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.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 5, Issue 3) |
| DOI | 10.11648/j.ajtas.20160503.19 |
| Page(s) | 138-145 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2016. Published by Science Publishing Group |
Group Testing, Maximum Likelihood Estimator, Almost Unbiased Estimator, Bias Adjuster Formula, Bias-Corrected Estimates
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APA Style
Langat Erick Kipyegon, Tonui Benard Cheruiyot, Langat Reuben Cheruiyot. (2016). An Almost Unbiased Estimator in Group Testing with Errors in Inspection. American Journal of Theoretical and Applied Statistics, 5(3), 138-145. https://doi.org/10.11648/j.ajtas.20160503.19
ACS Style
Langat Erick Kipyegon; Tonui Benard Cheruiyot; Langat Reuben Cheruiyot. An Almost Unbiased Estimator in Group Testing with Errors in Inspection. Am. J. Theor. Appl. Stat. 2016, 5(3), 138-145. doi: 10.11648/j.ajtas.20160503.19
AMA Style
Langat Erick Kipyegon, Tonui Benard Cheruiyot, Langat Reuben Cheruiyot. An Almost Unbiased Estimator in Group Testing with Errors in Inspection. Am J Theor Appl Stat. 2016;5(3):138-145. doi: 10.11648/j.ajtas.20160503.19
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Download@article{10.11648/j.ajtas.20160503.19,
author = {Langat Erick Kipyegon and Tonui Benard Cheruiyot and Langat Reuben Cheruiyot},
title = {An Almost Unbiased Estimator in Group Testing with Errors in Inspection},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {5},
number = {3},
pages = {138-145},
doi = {10.11648/j.ajtas.20160503.19},
url = {https://doi.org/10.11648/j.ajtas.20160503.19},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160503.19},
abstract = {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.},
year = {2016}
}
TY - JOUR T1 - An Almost Unbiased Estimator in Group Testing with Errors in Inspection AU - Langat Erick Kipyegon AU - Tonui Benard Cheruiyot AU - Langat Reuben Cheruiyot Y1 - 2016/05/25 PY - 2016 N1 - https://doi.org/10.11648/j.ajtas.20160503.19 DO - 10.11648/j.ajtas.20160503.19 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 138 EP - 145 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20160503.19 AB - 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. VL - 5 IS - 3 ER -
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