9 L.K. Nyongesa and J. P.Syaywa. “Block Testing Strategy with Imperfect Tests and its Improved Efficient Testing Model for Donor Blood”. Communication in StatisticsComputational Statistics, 2011.
10 L.K. Nyongesa, and J. P. Syaywa. “Group Testing with Test Errors Made Easier”.International Journal of Computational Statistics. Volume (1): Issue (1), 2010.
11 M. Sobel and R. M. Elashoff. “Group-testing with a new goal, Estimation”. Biometrika, 62,181-193,1975.
12 M. Sobel, and P. A. Groll. “Binomial Group-Testing with an Unknown Proportion of Defectives”. American Statistical Association and American Society for Quality, 8, pp 631-656, 1966.
13 N. L. Johnson, S. Kotz and X. Wu. “Inspection errors for attributes in quality control”. London;Chapman and Hall, 1992
14 O.T. Monzon, F. J. E. Palalin, E. Dimaal, A.M. Balis, C. Samson and S. Mitchel. “Relevance of antibody content and test format in HIV testing of grouped sera”. AIDS, 6, pp 43-48, 1992.
15 R. B. Hunt, L.L. Ronald and M. R. Jonathan. “A Guide to MATLAB for Beginners and Experienced Users”. Cambridge University Press, pp.101-119, 2004.
16 R. Dorfman. “The detection of defective members of large population”. Annals of Mathematical Statistics 14, pp 436-440, 1943.
17 R.L. Kline, T. Bothus, R. Brookmeyer, S. Zeyer, and T. Quinn. “Evaluation of Human Immunodeficiency Virus seroprevalence in population surveys using grouped sera”. Journal of clinical microbiology, 27, pp 1449-1452,1989.
18 S. Maheswaran, V. Haragopal, and S.N. Pandit. Group-testing using block testing strategy.Journal of statistical planning and inference, 2008.
Dr. Cox Lwaka Tamba
Faculty of Science/ Department of Mathematics /Division of Statistics Egerton University P.O Box 536, Egert on, Kenya - Kenya
Dr. Martin Wafula Nandelenga
Faculty of Arts and Social Sciences/Department of Economics Egerton University P.O Box 536, Egerton, Kenya - Kenya