Linear mixed models for replication data to efficiently allow for covariate measurement error

Statistics in Medicine

Volumn 28, Issue 25, 2009, Pages 3158-3178

  Bartlett, Jonathan W ^a   De Stavola, Bianca L ^a   Frost, Chris ^a  

^a LONDON SCHOOL OF HYGIENE AND TROPICAL MEDICINE   (United Kingdom)

Author keywords

Maximum likelihood; Measurement error; Regression calibration

Indexed keywords

ARTICLE; CALIBRATION; COVARIANCE; DATA ANALYSIS; EFFECT SIZE; LINEAR REGRESSION ANALYSIS; MAXIMUM LIKELIHOOD METHOD; MEASUREMENT ERROR; NORMAL DISTRIBUTION; REGRESSION CALIBRATION; SIMULATION; STATISTICAL MODEL;

COMPUTER SIMULATION; HUMANS; LINEAR MODELS; REPRODUCIBILITY OF RESULTS;

EID: 70449449705     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.3713     Document Type: Article

References (26)

1. Fuller WA. Measurement Error Models. Wiley: New York, 1987.
2. Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM. Measurement Error in Nonlinear Models (2nd edn). Chapman & Hall, CRC: Boca Raton, 2006.
3. Kuha J. Corrections for exposure measurement error in logistic regression models with an application to nutritional data. Statistics in Medicine 1994; 13:1135-1148. DOI: 10.1002/sim.4780131105. (Pubitemid 24191582)
4. Schafer DW, Purdy KG. Likelihood analysis for errors-in-variables regression with replicate measurements. Biometrika 1996; 83:813-824. DOI: 10.1093/biomet/83.4.813.
5. Rabe-Hesketh S, Skrondal A, Pickles A. Maximum likelihood estimation of generalized linear models with covariate measurement error. The Stata Journal 2003; 3:386-411.
6. Skrondal A, Rabe-Hesketh S. Generalized Latent Variable Modelling: Multilevel, Longitudinal, and Structural Equation Models. Chapman & Hall, CRC: Boca Raton, 2004.
7. Clayton D. Models for the analysis of cohort and case-control studies with inaccurately measured exposures. In Statistical Models for Longitudinal Studies of Health, Dwyer JH, Feinleib M, Lipsert P, Hoffmeister H (eds). Oxford University Press: New York, 1991.
8. Muthén LK, Muthén BO. Mplus User's Guide. Muthén & Muthén: Los Angeles, CA, 1998.
9. Messer K, Natarajan L. Maximum likelihood, multiple imputation and regression calibration for measurement error adjustment. Statistics in Medicine 2008; 27:6332-6350. DOI: 10.1002/sim.3458.
10. Searle SR, Casella G, McCulloch CE. Variance Components. Wiley: New York, 1992.
11. Lindsey JK. Parametric Statistical Inference. Oxford University Press: New York, 1996.
12. R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2008. Available from: http://www.R-project.org.
13. Westfall PH. A comparison of variance component estimates for arbitrary underlying distributions. Journal of the American Statistical Association 1987; 82:866-874.
14. Gleser LJ. Improvements in the naive approach to estimation in nonlinear errors-in-variables regression models. In Statistical Analysis of Measurement Error Models and Applications, Brown PJ, Fuller WA (eds). American Mathematical Society: Providence, 1990.
15. Casella G, Berger RL. Statistical Inference. Duxbury Press: Pacific Grove, CA, 2001.
16. Efron B. The efficiency of logistic regression compared to normal discriminant analysis. Journal of the American Statistical Association 1975; 70:892-898.
17. Freedman LS, Fainberg V, Kipnis D, Midthune D, Carroll RJ. A new method for dealing with measurement error in explanatory variables of regression models. Biometrics 2004; 60:172-181. DOI: 10.1111/j.0006-341X.2004.00164.x. (Pubitemid 38392629)
18. Freedman LS, Midthune D, Carroll RJ, Kipnis V. A comparison of regression calibration, moment reconstruction and imputation for adjusting for covariate measurement error in regression. Statistics in Medicine 2008; 27: 5195-5216. DOI: 10.1002/sim.3361.
19. Press SJ, Wilson S. Choosing between logistic regression and discriminant analysis. Journal of the American Statistical Association 1978; 73:699-705.
20. Stefanski LA, Carroll RJ. Conditional scores and optimal scores for generalized linear measurement error models. Biometrika 1987; 74:703-716. DOI: 10.1093/biomet/74.4.703.
21. Rabe-Hesketh S, Pickles A, Skrondal A. Correcting for covariate measurement error in logistic regression using nonparametric maximum likelihood estimation. Statistical Modelling 2003; 3:215-232. DOI: 10.1191/ 1471082X03st056oa.
22. Li E, Zhang D, Davidian M. Likelihood and pseudo-likelihood methods for semiparametric joint models for a primary endpoint and longitudinal data. Computational Statistics and Data Analysis 2007; 51:5776-5790. DOI: 10.1016/j.csda.2006.10.008. (Pubitemid 47125989)
23. Cole SR, Chu H, Greenland S. Multiple-imputation for measurement-error correction. International Journal of Epidemiology 2006; 35:1074-1081. DOI: 10.1093/ije/dyl097.
24. Verbeke G, Molenberghs G. Linear Mixed Models for Longitudinal Data. Springer: New York, 2000.
25. Wang N, Robins JM. Large-sample theory for parametric multiple imputation procedures. Biometrika 1998; 85:935-948. DOI: 10.1093/biomet/85.4.935.
26. Buonaccorsi JP. Fieller's theorem. In Encyclopedia of Biostatistics, Armitage P, Colton T (eds). Wiley: Chichester, 1998.