Regression analysis with covariates that have heteroscedastic measurement error

Statistics in Medicine

Volumn 30, Issue 18, 2011, Pages 2278-2294

  Guo, Ying ^a   Little, Roderick J ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Calibration sample; Data argumentation; Heteroscedastic; Measurement error; Multiple imputation; Regression calibration

Indexed keywords

ARTICLE; CALIBRATION; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MEASUREMENT ERROR; PREDICTION; REGRESSION ANALYSIS; SIMULATION; VARIANCE;

BAYES THEOREM; BETA CAROTENE; COMPUTER SIMULATION; DATA INTERPRETATION, STATISTICAL; FEMALE; HUMANS; MENSTRUAL CYCLE; MODELS, STATISTICAL; OXIDATIVE STRESS; PROGESTERONE; REGRESSION ANALYSIS;

EID: 79960222164     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.4261     Document Type: Article

References (36)

1. Kipnis V, Subar AF, Midthune D, Freedman LS. Structure of dietary measurement error: results of the open biomarker study. American Journal of Epidemiology 2003; 158:14-21.
2. Cotton SM, Crewther DP, Crewther SG. Measurement error: implications for diagnosis and discrepancy models of developmental dyslexia. Dyslexia 2005; 11:186-202.
3. Wannemuehler KA, Lyles RH, Waller LA, Hoekstra RM, Klein M, Tolbert P. A conditional expectation approach for associating ambient air pollutant exposures with health outcomes. Environmetrics 2009; 20:877-894.
4. Wactawski-Wende J, Schisterman EF, Hovey KM, Howards P, Browne RW, Hediger M, Liu A, Trevisan M. Biocycle study: design of the longitudinal study of the oxidative stress and hormone variation during the menstrual cycle. Paediatric and Perinatal Epidemiology 2009; 23:171-184.
5. Guo Y, Harel O, Little RJ. How well quantified is the limit of quantification? Epidemiology 2010; 21:S1-S7.
6. Fuller WA. Measurement Error Models. Wiley: New York, NY, 1987.
7. Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM. Measurement Error in Nonlinear Models: A Modern Perspective (2nd edn). Chapman & Hall/CRC: Boca Raton, FL, 2006.
8. Carroll RJ, Stefanski LA. Approximate quasi-likelihood estimation in problems with surrogate predictors. Journal of the American Statistical Association 1990; 85:652-663.
9. Freedman LS, Fainberg V, Kipnis V, Midthune D, Carroll RJ. A new method for dealing with measurement error in explanatory variables of regression models. Biometrika 2004; 60:172-181.
10. Spiegelman D, Carroll RJ, Kipnis V. Efficient regression calibration for logistic regression in main study/internal validation study designs with an imperfect reference instrument. Statistics in Medicine 2001; 20:139-160.
11. 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.
12. Schenker N, Raghunathan TE, Bondarenko I. Improving on analyses of self-reported data in a large-scale health survey by using information from an examination-based survey. Statistics in Medicine 2009; 29:533-545. DOI: 10.1002/sim.3809.
13. Clayton DG. 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, Lippert P, Hoffmeister H (eds). Oxford University Press: Cary, NC, 1992.
14. Richardson S, Gilks WR. Conditional independence models for epidemiological studies with covariate measurement error. Statistics in Medicine 1993; 12:1703-1722. DOI: 10.1002/sim.4780121806.
15. Richardson S, Green PJ. On bayesian analysis of mixtures with an unknown number of components (with Discussion). Journal of the Royal Statistics Society. Series B (Methodological) 1997; 59:731-792.
16. Hossian S, Gustafson P. Bayesian adjustment for covariate measurement errors: a flexible parametric approach. Statistics in Medicine 2009; 28:1580-1600. DOI: 10.1002/sim.3552.
17. Yucel RM, Zaslavsky AM. Imputation of binary treatment variables with measurement error in administrative data. Journal of the American Statistical Association 2005; 100:1123-1132.
18. Freedman LS, Midthune D, Carroll R, 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. Spiegelman D, Logan R, Grove D. Regression calibration with heteroscedastic error variance. The International Journal of Biostatistics 2011; 7. DOI: 10.2202/1557-4679.1259.
20. Tanner MA, Wong WH. The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association 1987; 52:528-540.
21. Hastings WK. Monte carlo sampling methods using Markov chains and their applications. Biometrika 1970; 57:97-109.
22. Heid IM, Kuchenhoff H, Miles J, Kreienbrock L, Wichmann HE. Two dimensions of measurement error: classical and berkson error in residential radon exposure assessment. Journal of Exposure Analysis and Environmental Epidemiology 2004; 14:365-377.
23. Guolo A, Brazzale AR. A simulation-based comparison of techniques to correct for measurement error in matched case-control studies. Statistics in Medicine 2008; 27:3755-3775. DOI: 10.1002/sim.3282.
24. Dellaportas P, Stephens DA. Bayesian analysis of errors-in-variables regression models. Biometrics 1995; 51:1085-1095.
25. Hyslop DR, Imbens GW. Bias from classical and other forms of measurement error. Journal of Business and Economic Statistics 2001; 19:475-481.
26. Kuha J, Temple J. Covariate measurement error in quadratic regression. International Statistical Review 2003; 71:131-150.
27. Roeder K, Carroll RJ, Lindsay BG. A semiparametric mixture approach to case-control studies with errors in covariables. Journal of the American Statistical Association 1996; 91:722-732.
28. Rodbard D, Frazier GR. Statistical analysis of radioligand assay data. Methods of Enzymology 1975; 37:839-841.
29. Finney DJ. Radioligand assay. Biometrics 1976; 32:721-740.
30. Higgins KM, Davidian M, Chew G, Burge H. The effect of serial dilution error on calibration inference in immunoassay. Biometrics 1998; 54:19-32.
31. Rubin DB. Multiple Imputation for Nonresponse in Surveys. Wiley Series in Probability and Statistics. Wiley: Hoboken, NJ, 1987.
32. Little RJ, Rubin DB. Statistical Analysis with Missing Data (2nd edn). Wiley: Hoboken, NJ, 2002.
33. Richardson S, Leblond L, Jaussent I, Green PJ. Mixture models in measurement error problems, with reference to epidemiological studies. Journal of the Royal Statistical Society, Series A 1999; 165:549-566.
34. Carroll RJ, Maca JD, Ruppert D. Nonparametric regression in the presence of measurement error. Biometrika 1999; 86:541-554.
35. Schafer JL. Analysis of Incomplete Multivariate Data. Chapman & Hall: London, 1997.
36. Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences (with Discussion). Statistical Science 1992; 7:457-472.