Power of Simulation Extrapolation in Correction of Covariates Measured with Errors

Joseph Njuguna Karomo; Samuel Musili Mwalili; Anthony Wanjoya

doi:doi:10.11648/j.ijdsa.20190502.11

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Power of Simulation Extrapolation in Correction of Covariates Measured with Errors

Joseph Njuguna Karomo, Samuel Musili Mwalili, Anthony Wanjoya

Published in International Journal of Data Science and Analysis (Volume 5, Issue 2)

Received: 18 April 2019 Accepted: 21 May 2019 Published: 5 June 2019

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Abstract

Statistics is one of the most vibrant disciplines where research is inevitable. Most researches in statistics are concerned with the measurement of values of variables in order to make valid conclusions for decision making. Often, researchers do not use the exact values of the variables since it’s difficult to establish the exact value of variables during data collection. This study aimed at using simulation studies to ascertain the power of Simulation Extrapolation (SIMEX) in correcting the bias of coefficients of a logistic regression model with one covariate measured with error. The corrected coefficient values of the model can then be used to predict the exact values of the explanatory variable. The Mean Square Error and the coverage probability were used to test the adequacy of the different model's estimates. The study showed that the use of SIMEX with the quadratic fitting method would give significantly good estimates of the model’s predictors’ coefficients. For further studies, the researcher recommends the study to be done using other models and with multiple covariates measured with errors.

Published in	International Journal of Data Science and Analysis (Volume 5, Issue 2)
DOI	10.11648/j.ijdsa.20190502.11
Page(s)	13-17
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), 2019. Published by Science Publishing Group

Keywords

Simulation Extrapolation, SIMEX, Measurement Errors, Berkson Error, Naive Estimator, Bias

References

[1]	Fuller, Wayne A. Measurement error models. Vol. 305. John Wiley & Sons, 2009.
[2]	Cook, John R., and Leonard A. Stefanski. "Simulation-extrapolation estimation in parametric measurement error models." Journal of the American Statistical association 89, no. 428 (1994): 1314-1328.
[3]	Freedman, Laurence S., Douglas Midthune, Raymond J. Carroll, and Victor Kipnis. "A comparison of regression calibration, moment reconstruction and imputation for adjusting for covariate measurement error in regression." Statistics in medicine 27, no. 25 (2008): 5195-5216.
[4]	Stefanski, Leonard A., and James R. Cook. "Simulation-extrapolation: the measurement error jackknife." Journal of the American Statistical Association 90, no. 432 (1995): 1247-1256.
[5]	Babanezhad, Manoochehr. "Measurement error and causal inference with instrumental variables." PhD diss., Ghent University, 2009.
[6]	Rudemo, Mats, David Ruppert, and J. C. Streibig. "Random-effect models in nonlinear regression with applications to bioassay." Biometrics (1989): 349-362.
[7]	Stefanski, Leonard A. "Measurement error models." Journal of the American Statistical Association 95, no. 452 (2000): 1353-1358.
[8]	Carroll, Raymond J., and Helmut Küchenhoff. "Approximative Methods for Regression Models with Errors in the Covariates." In XploRe: An Interactive Statistical Computing Environment, pp. 275-285. Springer, New York, NY, 1995.
[9]	Shang, Yi. "Measurement error adjustment using the SIMEX method: An application to student growth percentiles." Journal of Educational Measurement 49, no. 4 (2012): 446-465.
[10]	Weeding, Jennifer Lee. "Bayesian measurement error modeling with application to the area under the curve summary measure." PhD diss., Montana State University-Bozeman, College of Letters & Science, 2016.
[11]	Küchenhoff, Helmut, Samuel M. Mwalili, and Emmanuel Lesaffre. "A general method for dealing with misclassification in regression: The misclassification SIMEX." Biometrics 62, no. 1 (2006): 85-96.
[12]	Mwalili, Samuel Musili. "Bayesian and frequentist approaches to correct for misclassification error with applications to caries research." PhD diss., PhD thesis, Catholic University of Leuven, Leuven, Belgium, 2006.
[13]	Hasan, Mohammad Mahadi, Ashish Sharma, Fiona Johnson, Gregoire Mariethoz, and Alan Seed. "Correcting bias in radar Z–R relationships due to uncertainty in point rain gauge networks." Journal of hydrology 519 (2014): 1668-1676.
[14]	Tsamardinos, Ioannis, Amin Rakhshani, and Vincenzo Lagani. "Performance-estimation properties of cross-validation-based protocols with simultaneous hyper-parameter optimization." International Journal on Artificial Intelligence Tools 24, no. 05 (2015): 1540023.
[15]	Shao, Jun, and Dongsheng Tu. The jackknife and bootstrap. Springer Science & Business Media, 2012.

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APA Style

Joseph Njuguna Karomo, Samuel Musili Mwalili, Anthony Wanjoya. (2019). Power of Simulation Extrapolation in Correction of Covariates Measured with Errors. International Journal of Data Science and Analysis, 5(2), 13-17. https://doi.org/10.11648/j.ijdsa.20190502.11

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ACS Style

Joseph Njuguna Karomo; Samuel Musili Mwalili; Anthony Wanjoya. Power of Simulation Extrapolation in Correction of Covariates Measured with Errors. Int. J. Data Sci. Anal. 2019, 5(2), 13-17. doi: 10.11648/j.ijdsa.20190502.11

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AMA Style

Joseph Njuguna Karomo, Samuel Musili Mwalili, Anthony Wanjoya. Power of Simulation Extrapolation in Correction of Covariates Measured with Errors. Int J Data Sci Anal. 2019;5(2):13-17. doi: 10.11648/j.ijdsa.20190502.11

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@article{10.11648/j.ijdsa.20190502.11,
  author = {Joseph Njuguna Karomo and Samuel Musili Mwalili and Anthony Wanjoya},
  title = {Power of Simulation Extrapolation in Correction of Covariates Measured with Errors},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {2},
  pages = {13-17},
  doi = {10.11648/j.ijdsa.20190502.11},
  url = {https://doi.org/10.11648/j.ijdsa.20190502.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190502.11},
  abstract = {Statistics is one of the most vibrant disciplines where research is inevitable. Most researches in statistics are concerned with the measurement of values of variables in order to make valid conclusions for decision making. Often, researchers do not use the exact values of the variables since it’s difficult to establish the exact value of variables during data collection. This study aimed at using simulation studies to ascertain the power of Simulation Extrapolation (SIMEX) in correcting the bias of coefficients of a logistic regression model with one covariate measured with error. The corrected coefficient values of the model can then be used to predict the exact values of the explanatory variable. The Mean Square Error and the coverage probability were used to test the adequacy of the different model's estimates. The study showed that the use of SIMEX with the quadratic fitting method would give significantly good estimates of the model’s predictors’ coefficients. For further studies, the researcher recommends the study to be done using other models and with multiple covariates measured with errors.},
 year = {2019}
}

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TY  - JOUR
T1  - Power of Simulation Extrapolation in Correction of Covariates Measured with Errors
AU  - Joseph Njuguna Karomo
AU  - Samuel Musili Mwalili
AU  - Anthony Wanjoya
Y1  - 2019/06/05
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190502.11
DO  - 10.11648/j.ijdsa.20190502.11
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 13
EP  - 17
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190502.11
AB  - Statistics is one of the most vibrant disciplines where research is inevitable. Most researches in statistics are concerned with the measurement of values of variables in order to make valid conclusions for decision making. Often, researchers do not use the exact values of the variables since it’s difficult to establish the exact value of variables during data collection. This study aimed at using simulation studies to ascertain the power of Simulation Extrapolation (SIMEX) in correcting the bias of coefficients of a logistic regression model with one covariate measured with error. The corrected coefficient values of the model can then be used to predict the exact values of the explanatory variable. The Mean Square Error and the coverage probability were used to test the adequacy of the different model's estimates. The study showed that the use of SIMEX with the quadratic fitting method would give significantly good estimates of the model’s predictors’ coefficients. For further studies, the researcher recommends the study to be done using other models and with multiple covariates measured with errors.
VL  - 5
IS  - 2
ER  -

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Author Information

Joseph Njuguna Karomo

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Samuel Musili Mwalili

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Wanjoya

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Joseph Njuguna Karomo, Samuel Musili Mwalili, Anthony Wanjoya. (2019). Power of Simulation Extrapolation in Correction of Covariates Measured with Errors. International Journal of Data Science and Analysis, 5(2), 13-17. https://doi.org/10.11648/j.ijdsa.20190502.11

Copy | Download

ACS Style

Joseph Njuguna Karomo; Samuel Musili Mwalili; Anthony Wanjoya. Power of Simulation Extrapolation in Correction of Covariates Measured with Errors. Int. J. Data Sci. Anal. 2019, 5(2), 13-17. doi: 10.11648/j.ijdsa.20190502.11

Copy | Download

AMA Style

Joseph Njuguna Karomo, Samuel Musili Mwalili, Anthony Wanjoya. Power of Simulation Extrapolation in Correction of Covariates Measured with Errors. Int J Data Sci Anal. 2019;5(2):13-17. doi: 10.11648/j.ijdsa.20190502.11

Copy | Download

@article{10.11648/j.ijdsa.20190502.11,
  author = {Joseph Njuguna Karomo and Samuel Musili Mwalili and Anthony Wanjoya},
  title = {Power of Simulation Extrapolation in Correction of Covariates Measured with Errors},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {2},
  pages = {13-17},
  doi = {10.11648/j.ijdsa.20190502.11},
  url = {https://doi.org/10.11648/j.ijdsa.20190502.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190502.11},
  abstract = {Statistics is one of the most vibrant disciplines where research is inevitable. Most researches in statistics are concerned with the measurement of values of variables in order to make valid conclusions for decision making. Often, researchers do not use the exact values of the variables since it’s difficult to establish the exact value of variables during data collection. This study aimed at using simulation studies to ascertain the power of Simulation Extrapolation (SIMEX) in correcting the bias of coefficients of a logistic regression model with one covariate measured with error. The corrected coefficient values of the model can then be used to predict the exact values of the explanatory variable. The Mean Square Error and the coverage probability were used to test the adequacy of the different model's estimates. The study showed that the use of SIMEX with the quadratic fitting method would give significantly good estimates of the model’s predictors’ coefficients. For further studies, the researcher recommends the study to be done using other models and with multiple covariates measured with errors.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Power of Simulation Extrapolation in Correction of Covariates Measured with Errors
AU  - Joseph Njuguna Karomo
AU  - Samuel Musili Mwalili
AU  - Anthony Wanjoya
Y1  - 2019/06/05
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190502.11
DO  - 10.11648/j.ijdsa.20190502.11
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 13
EP  - 17
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190502.11
AB  - Statistics is one of the most vibrant disciplines where research is inevitable. Most researches in statistics are concerned with the measurement of values of variables in order to make valid conclusions for decision making. Often, researchers do not use the exact values of the variables since it’s difficult to establish the exact value of variables during data collection. This study aimed at using simulation studies to ascertain the power of Simulation Extrapolation (SIMEX) in correcting the bias of coefficients of a logistic regression model with one covariate measured with error. The corrected coefficient values of the model can then be used to predict the exact values of the explanatory variable. The Mean Square Error and the coverage probability were used to test the adequacy of the different model's estimates. The study showed that the use of SIMEX with the quadratic fitting method would give significantly good estimates of the model’s predictors’ coefficients. For further studies, the researcher recommends the study to be done using other models and with multiple covariates measured with errors.
VL  - 5
IS  - 2
ER  -

Copy | Download