Skip to main content

Measurement Error

  • Chapter
Handbook of Epidemiology

Abstract

Factors contributing to the presence or absence of disease are not always easily determined or accurately measured. Consequently epidemiologists are often faced with the task of inferring disease patterns using noisy or indirect measurements of risk factors or covariates. Problems of measurement arise for a number of reasons, including for example: reliance on self-reported information; the use of records of suspect quality; intrinsic biological variability; sampling variability; and laboratory analysis error. Although the reasons for imprecise measurement are diverse, the inference problems they create share in common the structure that statistical models must be fit to data formulated in terms of well-defined but unobservable variables X, using information on measurements W that are less than perfectly correlated with X. Problems of this nature are called measurement error problems and the statistical models and methods for analyzing such data are called measurement error models.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 199.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Amemiya Y (1985) Instrumental variable estimator for the nonlinear errors in variables model. Journal of Econometrics 28:273–289

    Article  Google Scholar 

  • Amemiya Y (1990a) Instrumental variable estimation of the nonlinear measurement errormodel. In: Brown PJ, Fuller WA (eds) Statistical analysis of measurement error models and application. American Mathematics Society, Providence

    Google Scholar 

  • Amemiya Y (1990b) Two-stage instrumental variable estimators for the nonlinear errors in variables model. Journal of Econometrics 44:311–332

    Article  MATH  Google Scholar 

  • Armstrong BK, White E, Saracci R (1992) Principles of exposure measurement error in epidemiology. Oxford University Press, Oxford

    Google Scholar 

  • Berkson J (1950) Are there two regressions? Journal of the American Statistical Association 45:164–180

    Article  MATH  Google Scholar 

  • Buonaccorsi JP (1988) Errors in variables with systematic biases. Communications in Statistics — Theory and Methods 18:1001–1021

    Article  Google Scholar 

  • Buzas JS (1997) Instrumental variable estimation in nonlinear measurement error models. Communications in Statistics — Theory and Methods 26:2861–2877

    Article  MATH  Google Scholar 

  • Buzas JS (1998) Unbiased scores in proportional hazards regression with covariate measurement error. Journal of Statistical Planning and Inference 67:247–257

    Article  MATH  Google Scholar 

  • Buzas JS, Stefanski LA (1996a) Instrumental variable estimation in probit measurement error models. Journal of Statistical Planning and Inference 55:47–62

    Article  MATH  Google Scholar 

  • Buzas JS, Stefanski LA (1996b) Instrumental variable estimation in generalized linear measurement error models. Journal of the American Statistical Association 91: 999–1006

    Article  MATH  Google Scholar 

  • Buzas, J.S., Stefanski, L.A. (1996c) A note on corrected score estimation. Statistics and Probability Letters 28:1–8

    Article  MATH  Google Scholar 

  • Cain KC, Breslow, NE (1988) Logistic regression analysis and efficient design for two-stage studies. American Journal of Epidemiology 128:1198–1206

    Google Scholar 

  • Carroll RJ (1989) Covariance analysis in generalized linear measurement error models. Statistics in Medicine 8:1075–1093

    Article  Google Scholar 

  • Carroll RJ (1998) Measurement error in epidemiologic studies. In: Armitage P, Colton T (eds) Encyclopedia of biostatistics. Wiley, New York, pp 2491–2519

    Google Scholar 

  • Carroll RJ, Stefanski LA (1990) Approximate quasilikelihood estimation in models with surrogate predictors. Journal of the American Statistical Association 85:652–663

    Article  Google Scholar 

  • Carroll RJ, Stefanski LA (1994) Measurement error, instrumental variables and corrections for attenuation with applications to meta-analyses. Statistics in Medicine 13:1265–1282

    Article  Google Scholar 

  • Carroll RJ, Gallo PP, Gleser LJ (1985) Comparison of least squares and errors-invariables regression, with special reference to randomized analysis of covariance. Journal of the American Statistical Association 80:929–932

    Article  MATH  Google Scholar 

  • Carroll RJ, Küchenhoff H, Lombard F, Stefanski LA (1996) Asymptotics for the SIMEX estimator in structural measurement error models. Journal of the American Statistical Association 91:242–250

    Article  MATH  Google Scholar 

  • Carroll RJ, Roeder K, Wasserman L (1999) Flexible parametric measurement error models. Biometrics 55:44–54

    Article  MATH  Google Scholar 

  • Carroll RJ, Ruppert D, Stefanski LA (1995) Measurement error in nonlinear models. Chapman & Hall, London

    MATH  Google Scholar 

  • Carroll RJ, Spiegelman, Lan KK, Bailey KT, Abbott RD (1984) Onerrors-in-variables for binary regression models. Biometrika 71:19–26

    Article  MATH  Google Scholar 

  • Clayton DG (1991) Models for the analysis of cohort and case-control studies with inaccurately measured exposures. In: Dwyer JH, Feinleib M, Lipsert P et al. (eds.) Statistical models for longitudinal studies of health. Oxford University Press, New York, pp 301–331

    Google Scholar 

  • Cochran WG (1968) Errors of measurement in statistics. Technometrics 10:637–666

    Article  MATH  Google Scholar 

  • Cook J, Stefanski LA (1995) A simulation extrapolation method for parametric measurement error models. Journal of the American Statistical Association 89:1314–1328

    Article  Google Scholar 

  • Devanarayan V, Stefanski LA (2002) Empirical simulation extrapolation for measurement error models with replicate measurements. Statistics and Probability Letters 59:219–225

    Article  MATH  Google Scholar 

  • Fleiss JL (1981) Statistical methods for rates and proportions. Wiley, New York

    MATH  Google Scholar 

  • Fuller WA (1987) Measurement error models. Wiley, New York

    MATH  Google Scholar 

  • Higdon R, Schafer DW (2001) Maximum likelihood computations for regression with measurement error. Computational Statistics and Data Analysis 35:283–299

    Article  MATH  Google Scholar 

  • Holcomb JP (1999) Regressionwith covariates and outcome calculated from a common set of variables measured with error: estimation using the SIMEX method. Statistics in Medicine, 18:2847–2862

    Article  Google Scholar 

  • Holcroft CA, Rotnitzky A, Robins JM (1997) Efficient estimation of regression parameters from multistage studies with validation of outcome and covariates. Journal of Statistical Planning and Inference 65:349–374

    Article  MATH  Google Scholar 

  • Huang Y, Wang CY (2000) Cox regression with accurate covariates unascertainable: a nonparametric-correction approach. Journal of the American Statistical Association 95:1209–1219

    Article  MATH  Google Scholar 

  • Huang Y, Wang CY (2001) Consistent functional methods for logistic regression with errors in covariates. Journal of the American Statistical Association 95:1209–1219

    Article  Google Scholar 

  • Hughes MD (1993) Regression dilution in the proportional hazards model. Biometrics 49:1056–1066

    Article  MATH  Google Scholar 

  • Hwang JT, Stefanski LA (1994) Monotonicity of regression functions in structural measurement error models. Statistics and Probability Letters 20:113–116

    Article  MATH  Google Scholar 

  • Karagas MR, Tosteson TD, Blum J, Morris SJ, Baron JA, Klaue B (1998) Design of an epidemiologic study of drinking water arsenic and skin and bladder cancer risk in a U.S. population. Environmental Health Perspectives 106:1047–1050

    Article  Google Scholar 

  • Karagas MR, Tosteson TD, Blum J, Klaue B, Weiss JE, Stannard V, Spate V, Morris JS (2000) Measurement of low levels of arsenic exposure: a comparison of water and toenail concentrations. American Journal of Epidemiology 152:84–90

    Article  Google Scholar 

  • Karagas MR, Stukel TA, Morris JS, Tosteson TD, Weiss JE, Spencer SK, Greenberg ER (2001) Skin cancer risk in relation to toenail arsenic concentrations in a US population-based case-control study. American Journal of Epidemiology 153:559–565

    Article  Google Scholar 

  • Karagas MR, Stukel TA, Tosteson TD (2002) Assessment of cancer risk and environmental levels of arsenic in New Hampshire. International Journal of Hygiene and Environmental Health 205:85–94

    Article  Google Scholar 

  • Kim C, Hong C, Jeong M (2000) Simulation-extrapolation via the Bezier curve in measurement error models. Communications in Statistics — Simulation and Computation 29:1135–1147

    Article  MATH  Google Scholar 

  • Kim J, Gleser LJ (2000) SIMEX approaches to measurement error in ROC studies. Communications in Statistics — Theory and Methods 29:2473–2491

    Article  MATH  Google Scholar 

  • Kipnis V, Carroll RJ, Freedman LS, Li L (1999) Implications of a new dietary measurement error model for estimation of relative risk: application to four calibration studies. American Journal of Epidemiology 150: 642–651

    Google Scholar 

  • Küchenhoff H, Carroll RJ (1997) Segmented regression with errors in predictors: semi-parametric and parametric methods. Statistics in Medicine 16:169–188

    Article  Google Scholar 

  • Li Y, Lin X (2003) Functional inference in frailty measurement error models for clustered survival data using the SIMEX approach. Journal of the American Statistical Association 98:191–203

    Article  MATH  Google Scholar 

  • Lin X, Carroll RJ (1999) SIMEX variance component tests in generalized linear mixed measurement error models. Biometrics 55:613–619

    Article  MATH  Google Scholar 

  • MacMahon S, Peto R, Cutler J, Collins R, Sorlie P, Neaton J, Abbott R, Godwin J, Dyer A, Stamler J (1990) Blood pressure, stroke and coronary heart disease: Part 1, prolonged differences in blood pressure: prospective observational studies corrected for the regression dilution bias. Lancet 335:765–774

    Article  Google Scholar 

  • Marcus AH, Elias RW (1998) Some useful statistical methods for model validation. Environmental Health Perspectives 106:1541–1550

    Google Scholar 

  • McKeown-Eyssen GE, Tibshirani R (1994) Implications of measurement error in exposure for the sample sizes of case-control studies. American Journal of Epidemiology 139:415–421

    Google Scholar 

  • Nakamura T (1990) Corrected score functions for errors-in-variables models: methodology and application to generalized linear models. Biometrika 77:127–137

    Article  MATH  Google Scholar 

  • Nakamura T (1992) Proportional hazards models with covariates subject to measurement error. Biometrics 48:829–838

    Article  Google Scholar 

  • Novick SJ, Stefanski LA (2002) Corrected score estimation via complex variable simulation extrapolation. Journal of the American Statistical Association 97:472–481

    Article  MATH  Google Scholar 

  • Prentice RL (1982) Covariate measurement errors and parameter estimation in a failure time regression model. Biometrika 69:331–342

    Article  MATH  Google Scholar 

  • Reilly M (1996) Optimal sampling strategies for two phase studies. American Journal of Epidemiology 143:92–100

    Google Scholar 

  • Richardson S, Leblond L (1997) Some comments on misspecification of priors in Bayesian modelling of measurement error problems. Statistics in Medicine 16:203–213

    Article  Google Scholar 

  • Roeder K, Carroll RJ, Lindsay BG (1996) A nonparametric mixture approach to case-control studies with errors in covariables. Journal of the American Statistical Association 91:722–732

    Article  MATH  Google Scholar 

  • Rosner B, Willett WC, Spiegelman D (1989) Correction of logistic regression-relative risk estimates and confidence intervals for systematic within-person measurement error. Statistics in Medicine 8:1051–1070

    Article  Google Scholar 

  • Rosner B, Spiegelman D, Willett WC (1990) Correction of logistic regression relative riskestimatesandconfidenceintervalsformeasurementerror:thecaseofmultiple covariates measured with error. American Journal of Epidemiology 132:734–745

    Google Scholar 

  • Schafer D (1993) Likelihood analysis for probit regression with measurement errors. Biometrika 80:899–904

    Article  MATH  Google Scholar 

  • Schafer D (2001) Semiparametric maximum likelihood for measurement error model regression. Biometrics 57:53–61

    Article  Google Scholar 

  • Schafer D (2002) Likelihood analysis and flexible structural modeling for measurement error model regression. Journal of Computational Statistics and Data analysis 72:33–45

    MATH  Google Scholar 

  • Schafer D, Purdy K (1996) Likelihood analysis for errors-in-variables regression with replicate measurements. Biometrika 83:813–824

    Article  MATH  Google Scholar 

  • Spiegelman D, Gray R (1991) Cost-efficient study designs for binary response data with Gaussian covariate measurement error. Biometrics 47:851–869

    Article  MATH  Google Scholar 

  • Spiegelman D, Carroll RJ, Kipnis V (2001) Efficient regression calibration for logistic regression in mainstudy/internal validation study designs with an imperfect reference instrument. Statistics in Medicine 20:139–160

    Article  Google Scholar 

  • Stefanski LA (1985) The effects of measurement error on parameter estimation. Biometrika 72:583–592

    Article  MATH  Google Scholar 

  • Stefanski LA (1989) Unbiased estimation of a nonlinear function of a normal mean with application to measurement error models. Communications in Statistics — Theory and Methods 18:4335–4358

    Article  MATH  Google Scholar 

  • Stefanski LA, Bay JM (1996) Simulation extrapolation deconvolution of finite population cumulative distribution function estimators. Biometrika 83:407–417

    Article  MATH  Google Scholar 

  • Stefanski LA, Buzas JS (1995) Instrumental variable estimation in binary measurement error models. Journal of the American Statistical Association 90: 541–550

    Article  MATH  Google Scholar 

  • Stefanski LA, Carroll RJ (1985) Covariate measurement error in logistic regression. Annals of Statistics 13:1335–1351

    MATH  Google Scholar 

  • Stefanski LA, Carroll RJ (1987) Conditional scores and optimal scores in generalized linear measurement error models. Biometrika 74:703–716

    MATH  Google Scholar 

  • Stefanski LA, Carroll RJ (1990a) Score tests in generalized linear measurement error models. Journal of the Royal Statistical Society B 52:345–359

    MATH  Google Scholar 

  • Stefanski LA, Carroll RJ (1990b) Structural logistic regression measurement error models. In: Brown PJ, Fuller WA (eds) Proceedings of the conference on measurement error models, Wiley, New York, pp 115–127

    Google Scholar 

  • Stefanski LA, Cook J (1995) Simulation extrapolation: the measurement error jackknife. Journal of the American Statistical Association 90:1247–1256

    Article  MATH  Google Scholar 

  • Stram DO, Longnecker MP, Shames L, Kolonel LN, Wilkens LR, Pike MC, Henderson BE (1995) Cost-efficient design of a diet validation-study. American Journal of Epidemiology 142(3):353–362

    Google Scholar 

  • Taupin M (2001) Semi-parametric estimation in the nonlinear structural errors-in-variables model. Annals of Statistics 29:66–93

    MATH  Google Scholar 

  • Thomas D, Stram D, Dwyer J (1993) Exposure measurement error: influence on exposure-disease relationships and methods of correction. Annual Review of Public Health 14:69–93

    Article  Google Scholar 

  • Tosteson TD, Tsiatis AA (1988) The asymptotic relative efficiency of score tests in the generalized linear model with surrogate covariates. Biometrika 75: 507–514

    Article  MATH  Google Scholar 

  • Tosteson TD, Ware JH (1990) Designing a logistic regression study using surrogate measures of exposure and outcome. Biometrika 77:11–20

    Article  MATH  Google Scholar 

  • Tosteson T, Stefanski LA, Schafer DW (1989) A measurement error model for binary and ordinal regression. Statistics in Medicine 8:1139–1147

    Article  Google Scholar 

  • Tosteson TD, Titus-Ernstoff L, Baron JA, Karagas MR (1994) A two-stage validation study for determining sensitivity and specificity. Environmental Health Perspectives 102:11–14

    Google Scholar 

  • Tosteson TD, Buzas JS, Demidenko D, Karagas MR (2003) Power and sample size calculations for generalized regression models with covariate measurement error. Statistics in Medicine 22:1069–1082

    Article  Google Scholar 

  • Tsiatis AA, Davidian M (2001) A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error. Biometrika 88:447–458

    Article  MATH  Google Scholar 

  • Tsiatis AA, DeGruttola V, Wulfsohn MS (1995) Modeling the relationship of survival to longitudinal data measured with error: Applications to survival and CD4 counts in patients with AIDS. Journal of the American Statistical Association 90:27–37

    Article  MATH  Google Scholar 

  • Wang CY, Hsu ZD, Feng ZD, Prentice RL (1997) Regression calibration in failure time regression. Biometrics 53:131–145

    Article  MATH  Google Scholar 

  • Wang N, Lin X, Gutierrez R, Carroll RJ (1998) Bias analysis and the SIMEX approach in generalized linear mixed effects models. Journal of the American Statistical Association 93:249–261

    Article  MATH  Google Scholar 

  • White E, Kushi LH, Pepe MS (1994) The effect of exposure variance and exposure measurement error on study sample size. Implications for design of epidemiologic studies. Journal of Clinical Epidemiology 47:873–880

    Article  Google Scholar 

  • Xie SX, Wang CY, Prentice RL (2001) A risk set calibration method for failure time regression by using a covariate reliability sample. Journal of the Royal Statistical Society B 63:855–870

    Article  MATH  Google Scholar 

  • Zhou H, Pepe MS (1995) Auxiliary covariate data in failure time regression analysis. Biometrika 82:139–149

    Article  MATH  Google Scholar 

  • Zhou H, Wang CY (2000) Failure time regression with continuous covariates measured with error. Journal of the Royal Statistical Society, Series B 62:657–665

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Buzas, J.S., Stefanski, L.A., Tosteson, T.D. (2005). Measurement Error. In: Ahrens, W., Pigeot, I. (eds) Handbook of Epidemiology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-26577-1_19

Download citation

Publish with us

Policies and ethics