Two Sample Approaches to Regression Calibration for Measurement Error Correction

Samuel Joel Kamun; Cornelious Nyakundi; Richard Simwa

doi:doi:10.11648/j.ijsd.20230901.14

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Two Sample Approaches to Regression Calibration for Measurement Error Correction

Samuel Joel Kamun, Cornelious Nyakundi, Richard Simwa

Published in International Journal of Statistical Distributions and Applications (Volume 9, Issue 1)

Received: 1 February 2023 Accepted: 1 March 2023 Published: 9 March 2023

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Abstract

The goal of this work is to create methods for enhancing measurement error using regression calibration as a strategy by combining two samples, thereby increasing the relative efficiency of linear regression models. Because two or more samples are more likely to provide an accurate representation of the population than a single sample under inquiry, utilizing two samples in regression calibration is likely to produce a realistic depiction of what the actual population is when error-free. This study has generated independent estimates from two samples and combined them with weights equal to the inverse of their estimated probabilities of sample inclusion. It has also integrated two data sets into a single data set and suitably adjusted the weights on each sampled unit. The regression calibration method is most commonly used to correct predictor-response bias caused by variable measurement imperfections. Because of its simplicity, this method is often used. The fundamental principle behind regression calibration is to estimate the conditional expectation of a genuine response, given predictors measured with error and other covariates supposed to be measured without error. The predicted values are then estimated and used to assess the relationship between the response and an outcome in place of the unknown genuine response. Further information on the unobservable true predictors is required by the regression calibration program. This data is frequently obtained from a validation study that employs unbiased measurements for genuine predictors. This study has employed and compared the results obtained from the two sample approaches. Measuring errors can be produced by a variety of sources, including instrument error, laboratory error, human error, problems in documenting or executing measurements, self-reporting errors, and natural oscillations in the underlying amount. Covariate measurement error has three effects: In addition to hiding the properties of the data, which makes graphical model analysis difficult, it produces bias in parameter estimates for statistical models, resulting in a sometimes significant loss of power for detecting fascinating correlations between variables. The two sample approaches employed by the study have yielded acceptable results.

Published in	International Journal of Statistical Distributions and Applications (Volume 9, Issue 1)
DOI	10.11648/j.ijsd.20230901.14
Page(s)	35-40
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

Multiple Samples, Regression Calibration, Population, Error Free, Inclusion Probabilities

References

[1]	Agogo, G. O., van der Voet, H., van't Veer, P., Ferrari, P., et al. (2014). Use of Two-Part Regression Calibration Model to Correct for Measurement Error in Episodically Consumed Foods in a Single-Replicate Study Design: EPIC Case Study. PLoS ONE 9 (11): e113160. doi: 10.1371/journal.pone.0113160.
[2]	Brazzale, A. R. and Guolo, A. (2008). A simulation-based comparison of techniques to correct for measurement error in matched case-control studies. Stat.med, vol. 27, issue 19, pp. 3755-3775.
[3]	Breidt, F. J. and Opsomer, J. D. (2000), Local polynomial regression estimators in survey sampling, Annals of Statistics, 28, 1026-1053.
[4]	Buonaccorsi, J. P. (2010). Measurement Error: Models, Methods and Application. Chapman Hall/CRC.
[5]	Buzas, J. S., Stefanski, L. A. and Tosteson, D. (2014). Measurement Error. In: Ahrens, W., Pigeot, I (eds). Handbook of Epidemiology. Springer, New York, NY. https://doi.org/10.1007/978-0-387-09834-0_19.
[6]	Carroll, R. J., Ruppert, D. and Stefanski, L. A. (2006). Measurement Error in Nonlinear Models. Chapman and Hall/CRC. DOI: https://doi.org/10.1201/9781420010138.
[7]	Dorfman, A. H. (2008), The two sample problem, Proceedings of the Joint Statistical Meetings, Section of Survey Research Methods. Journal of the American Statistical Association, 87, 998-1004.
[8]	Fraser, G. E. and Stram, D. O. (2001). Regression Calibration in studies with correlated variables measured with error. Americal Journal of Epidemiology, vol. 154, issue 9, pp. 836-844.
[9]	Freedman, L. S., Midhune, D., Carroll, R. J. and Kipnis, V. (2008). A Comparison of regression Calibration, Moment Reconstruction and imputation for adjusting for covariate measurement error in regression. Stat. Med. 27 (25): 5195-5216; doi: 10.1002/sim3361.
[10]	Keogh, R. H. and White, I. R. (2014). A toolkit for Measurement Error correction, with focus on nutritional epidemiology. Stat.Med. 33 (12): 2135-55.
[11]	Masser, K. and Natarajan, L. (2008). Maximum Likelihood, Multiple imputation and regression calibration for measurement error adjustment. Stat.Med. vol. 27, issue 30, Annual Conference of the International Society for Clinical Biostatistics, pp 6332-6350.
[12]	Merkouris, T. (2004), Combining independent regression estimators from multiple surveys, Journal of the American Statistical Association, 99, 1131-1139.
[13]	Rothman, K. J., Greenland, S. and Lash, T. L. (2008). Modern Epidemiology. Wolters Kluwer\|Lippincott Williams & Williams.
[14]	Spiegelman, D. (2013). Regression Calibration in air pollution Epidemiology with exposure estimated by spatio-temporal modelling. Environmetrics, 24 (8), 521. https://doi.org/10..1002/env.2249.
[15]	THOMAS, d., Stram, D. and Dwyer, J. (1993). Exposure Measurement Error: Influence on Exposure-Disease relationships and Methods of correction. Annu. Rev. Publ. Health. 14; 69-93.

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APA Style

Samuel Joel Kamun, Cornelious Nyakundi, Richard Simwa. (2023). Two Sample Approaches to Regression Calibration for Measurement Error Correction. International Journal of Statistical Distributions and Applications, 9(1), 35-40. https://doi.org/10.11648/j.ijsd.20230901.14

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ACS Style

Samuel Joel Kamun; Cornelious Nyakundi; Richard Simwa. Two Sample Approaches to Regression Calibration for Measurement Error Correction. Int. J. Stat. Distrib. Appl. 2023, 9(1), 35-40. doi: 10.11648/j.ijsd.20230901.14

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AMA Style

Samuel Joel Kamun, Cornelious Nyakundi, Richard Simwa. Two Sample Approaches to Regression Calibration for Measurement Error Correction. Int J Stat Distrib Appl. 2023;9(1):35-40. doi: 10.11648/j.ijsd.20230901.14

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@article{10.11648/j.ijsd.20230901.14,
  author = {Samuel Joel Kamun and Cornelious Nyakundi and Richard Simwa},
  title = {Two Sample Approaches to Regression Calibration for Measurement Error Correction},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {9},
  number = {1},
  pages = {35-40},
  doi = {10.11648/j.ijsd.20230901.14},
  url = {https://doi.org/10.11648/j.ijsd.20230901.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20230901.14},
  abstract = {The goal of this work is to create methods for enhancing measurement error using regression calibration as a strategy by combining two samples, thereby increasing the relative efficiency of linear regression models. Because two or more samples are more likely to provide an accurate representation of the population than a single sample under inquiry, utilizing two samples in regression calibration is likely to produce a realistic depiction of what the actual population is when error-free. This study has generated independent estimates from two samples and combined them with weights equal to the inverse of their estimated probabilities of sample inclusion. It has also integrated two data sets into a single data set and suitably adjusted the weights on each sampled unit. The regression calibration method is most commonly used to correct predictor-response bias caused by variable measurement imperfections. Because of its simplicity, this method is often used. The fundamental principle behind regression calibration is to estimate the conditional expectation of a genuine response, given predictors measured with error and other covariates supposed to be measured without error. The predicted values are then estimated and used to assess the relationship between the response and an outcome in place of the unknown genuine response. Further information on the unobservable true predictors is required by the regression calibration program. This data is frequently obtained from a validation study that employs unbiased measurements for genuine predictors. This study has employed and compared the results obtained from the two sample approaches. Measuring errors can be produced by a variety of sources, including instrument error, laboratory error, human error, problems in documenting or executing measurements, self-reporting errors, and natural oscillations in the underlying amount. Covariate measurement error has three effects: In addition to hiding the properties of the data, which makes graphical model analysis difficult, it produces bias in parameter estimates for statistical models, resulting in a sometimes significant loss of power for detecting fascinating correlations between variables. The two sample approaches employed by the study have yielded acceptable results.},
 year = {2023}
}

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TY  - JOUR
T1  - Two Sample Approaches to Regression Calibration for Measurement Error Correction
AU  - Samuel Joel Kamun
AU  - Cornelious Nyakundi
AU  - Richard Simwa
Y1  - 2023/03/09
PY  - 2023
N1  - https://doi.org/10.11648/j.ijsd.20230901.14
DO  - 10.11648/j.ijsd.20230901.14
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 35
EP  - 40
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20230901.14
AB  - The goal of this work is to create methods for enhancing measurement error using regression calibration as a strategy by combining two samples, thereby increasing the relative efficiency of linear regression models. Because two or more samples are more likely to provide an accurate representation of the population than a single sample under inquiry, utilizing two samples in regression calibration is likely to produce a realistic depiction of what the actual population is when error-free. This study has generated independent estimates from two samples and combined them with weights equal to the inverse of their estimated probabilities of sample inclusion. It has also integrated two data sets into a single data set and suitably adjusted the weights on each sampled unit. The regression calibration method is most commonly used to correct predictor-response bias caused by variable measurement imperfections. Because of its simplicity, this method is often used. The fundamental principle behind regression calibration is to estimate the conditional expectation of a genuine response, given predictors measured with error and other covariates supposed to be measured without error. The predicted values are then estimated and used to assess the relationship between the response and an outcome in place of the unknown genuine response. Further information on the unobservable true predictors is required by the regression calibration program. This data is frequently obtained from a validation study that employs unbiased measurements for genuine predictors. This study has employed and compared the results obtained from the two sample approaches. Measuring errors can be produced by a variety of sources, including instrument error, laboratory error, human error, problems in documenting or executing measurements, self-reporting errors, and natural oscillations in the underlying amount. Covariate measurement error has three effects: In addition to hiding the properties of the data, which makes graphical model analysis difficult, it produces bias in parameter estimates for statistical models, resulting in a sometimes significant loss of power for detecting fascinating correlations between variables. The two sample approaches employed by the study have yielded acceptable results.
VL  - 9
IS  - 1
ER  -

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Author Information

Samuel Joel Kamun

Department of Mathematics and Actuarial Sciences, Catholic University of Eastern Africa, Nairobi, Kenya
Cornelious Nyakundi

Department of Mathematics and Actuarial Sciences, Catholic University of Eastern Africa, Nairobi, Kenya
Richard Simwa

Department of Account, Finance and Economics, School of Business, KCA University, Nairobi, Kenya

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APA Style

Samuel Joel Kamun, Cornelious Nyakundi, Richard Simwa. (2023). Two Sample Approaches to Regression Calibration for Measurement Error Correction. International Journal of Statistical Distributions and Applications, 9(1), 35-40. https://doi.org/10.11648/j.ijsd.20230901.14

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ACS Style

Samuel Joel Kamun; Cornelious Nyakundi; Richard Simwa. Two Sample Approaches to Regression Calibration for Measurement Error Correction. Int. J. Stat. Distrib. Appl. 2023, 9(1), 35-40. doi: 10.11648/j.ijsd.20230901.14

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AMA Style

Samuel Joel Kamun, Cornelious Nyakundi, Richard Simwa. Two Sample Approaches to Regression Calibration for Measurement Error Correction. Int J Stat Distrib Appl. 2023;9(1):35-40. doi: 10.11648/j.ijsd.20230901.14

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@article{10.11648/j.ijsd.20230901.14,
  author = {Samuel Joel Kamun and Cornelious Nyakundi and Richard Simwa},
  title = {Two Sample Approaches to Regression Calibration for Measurement Error Correction},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {9},
  number = {1},
  pages = {35-40},
  doi = {10.11648/j.ijsd.20230901.14},
  url = {https://doi.org/10.11648/j.ijsd.20230901.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20230901.14},
  abstract = {The goal of this work is to create methods for enhancing measurement error using regression calibration as a strategy by combining two samples, thereby increasing the relative efficiency of linear regression models. Because two or more samples are more likely to provide an accurate representation of the population than a single sample under inquiry, utilizing two samples in regression calibration is likely to produce a realistic depiction of what the actual population is when error-free. This study has generated independent estimates from two samples and combined them with weights equal to the inverse of their estimated probabilities of sample inclusion. It has also integrated two data sets into a single data set and suitably adjusted the weights on each sampled unit. The regression calibration method is most commonly used to correct predictor-response bias caused by variable measurement imperfections. Because of its simplicity, this method is often used. The fundamental principle behind regression calibration is to estimate the conditional expectation of a genuine response, given predictors measured with error and other covariates supposed to be measured without error. The predicted values are then estimated and used to assess the relationship between the response and an outcome in place of the unknown genuine response. Further information on the unobservable true predictors is required by the regression calibration program. This data is frequently obtained from a validation study that employs unbiased measurements for genuine predictors. This study has employed and compared the results obtained from the two sample approaches. Measuring errors can be produced by a variety of sources, including instrument error, laboratory error, human error, problems in documenting or executing measurements, self-reporting errors, and natural oscillations in the underlying amount. Covariate measurement error has three effects: In addition to hiding the properties of the data, which makes graphical model analysis difficult, it produces bias in parameter estimates for statistical models, resulting in a sometimes significant loss of power for detecting fascinating correlations between variables. The two sample approaches employed by the study have yielded acceptable results.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Two Sample Approaches to Regression Calibration for Measurement Error Correction
AU  - Samuel Joel Kamun
AU  - Cornelious Nyakundi
AU  - Richard Simwa
Y1  - 2023/03/09
PY  - 2023
N1  - https://doi.org/10.11648/j.ijsd.20230901.14
DO  - 10.11648/j.ijsd.20230901.14
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 35
EP  - 40
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20230901.14
AB  - The goal of this work is to create methods for enhancing measurement error using regression calibration as a strategy by combining two samples, thereby increasing the relative efficiency of linear regression models. Because two or more samples are more likely to provide an accurate representation of the population than a single sample under inquiry, utilizing two samples in regression calibration is likely to produce a realistic depiction of what the actual population is when error-free. This study has generated independent estimates from two samples and combined them with weights equal to the inverse of their estimated probabilities of sample inclusion. It has also integrated two data sets into a single data set and suitably adjusted the weights on each sampled unit. The regression calibration method is most commonly used to correct predictor-response bias caused by variable measurement imperfections. Because of its simplicity, this method is often used. The fundamental principle behind regression calibration is to estimate the conditional expectation of a genuine response, given predictors measured with error and other covariates supposed to be measured without error. The predicted values are then estimated and used to assess the relationship between the response and an outcome in place of the unknown genuine response. Further information on the unobservable true predictors is required by the regression calibration program. This data is frequently obtained from a validation study that employs unbiased measurements for genuine predictors. This study has employed and compared the results obtained from the two sample approaches. Measuring errors can be produced by a variety of sources, including instrument error, laboratory error, human error, problems in documenting or executing measurements, self-reporting errors, and natural oscillations in the underlying amount. Covariate measurement error has three effects: In addition to hiding the properties of the data, which makes graphical model analysis difficult, it produces bias in parameter estimates for statistical models, resulting in a sometimes significant loss of power for detecting fascinating correlations between variables. The two sample approaches employed by the study have yielded acceptable results.
VL  - 9
IS  - 1
ER  -

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