Sequentially Selecting Between Two Experiment for Optimal Estimation of a Trait with Misclassification

George Matiri; Kennedy Nyongesa; Ali Islam

doi:doi:10.11648/j.ajtas.20170602.12

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Sequentially Selecting Between Two Experiment for Optimal Estimation of a Trait with Misclassification

George Matiri, Kennedy Nyongesa, Ali Islam

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 2)

Received: 18 January 2017 Accepted: 3 February 2017 Published: 27 February 2017

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Abstract

The idea of pool testing originated with Dorfman during the World War II as an economical method of testing blood samples of army inductees in order to detect the presence of infection. Dorfman proposed that rather than testing each blood sample individually, portions of each of the samples can be pooled and the pooled sample tested first. If the pooled sample is free of infection, all inductees in the pooled sample are passed with no further tests otherwise the remaining portions of each of the blood samples are tested individually. Apart from classification problem, pool testing can also be used in estimating the prevalence rate of a trait in a population which was the focus of our study. In approximating the prevalence rate, one-at-a-time testing is time consuming, non-cost effective and is bound to errors hence pool testing procedures have been proposed to address these problems. This study has developed statistical model which is used to sequentially switching between two experiments when the sensitivity and specificity of the test kits is less than 100%. The experiments are selected sequentially, so that at each stage, the information available at that stage is used to determine which experiment to carry out at the next stage. The method of maximum likelihood estimator (MLE) was used in obtaining the estimators. The fisher information of different experiments is compared and the cut off values where one experiment is better than the other are calculated. The variance of the estimators has also been compared. The joint model has been compared to one-at-a-time and pool testing models by computing ARE. The joint model is found to be more efficient.

Published in	American Journal of Theoretical and Applied Statistics (Volume 6, Issue 2)
DOI	10.11648/j.ajtas.20170602.12
Page(s)	79-89
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), 2024. Published by Science Publishing Group

Keywords

Pool, Pool Testing, Cut off Value, Prevalence Rate, Sensitivity, Specificity

References

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[2]	Dorfman, R. (1943). The detection of defective members of large population. Annals of Mathematical Statistics 14, 436-440.
[3]	Gastwirth, J. L., and Johnson, W. O. (1994). Screening with cost-effective quality control: Estimation of prevalence of a rare disease, preserving the anonymity of the subject by Pool- testing; Application to estimating the prevalence of AIDS antibodies in blood donors. Journal of statistical planning and inferences, 22, 15–27.
[4]	Hammick, P. A. and Gastwirth, J. L. (1994). Extending the applicability of estimation of prevalence of sensitive characteristics by pool testing to moderate prevalence populations. International Statistical Review 62, 319-331.
[5]	Janis H., Connie P., and Quentin F. S. (1998). Sequentially deciding between two experiments for estimating a common success probability. Journal of the American statistical association. December 1998, vol 93 no 444, 1502-1511.
[6]	Johnson, N. L., Kotz, S. and Wu, X. (1991). Inspection errors for attributes in quality control. London; Chapman and Hall.
[7]	Juan, D. and Wenjun, X. (2015). Robust group testing for multiple traits with misclassifications. Journal of Applied statistics, vol 42 no. 10, 2115-2015.
[8]	Kline, R. L., Bothus, T., Brookmeyer, R., Zeyer, S., and Quinn, T. (1989). Evaluation of human Immunodeficiency virus seroprevalence in population surveys using pooled sera. Journal of clinical microbiology, 27, 1449-1452.
[9]	Litvak, E., Tu, X. M. and Pagano, M. (1994). Screening for the presence of a disease by pooling sera samples. Journal of the America statistical Association, 89, 424-434.
[10]	Maheswaran, S., Haragopal, V. V., and Pandit, S. N. N, (2008). Pool-testing using block testing strategy. Journal of statistical planning and inference (Submitted).
[11]	Manzon, O. T., Palalin, F. J. E., Dimaal, E., Balis, A. M., Samson, C., and Mitchel, S. (1992). Relevance of antibody content and test format in HIV testing of pooled sera. AIDS, 6, 43-48.
[12]	Mundel (1984). Group-testing. Journal of quality technology, 16, 181-187.
[13]	Nyongesa, L. K. (2011). Dual Estimation of Prevalence and Disease Incidence in Pool-Testing Strategy. Communication in Statistics Theory and Method, 40, 3218-3229.
[14]	Nyongesa, L. K. (2004). Multistage Pool Testing Procedure (Pool screening). Communication in Statistics-Simulation and computation, 33, 621-637.
[15]	Sobel, M. and Groll P. A., (1966). Binomial Group-Testing with an Unknown Proportion of Defectives. American Statistical Association and American Society for Quality, 8, 631-656.
[16]	Syaywa, J. P and Nyongesa, L. K. (2010). Pool Testing with Test Errors Made Easier. International Journal of Computational Statistics.
[17]	Tamba C. L, Nyongesa K. L., Mwangi J. W., (2012). Computational Pool-Testing Strategy. Egerton University Journal, 11: 51-56.
[18]	Thomson, K. H. (1962). Estimation of the Population of Vectors in a Natural Population of Insects. Biometrics, 18, 568-578.
[19]	Xie, M., Tatsuoka, K., Sacks, J and Young, S. (2001). Pool Testing with Blockers and Synergism. Journal of American Statistical Association 96, 92-102.

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APA Style

George Matiri, Kennedy Nyongesa, Ali Islam. (2017). Sequentially Selecting Between Two Experiment for Optimal Estimation of a Trait with Misclassification. American Journal of Theoretical and Applied Statistics, 6(2), 79-89. https://doi.org/10.11648/j.ajtas.20170602.12

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George Matiri; Kennedy Nyongesa; Ali Islam. Sequentially Selecting Between Two Experiment for Optimal Estimation of a Trait with Misclassification. Am. J. Theor. Appl. Stat. 2017, 6(2), 79-89. doi: 10.11648/j.ajtas.20170602.12

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AMA Style

George Matiri, Kennedy Nyongesa, Ali Islam. Sequentially Selecting Between Two Experiment for Optimal Estimation of a Trait with Misclassification. Am J Theor Appl Stat. 2017;6(2):79-89. doi: 10.11648/j.ajtas.20170602.12

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@article{10.11648/j.ajtas.20170602.12,
  author = {George Matiri and Kennedy Nyongesa and Ali Islam},
  title = {Sequentially Selecting Between Two Experiment for Optimal Estimation of a Trait with Misclassification},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {6},
  number = {2},
  pages = {79-89},
  doi = {10.11648/j.ajtas.20170602.12},
  url = {https://doi.org/10.11648/j.ajtas.20170602.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170602.12},
  abstract = {The idea of pool testing originated with Dorfman during the World War II as an economical method of testing blood samples of army inductees in order to detect the presence of infection. Dorfman proposed that rather than testing each blood sample individually, portions of each of the samples can be pooled and the pooled sample tested first. If the pooled sample is free of infection, all inductees in the pooled sample are passed with no further tests otherwise the remaining portions of each of the blood samples are tested individually. Apart from classification problem, pool testing can also be used in estimating the prevalence rate of a trait in a population which was the focus of our study. In approximating the prevalence rate, one-at-a-time testing is time consuming, non-cost effective and is bound to errors hence pool testing procedures have been proposed to address these problems. This study has developed statistical model which is used to sequentially switching between two experiments when the sensitivity and specificity of the test kits is less than 100%. The experiments are selected sequentially, so that at each stage, the information available at that stage is used to determine which experiment to carry out at the next stage. The method of maximum likelihood estimator (MLE) was used in obtaining the estimators. The fisher information of different experiments is compared and the cut off values where one experiment is better than the other are calculated. The variance of the estimators has also been compared. The joint model has been compared to one-at-a-time and pool testing models by computing ARE. The joint model is found to be more efficient.},
 year = {2017}
}

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TY - JOUR
T1 - Sequentially Selecting Between Two Experiment for Optimal Estimation of a Trait with Misclassification
AU - George Matiri
AU - Kennedy Nyongesa
AU - Ali Islam
Y1 - 2017/02/27
PY - 2017
N1 - https://doi.org/10.11648/j.ajtas.20170602.12
DO - 10.11648/j.ajtas.20170602.12
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 - 79
EP - 89
PB - Science Publishing Group
SN - 2326-9006
UR - https://doi.org/10.11648/j.ajtas.20170602.12
AB - The idea of pool testing originated with Dorfman during the World War II as an economical method of testing blood samples of army inductees in order to detect the presence of infection. Dorfman proposed that rather than testing each blood sample individually, portions of each of the samples can be pooled and the pooled sample tested first. If the pooled sample is free of infection, all inductees in the pooled sample are passed with no further tests otherwise the remaining portions of each of the blood samples are tested individually. Apart from classification problem, pool testing can also be used in estimating the prevalence rate of a trait in a population which was the focus of our study. In approximating the prevalence rate, one-at-a-time testing is time consuming, non-cost effective and is bound to errors hence pool testing procedures have been proposed to address these problems. This study has developed statistical model which is used to sequentially switching between two experiments when the sensitivity and specificity of the test kits is less than 100%. The experiments are selected sequentially, so that at each stage, the information available at that stage is used to determine which experiment to carry out at the next stage. The method of maximum likelihood estimator (MLE) was used in obtaining the estimators. The fisher information of different experiments is compared and the cut off values where one experiment is better than the other are calculated. The variance of the estimators has also been compared. The joint model has been compared to one-at-a-time and pool testing models by computing ARE. The joint model is found to be more efficient.
VL - 6
IS - 2
ER -

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Author Information

George Matiri

Department of Mathematics, Egerton University, Nakuru, Kenya
Kennedy Nyongesa

Department of Mathematics, Masinde Muliro University of Science and Technology, Kakamega, Kenya
Ali Islam

Department of Mathematics, Egerton University, Nakuru, Kenya

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APA Style

George Matiri, Kennedy Nyongesa, Ali Islam. (2017). Sequentially Selecting Between Two Experiment for Optimal Estimation of a Trait with Misclassification. American Journal of Theoretical and Applied Statistics, 6(2), 79-89. https://doi.org/10.11648/j.ajtas.20170602.12

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ACS Style

George Matiri; Kennedy Nyongesa; Ali Islam. Sequentially Selecting Between Two Experiment for Optimal Estimation of a Trait with Misclassification. Am. J. Theor. Appl. Stat. 2017, 6(2), 79-89. doi: 10.11648/j.ajtas.20170602.12

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AMA Style

George Matiri, Kennedy Nyongesa, Ali Islam. Sequentially Selecting Between Two Experiment for Optimal Estimation of a Trait with Misclassification. Am J Theor Appl Stat. 2017;6(2):79-89. doi: 10.11648/j.ajtas.20170602.12

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@article{10.11648/j.ajtas.20170602.12,
  author = {George Matiri and Kennedy Nyongesa and Ali Islam},
  title = {Sequentially Selecting Between Two Experiment for Optimal Estimation of a Trait with Misclassification},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {6},
  number = {2},
  pages = {79-89},
  doi = {10.11648/j.ajtas.20170602.12},
  url = {https://doi.org/10.11648/j.ajtas.20170602.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170602.12},
  abstract = {The idea of pool testing originated with Dorfman during the World War II as an economical method of testing blood samples of army inductees in order to detect the presence of infection. Dorfman proposed that rather than testing each blood sample individually, portions of each of the samples can be pooled and the pooled sample tested first. If the pooled sample is free of infection, all inductees in the pooled sample are passed with no further tests otherwise the remaining portions of each of the blood samples are tested individually. Apart from classification problem, pool testing can also be used in estimating the prevalence rate of a trait in a population which was the focus of our study. In approximating the prevalence rate, one-at-a-time testing is time consuming, non-cost effective and is bound to errors hence pool testing procedures have been proposed to address these problems. This study has developed statistical model which is used to sequentially switching between two experiments when the sensitivity and specificity of the test kits is less than 100%. The experiments are selected sequentially, so that at each stage, the information available at that stage is used to determine which experiment to carry out at the next stage. The method of maximum likelihood estimator (MLE) was used in obtaining the estimators. The fisher information of different experiments is compared and the cut off values where one experiment is better than the other are calculated. The variance of the estimators has also been compared. The joint model has been compared to one-at-a-time and pool testing models by computing ARE. The joint model is found to be more efficient.},
 year = {2017}
}

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