American Journal of Theoretical and Applied Statistics
Volume 5, Issue 3, May 2016, Pages: 138-145
Received: Apr. 26, 2016;
Accepted: May 9, 2016;
Published: May 25, 2016
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Langat Erick Kipyegon, Department of Mathematics & Computer Science, University of Kabianga, Kericho, Kenya
Tonui Benard Cheruiyot, Department of Mathematics & Computer Science, University of Kabianga, Kericho, Kenya
Langat Reuben Cheruiyot, Department of Mathematics & Computer Science, University of Kabianga, Kericho, Kenya
The idea of pooling samples into pools as a cost effective method of screening individuals for the presence of a disease in a large population is discussed. Group testing was designed to reduce diagnostic cost. Testing population in pools also lower misclassification errors in low prevalence population. In this study we violate the assumption of homogeneity and perfect tests by investigating estimation problem in the presence of test errors. This is accomplished through Maximum Likelihood Estimation (MLE). The purpose of this study is to determine an analytical procedure for bias reduction in estimating population prevalence using group testing procedure in presence of tests errors. Specifically, we construct an almost unbiased estimator in pool-testing strategy in presence of test errors and compute the modified MLE of the prevalence of the population. For single stage procedures, with equal group sizes, we also propose a numerical method for bias correction which produces an almost unbiased estimator with errors. The existence of bias has been shown with the help of Taylor's expansion series, for group sizes greater than one. The indicator function with errors is used in the development of the model. A modified formula for bias correction has been analytically shown to reduce the bias of a group testing model. Also, the Fisher information and asymptotic variance has been shown to exist. We use MATLAB software for simulation and verification of the model. Then various tables are drawn to illustrate how the modified bias formula behaves for different values of sensitivities and specificities.
Langat Erick Kipyegon,
Tonui Benard Cheruiyot,
Langat Reuben Cheruiyot,
An Almost Unbiased Estimator in Group Testing with Errors in Inspection, American Journal of Theoretical and Applied Statistics.
Vol. 5, No. 3,
2016, pp. 138-145.
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
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Dorfman, R. (1943). The detection of defective members of large population. Ann. Math. Statistics: 14, 436-440.
Walter, S. D., Hildreth, S. W and Beaty, B. J (1980). Estimation of Infection Rates in Population of Organisms using Pools of Variable Size. Ann. J. Epidem, 112, 124-128.
Chick, S. E (1996). Bayesian Models for limiting dilution assay and group test data. Biometrics, 52, 1055-1062.
Fletcher, J. D, Rusell. A. C and Butler. R. C (1999). Seed borne cucumber Mosaic virus in New Zealand lentil groups: yield effects and disease incidence. New Zeal J. Crop Hort 27, 197-204.
Wanyonyi, R. W, Nyongesa, L. K, Wasike, A. (2015). Estimation of Proportion of a Trait by Batch Testing with Errors in Inspection in a Quality Control Process. International Journal of Statistics and Application, 5(6), 268-278.
Johnson, N. L, Kotz, S, Wu, X. (1992). Inspection Errors for Attributes in Quality Control. Chapman & Hall.
Nyongesa, L. K (2004). Multistage group testing procedure (group screening). Communication in Statistics-Simulation and Computation, 33, 621–637.
Thompson, K. H (1962). Estimation of the Proportions of Vectors in a Natural Population of Insects; Biometrics, 18, 568-578.
Bilder, C. R and Tebbs J. M (2005). Empirical Bayes Estimation of the Disease Transmission Probability in Multiple Vector Transfer Designs. Biometrika. J. 47, 502-516.
Hepworth, G. (2005). Confidence intervals for proportions estimated by group testing with groups of unequal sizes. Journal of Agricultural, Biological and Environmental Statistics, 10, 478–497.
Tu, M. X, Litvak, E. and Pagano, M. (1995). On the Informative and Accuracy of Pooled Testing in Estimating Prevalence of a Rare Disease: Application to HIV Screening. Biometrika, 82, 287–297.
Brookmeyer, R. (1999). Analysis of multistage pooling studies of Biological specimens for Estimating Disease Incidents and prevalence. Biometrics, 55, 608-612.
Hepworth, G and Watson, R. (2009). Debiased Estimation of proportions in group testing. Applied Statistics, 58, 105–121.
Nyongesa, L. K (2011). Dual Estimation of Prevalence and Disease Incidence in pooling strategy. Communication in Statistics Theory and Method, 40, 1–12.
Gart, J. J. (1991). An application of score methodology: confidence intervals and tests of fit for one-hit curves. In Handbook of Statistics (Eds C. R. Rao and R. Chakraborty), Vol. 8, pp. 395–406. Amsterdam: Elsevier.