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Vol. 68, No. 1, 2009
Issue release date: April 2009
Free Access
Hum Hered 2009;68:65–72
(DOI:10.1159/000210450)

Multiple Imputation to Correct for Measurement Error in Admixture Estimates in Genetic Structured Association Testing

Padilla M.A.a, b · Divers J.c · Vaughan L.K.d · Allison D.B.d, e · Tiwari H.K.d
Departments of aPsychology and bMathematics and Statistics, Old Dominion University, Norfolk, Va., cDepartment of Biostatistical Sciences, Section on Statistical Genetics, Wake Forest University Health Sciences, Winston-Salem, N.C., dDepartment of Biostatistics, Section on Statistical Genetics and eClinical Nutrition Research Center, University of Alabama at Birmingham, Birmingham, Ala., USA
email Corresponding Author

Abstract

Objectives: Structured association tests (SAT), like any statistical model, assumes that all variables are measured without error. Measurement error can bias parameter estimates and confound residual variance in linear models. It has been shown that admixture estimates can be contaminated with measurement error causing SAT models to suffer from the same afflictions. Multiple imputation (MI) is presented as a viable tool for correcting measurement error problems in SAT linear models with emphasis on correcting measurement error contaminated admixture estimates. Methods: Several MI methods are presented and compared, via simulation, in terms of controlling Type I error rates for both non-additive and additive genotype coding. Results: Results indicate that MI using the Rubin or Cole method can be used to correct for measurement error in admixture estimates in SAT linear models. Conclusion: Although MI can be used to correct for admixture measurement error in SAT linear models, the data should be of reasonable quality, in terms of marker informativeness, because the method uses the existing data to borrow information in which to make the measurement error corrections. If the data are of poor quality there is little information to borrow to make measurement error corrections.


 goto top of outline Key Words

  • Multiple imputation
  • Measurement error
  • Admixture
  • Ancestry
  • Structured association testing

 goto top of outline Abstract

Objectives: Structured association tests (SAT), like any statistical model, assumes that all variables are measured without error. Measurement error can bias parameter estimates and confound residual variance in linear models. It has been shown that admixture estimates can be contaminated with measurement error causing SAT models to suffer from the same afflictions. Multiple imputation (MI) is presented as a viable tool for correcting measurement error problems in SAT linear models with emphasis on correcting measurement error contaminated admixture estimates. Methods: Several MI methods are presented and compared, via simulation, in terms of controlling Type I error rates for both non-additive and additive genotype coding. Results: Results indicate that MI using the Rubin or Cole method can be used to correct for measurement error in admixture estimates in SAT linear models. Conclusion: Although MI can be used to correct for admixture measurement error in SAT linear models, the data should be of reasonable quality, in terms of marker informativeness, because the method uses the existing data to borrow information in which to make the measurement error corrections. If the data are of poor quality there is little information to borrow to make measurement error corrections.

Copyright © 2009 S. Karger AG, Basel


 goto top of outline References
  1. Weinberg CR: Toward a clearer definition of confounding. Am J Epidemiol 1993;137: 1–8.
  2. Knowler WC, Williams RC, Pettitt DJ, Steinberg AG: Gm3;5,13,14 and type 2 diabetes mellitus: An association in american indians with genetic admixture. Am J Hum Genet 1988;43:520–526.
  3. Spielman RS, McGinnis RE, Ewens WJ: Transmission test for linkage disequilibrium: The insulin gene region and insulin-dependent diabetes mellitus (iddm). Am J Hum Genet 1993;52:506–516.
  4. Devlin B, Roeder K: Genomic control for association studies. Biometrics 1999;55:997–1004.
  5. Freedman ML, Reich D, Penney KL, McDonald GJ, Mignault AA, Patterson N, Gabriel SB, Topol EJ, Smoller JW, Pato CN, Pato MT, Petryshen TL, Kolonel LN, Lander ES, Sklar P, Henderson B, Hirschhorn JN, Altshuler D: Assessing the impact of population stratification on genetic association studies. Nat Genet 2004;36:388–393.
  6. Redden DT, Allison DB: The effect of assortative mating upon genetic association studies: Spurious associations and population substructure in the absence of admixture. Behav Genet 2006;36:678–686.
  7. Redden DT, Divers J, Vaughan LK, Tiwari HK, Beasley TM, Fernández JR, Kimberly RP, Feng R, Padilla MA, Liu N, Miller MB, Allison DB: Regional admixture mapping and structured association testing: Conceptual unification and an extensible general linear model. Plos Genetics 2006;2:1254–1264.
  8. Devlin B, Bacanu SA, Roeder K: Genomic control to the extreme. Nat Genet 2004;36:1129–1130;author reply 1131.
  9. Devlin B, Roeder K, Wasserman L: Genomic control, a new approach to genetic-based association studies. Theor Popul Biol 2001;60:155–166.
  10. Pritchard JK, Donnelly P: Case-control studies of association in structured or admixed populations. Theor Popul Biol 2001;60:227–237.
  11. Satten GA, Flanders WD, Yang Q: Accounting for unmeasured population substructure in case-control studies of genetic association using a novel latent-class model. Am J Hum Genet 2001;68:466–477.
  12. Chen HS, Zhu X, Zhao H, Zhang S: Qualitative semi-parametric test for genetic associations in case-control designs under structured populations. Ann Hum Genet 2003;67:250–264.
  13. Zhang S, Zhu X, Zhao H: On a semiparametric test to detect associations between quantitative traits and candidate genes using unrelated individuals. Genet Epidemiol 2003;24:44–56.
  14. Ziv E, Burchard EG: Human population structure and genetic association studies. Pharmacogenomics 2003;4:431–441.
  15. Hoggart CJ, Parra EJ, Shriver MD, Bonilla C, Kittles RA, Clayton DG, McKeigue PM: Control of confounding of genetic associations in stratified populations. Am J Hum Genet 2003;72:1492–1504.
  16. Halder I, Shriver MD: Measuring and using admixture to study the genetics of complex diseases. Hum Genomics 2003;1:52–62.
  17. Marchini J, Cardon LR, Phillips MS, Donnelly P: The effects of human population structure on large genetic association studies. Nat Genet 2004;36:512–517.
  18. Deng HW: Population admixture may appear to mask, change or reverse genetic effects of genes underlying complex traits. Genetics 2001;159:1319–1323.
  19. Divers J, Vaughan LK, Padilla MA, Fernandez JR, Allison DB, Redden DT: Correcting for measurement error in individual ancestry estimates in structured association tests. Genetics 2007;176:1823–1833.
  20. Allen MJ, Yen WM: Introduction to measurement theory. Monterey, CA, Brooks/Cole Pub. Co., 1979.
  21. Crocker LM, Algina J: Introduction to classical and modern test theory. New York, Holt, Rinehart, and Winston, 1986.
  22. Bollen KA: Structural equations with latent variables. New York, Wiley, 1989.
  23. Cheng C-L, Van Ness JW: Statistical regression with measurement error. London, Arnold, 1999.
  24. Cheng CL, Schneeweiss H: Polynomial regression with errors in the variables. J R Stat Soc Ser B (Statistical Methodology) 1998;60:189–199.

    External Resources

  25. Carroll RJ, Stefanski LA: Approximate quasi-likelihood estimation in models with surrogate predictors. J Am Stat Ass 1990;85:652–663.

    External Resources

  26. Schneeweiss H, Nitter T: Estimating a polynomial regression with measurement errors in the structural and in the functional case – a comparison; in Mohammed AK, Saleh E (eds): Data Analysis from Statistical Foundations: A Festschrift in Honour of the 75th Birthday of Das Fraser. Huntington, NY, Nova Science Publishers, 2001, pp 195–207.
  27. Kuha J, Temple J: Covariate measurement error in quadratic regression. Int Stat Rev 2003;71:131–150.

    External Resources

  28. Cook JR, Stefanski LA: Simulation-extrapolation estimation in parametric measurement error models. J Am Stat Ass 1994;89:1314–1328.

    External Resources

  29. Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM: Measurement error in nonlinear models : A modern perspective, ed 2. Boca Raton, Chapman & Hall/CRC, 2006.
  30. Lindley DV, Smith AFM: Bayes estimates for the linear model. J R Stat Soc 1972;34:1–41.
  31. Rubin DB: Multiple imputation for nonresponse in surveys. New York, Wiley, 1987.
  32. Little RJA, Rubin DB: Statistical Analysis with Missing Data, ed 2. Hoboken, NJ, Wiley-Interscience, 2002.
  33. Barnard J, Rubin DB: Small-sample degrees of freedom with multiple imputation. Biometrika 1999;86:948–955.

    External Resources

  34. Tang H, Peng J, Wang P, Risch NJ: Estimation of individual admixture: Analytical and study design considerations. Genet Epidemiol 2005;28:289–301.
  35. Cronbach LJ: Coefficient alpha and the internal structure of tests. Psychometrika 1951;16:297–334.

 goto top of outline Author Contacts

Miguel A. Padilla, PhD
Department of Psychology, Old Dominion University
250 Mills Godwin Building
Norfolk, VA 23505 (USA)
Tel. +1 757 683 4448, Fax +1 757 683 5087, E-Mail mapadill@odu.edu


 goto top of outline Article Information

Received: June 30, 2008
Accepted after revision: November 6, 2008
Published online: April 1, 2009
Number of Print Pages : 8
Number of Figures : 0, Number of Tables : 5, Number of References : 35


 goto top of outline Publication Details

Human Heredity (International Journal of Human and Medical Genetics)

Vol. 68, No. 1, Year 2009 (Cover Date: April 2009)

Journal Editor: Devoto M. (Philadelphia, Pa.)
ISSN: 0001-5652 (Print), eISSN: 1423-0062 (Online)

For additional information: http://www.karger.com/HHE


Copyright / Drug Dosage / Disclaimer

Copyright: All rights reserved. No part of this publication may be translated into other languages, reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, microcopying, or by any information storage and retrieval system, without permission in writing from the publisher or, in the case of photocopying, direct payment of a specified fee to the Copyright Clearance Center.
Drug Dosage: The authors and the publisher have exerted every effort to ensure that drug selection and dosage set forth in this text are in accord with current recommendations and practice at the time of publication. However, in view of ongoing research, changes in goverment regulations, and the constant flow of information relating to drug therapy and drug reactions, the reader is urged to check the package insert for each drug for any changes in indications and dosage and for added warnings and precautions. This is particularly important when the recommended agent is a new and/or infrequently employed drug.
Disclaimer: The statements, opinions and data contained in this publication are solely those of the individual authors and contributors and not of the publishers and the editor(s). The appearance of advertisements or/and product references in the publication is not a warranty, endorsement, or approval of the products or services advertised or of their effectiveness, quality or safety. The publisher and the editor(s) disclaim responsibility for any injury to persons or property resulting from any ideas, methods, instructions or products referred to in the content or advertisements.

Abstract

Objectives: Structured association tests (SAT), like any statistical model, assumes that all variables are measured without error. Measurement error can bias parameter estimates and confound residual variance in linear models. It has been shown that admixture estimates can be contaminated with measurement error causing SAT models to suffer from the same afflictions. Multiple imputation (MI) is presented as a viable tool for correcting measurement error problems in SAT linear models with emphasis on correcting measurement error contaminated admixture estimates. Methods: Several MI methods are presented and compared, via simulation, in terms of controlling Type I error rates for both non-additive and additive genotype coding. Results: Results indicate that MI using the Rubin or Cole method can be used to correct for measurement error in admixture estimates in SAT linear models. Conclusion: Although MI can be used to correct for admixture measurement error in SAT linear models, the data should be of reasonable quality, in terms of marker informativeness, because the method uses the existing data to borrow information in which to make the measurement error corrections. If the data are of poor quality there is little information to borrow to make measurement error corrections.



 goto top of outline Author Contacts

Miguel A. Padilla, PhD
Department of Psychology, Old Dominion University
250 Mills Godwin Building
Norfolk, VA 23505 (USA)
Tel. +1 757 683 4448, Fax +1 757 683 5087, E-Mail mapadill@odu.edu


 goto top of outline Article Information

Received: June 30, 2008
Accepted after revision: November 6, 2008
Published online: April 1, 2009
Number of Print Pages : 8
Number of Figures : 0, Number of Tables : 5, Number of References : 35


 goto top of outline Publication Details

Human Heredity (International Journal of Human and Medical Genetics)

Vol. 68, No. 1, Year 2009 (Cover Date: April 2009)

Journal Editor: Devoto M. (Philadelphia, Pa.)
ISSN: 0001-5652 (Print), eISSN: 1423-0062 (Online)

For additional information: http://www.karger.com/HHE


Copyright / Drug Dosage

Copyright: All rights reserved. No part of this publication may be translated into other languages, reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, microcopying, or by any information storage and retrieval system, without permission in writing from the publisher or, in the case of photocopying, direct payment of a specified fee to the Copyright Clearance Center.
Drug Dosage: The authors and the publisher have exerted every effort to ensure that drug selection and dosage set forth in this text are in accord with current recommendations and practice at the time of publication. However, in view of ongoing research, changes in goverment regulations, and the constant flow of information relating to drug therapy and drug reactions, the reader is urged to check the package insert for each drug for any changes in indications and dosage and for added warnings and precautions. This is particularly important when the recommended agent is a new and/or infrequently employed drug.
Disclaimer: The statements, opinions and data contained in this publication are solely those of the individual authors and contributors and not of the publishers and the editor(s). The appearance of advertisements or/and product references in the publication is not a warranty, endorsement, or approval of the products or services advertised or of their effectiveness, quality or safety. The publisher and the editor(s) disclaim responsibility for any injury to persons or property resulting from any ideas, methods, instructions or products referred to in the content or advertisements.

References

  1. Weinberg CR: Toward a clearer definition of confounding. Am J Epidemiol 1993;137: 1–8.
  2. Knowler WC, Williams RC, Pettitt DJ, Steinberg AG: Gm3;5,13,14 and type 2 diabetes mellitus: An association in american indians with genetic admixture. Am J Hum Genet 1988;43:520–526.
  3. Spielman RS, McGinnis RE, Ewens WJ: Transmission test for linkage disequilibrium: The insulin gene region and insulin-dependent diabetes mellitus (iddm). Am J Hum Genet 1993;52:506–516.
  4. Devlin B, Roeder K: Genomic control for association studies. Biometrics 1999;55:997–1004.
  5. Freedman ML, Reich D, Penney KL, McDonald GJ, Mignault AA, Patterson N, Gabriel SB, Topol EJ, Smoller JW, Pato CN, Pato MT, Petryshen TL, Kolonel LN, Lander ES, Sklar P, Henderson B, Hirschhorn JN, Altshuler D: Assessing the impact of population stratification on genetic association studies. Nat Genet 2004;36:388–393.
  6. Redden DT, Allison DB: The effect of assortative mating upon genetic association studies: Spurious associations and population substructure in the absence of admixture. Behav Genet 2006;36:678–686.
  7. Redden DT, Divers J, Vaughan LK, Tiwari HK, Beasley TM, Fernández JR, Kimberly RP, Feng R, Padilla MA, Liu N, Miller MB, Allison DB: Regional admixture mapping and structured association testing: Conceptual unification and an extensible general linear model. Plos Genetics 2006;2:1254–1264.
  8. Devlin B, Bacanu SA, Roeder K: Genomic control to the extreme. Nat Genet 2004;36:1129–1130;author reply 1131.
  9. Devlin B, Roeder K, Wasserman L: Genomic control, a new approach to genetic-based association studies. Theor Popul Biol 2001;60:155–166.
  10. Pritchard JK, Donnelly P: Case-control studies of association in structured or admixed populations. Theor Popul Biol 2001;60:227–237.
  11. Satten GA, Flanders WD, Yang Q: Accounting for unmeasured population substructure in case-control studies of genetic association using a novel latent-class model. Am J Hum Genet 2001;68:466–477.
  12. Chen HS, Zhu X, Zhao H, Zhang S: Qualitative semi-parametric test for genetic associations in case-control designs under structured populations. Ann Hum Genet 2003;67:250–264.
  13. Zhang S, Zhu X, Zhao H: On a semiparametric test to detect associations between quantitative traits and candidate genes using unrelated individuals. Genet Epidemiol 2003;24:44–56.
  14. Ziv E, Burchard EG: Human population structure and genetic association studies. Pharmacogenomics 2003;4:431–441.
  15. Hoggart CJ, Parra EJ, Shriver MD, Bonilla C, Kittles RA, Clayton DG, McKeigue PM: Control of confounding of genetic associations in stratified populations. Am J Hum Genet 2003;72:1492–1504.
  16. Halder I, Shriver MD: Measuring and using admixture to study the genetics of complex diseases. Hum Genomics 2003;1:52–62.
  17. Marchini J, Cardon LR, Phillips MS, Donnelly P: The effects of human population structure on large genetic association studies. Nat Genet 2004;36:512–517.
  18. Deng HW: Population admixture may appear to mask, change or reverse genetic effects of genes underlying complex traits. Genetics 2001;159:1319–1323.
  19. Divers J, Vaughan LK, Padilla MA, Fernandez JR, Allison DB, Redden DT: Correcting for measurement error in individual ancestry estimates in structured association tests. Genetics 2007;176:1823–1833.
  20. Allen MJ, Yen WM: Introduction to measurement theory. Monterey, CA, Brooks/Cole Pub. Co., 1979.
  21. Crocker LM, Algina J: Introduction to classical and modern test theory. New York, Holt, Rinehart, and Winston, 1986.
  22. Bollen KA: Structural equations with latent variables. New York, Wiley, 1989.
  23. Cheng C-L, Van Ness JW: Statistical regression with measurement error. London, Arnold, 1999.
  24. Cheng CL, Schneeweiss H: Polynomial regression with errors in the variables. J R Stat Soc Ser B (Statistical Methodology) 1998;60:189–199.

    External Resources

  25. Carroll RJ, Stefanski LA: Approximate quasi-likelihood estimation in models with surrogate predictors. J Am Stat Ass 1990;85:652–663.

    External Resources

  26. Schneeweiss H, Nitter T: Estimating a polynomial regression with measurement errors in the structural and in the functional case – a comparison; in Mohammed AK, Saleh E (eds): Data Analysis from Statistical Foundations: A Festschrift in Honour of the 75th Birthday of Das Fraser. Huntington, NY, Nova Science Publishers, 2001, pp 195–207.
  27. Kuha J, Temple J: Covariate measurement error in quadratic regression. Int Stat Rev 2003;71:131–150.

    External Resources

  28. Cook JR, Stefanski LA: Simulation-extrapolation estimation in parametric measurement error models. J Am Stat Ass 1994;89:1314–1328.

    External Resources

  29. Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM: Measurement error in nonlinear models : A modern perspective, ed 2. Boca Raton, Chapman & Hall/CRC, 2006.
  30. Lindley DV, Smith AFM: Bayes estimates for the linear model. J R Stat Soc 1972;34:1–41.
  31. Rubin DB: Multiple imputation for nonresponse in surveys. New York, Wiley, 1987.
  32. Little RJA, Rubin DB: Statistical Analysis with Missing Data, ed 2. Hoboken, NJ, Wiley-Interscience, 2002.
  33. Barnard J, Rubin DB: Small-sample degrees of freedom with multiple imputation. Biometrika 1999;86:948–955.

    External Resources

  34. Tang H, Peng J, Wang P, Risch NJ: Estimation of individual admixture: Analytical and study design considerations. Genet Epidemiol 2005;28:289–301.
  35. Cronbach LJ: Coefficient alpha and the internal structure of tests. Psychometrika 1951;16:297–334.