Density estimation of a biomedical variable subject to measurement error using an auxiliary set of replicate observations

Statistics in Medicine

Volumn 31, Issue 30, 2012, Pages 4154-4163

  Stirnemann, J J ^a,b   Comte, F ^a   Samson, A ^a  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b HÔPITAL NECKER ENFANTS MALADES   (France)

Author keywords

Density estimation; Gestational age; Measurement error; Non parametric methods; Replicate measurements

Indexed keywords

ANALYTICAL ERROR; ARTICLE; BIOMEDICAL VARIABLE; BIOMETRY; BLOOD PRESSURE MEASUREMENT; COVARIANCE; CROWN RUMP LENGTH; DENSITY; FERTILIZATION IN VITRO; FRAMINGHAM RISK SCORE; GESTATIONAL AGE; HUMAN; ISCHEMIC HEART DISEASE; KERNEL METHOD; MATERNAL AGE; MATHEMATICAL VARIABLE; MENSTRUAL CYCLE; NONPARAMETRIC TEST; OBSERVATIONAL STUDY; PREGNANCY; REFERENCE VALUE; STATISTICAL ANALYSIS; SYSTOLIC BLOOD PRESSURE; THEORETICAL MODEL;

BIAS (EPIDEMIOLOGY); BIOMETRY; BLOOD PRESSURE; CORONARY DISEASE; DATA INTERPRETATION, STATISTICAL; FEMALE; GESTATIONAL AGE; HUMANS; LONGITUDINAL STUDIES; MALE; MENSTRUAL CYCLE; PREGNANCY; PREGNANCY TRIMESTER, FIRST; REFERENCE VALUES; STATISTICAL DISTRIBUTIONS; STATISTICS, NONPARAMETRIC; SYSTOLE; TIME FACTORS; ULTRASONOGRAPHY, PRENATAL;

EID: 84870871326     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.5392     Document Type: Article

References (39)

1. Budtz-Jørgensen E, Keiding N, Grandjean P, Weihe P, White RF.Consequences of exposure measurement error for confounder identification in environmental epidemiology. Statistics in Medicine October 2003; 22(19):3089-3100.
2. 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 November 2008; 27(25):5195-5216.
3. Sarkar S, Qu Y.Quantifying the treatment effect explained by markers in the presence of measurement error. Statistics in Medicine April 2007; 26(9):1955-1963.
4. Li W, Qu Y.Adjustment for the measurement error in evaluating biomarkers. Statistics in Medicine September 2010; 29(22):2338-2346.
5. Lobach I, Carroll RJ, Spinka C, Gail MH, Chatterjee N.Haplotype-based regression analysis and inference of case-control studies with unphased genotypes and measurement errors in environmental exposures. Biometrics September 2008; 64(3):673-684.
6. Barendse W.The effect of measurement error of phenotypes on genome wide association studies. BMC Genomics 2011; 12:232.
7. Bergemann TL, Zhao LP.Signal quality measurements for cDNA microarray data. IEEE/ACM Transactions on Computational Biology and Bioinformatics/IEEE, ACM June 2010; 7(2):299-308.
8. Fan J.On the optimal rates of convergence for nonparametric deconvolution problems. The Annals of Statistics September 1991; 19(3):1257-1272.
9. Liu MC, Taylor RL.A consistent nonparametric density estimator for the deconvolution problem. Canadian Journal of Statistics 1989; 17(4):427-438.
10. Stefanski LA, Carroll RJ.Deconvoluting kernel density estimators. Statistics 1990; 21(2):169-184.
11. Hesse CH.Data-driven deconvolution. Journal of Nonparametric Statistics 1999; 10(4):343-373.
12. Delaigle A, Gijbels I.Bootstrap bandwidth selection in kernel density estimation from a contaminated sample. Annals of the Institute of Statistical Mathematics 2004; 56(1):19-47.
13. Fan J, Koo JY.Wavelet deconvolution. Information Theory, IEEE Transactions on 2002; 48(3):734-747.
14. Pensky M, Vidakovic B.Adaptive wavelet estimator for nonparametric density deconvolution. Annals of Statistics 1999:2033-2053.
15. R Development Core Team. R: a language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, 2010. http://www.R-project.org, ISBN 3-900051-07-0.
16. Wang X, Wang B.Deconvolution estimation in measurement error models: the R package decon. Journal of Statistical Software March 2011; 39(10).
17. Diggle PJ, Hall P.A fourier approach to nonparametric deconvolution of a density estimate. Journal of the Royal Statistical Society. Series B (Methodological) 1993; 55(2):523-531.
18. Neumann MH.On the effect of estimating the error density in nonparametric deconvolution. Journal of Nonparametric Statistics 1997; 7(4):307.
19. Comte F, Lacour C.Data-driven density estimation in the presence of additive noise with unknown distribution. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 2011; 73(4):601-627.
20. Wang X, Ye D.The effects of error magnitude and bandwidth selection for deconvolution with unknown error distribution. Journal of Nonparametric Statistics 2012; 24(1):153-167.
21. Comte F, Samson A, Stirnemann JJ.Deconvolution estimation of onset of pregnancy with replicate observations, 2011. http://hal.archives-ouvertes.fr/hal-00588235.
22. Delaigle A, Hall P, Meister A.On deconvolution with repeated measurements. The Annals of Statistics 2008; 36(2):665-685.
23. Li T, Vuong Q.Nonparametric estimation of the measurement error model using multiple indicators. Journal of Multivariate Analysis 1998; 65:139-165.
24. Meister A, Neumann M.Deconvolution from non-standard error densities under replicated measurements. Statistica Sinica 2009; 20(4):1609-1936.
25. Comte F, Rozenholc Y, Taupin ML.Penalized contrast estimator for adaptive density deconvolution. Canadian Journal of Statistics 2006; 34(3):431-452.
26. Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM.Measurement Error in Nonlinear Models: a Modern Perspective, Second Edition, 2nd ed. Chapman and Hall/CRC, 2006.
27. Dunson DB, Baird DD, Wilcox AJ, Weinberg CR.Day-specific probabilities of clinical pregnancy based on two studies with imperfect measures of ovulation. Human Reproduction (Oxford, England) July 1999; 14(7):1835-1839.
28. Dunson DB, Weinberg CR, Baird DD, Kesner JS, Wilcox AJ.Assessing human fertility using several markers of ovulation. Statistics in Medicine 2001; 20(6):965-978.
29. Gardosi J, Vanner T, Francis A.Gestational age and induction of labour for prolonged pregnancy. British Journal of Obstetrics and Gynaecology 1997; 104(7):792-797.
30. Gardosi J, Mul T, Francis A, Hall J, Fishel S.Comparison of second trimester biometry in singleton and twin pregnancies conceived with assisted reproductive techniques. British Journal of Obstetrics and Gynaecology 1997; 104(6):737-740.
31. Mongelli M, Gardosi J.Birth weight, prematurity and accuracy of gestational age. International Journal of Gynaecology and Obstetrics: The Official Organ of the International Federation of Gynaecology and Obstetrics 1997; 56(3):251-256.
32. Tunón K, Eik-Nes SH, Grøttum P.A comparison between ultrasound and a reliable last menstrual period as predictors of the day of delivery in 15, 000 examinations. Ultrasound in Obstetrics and Gynecology: The Official Journal of the International Society of Ultrasound in Obstetrics and Gynecology 1996; 8(3):178-185.
33. Sladkevicius P, Saltvedt S, Almström H, Kublickas M, Grunewald C, Valentin L.Ultrasound dating at 12-14 weeks of gestation: a prospective cross-validation of established dating formulae in in-vitro fertilized pregnancies. Ultrasound in Obstetrics and Gynecology: The Official Journal of the International Society of Ultrasound in Obstetrics and Gynecology 2005; 26(5):504-511.
34. Robinson HP.Sonar measurement of fetal crown-rump length as means of assessing maturity in first trimester of pregnancy. British Medical Journal 1973; 4(5883):28-31.
35. Ostchega Y, Prineas RJ, Paulose-Ram R, Grim CM, Willard G, Collins D.National Health and Nutrition Examination Survey 1999-2000: effect of observer training and protocol standardization on reducing blood pressure measurement error. Journal of Clinical Epidemiology 2003; 56(8):768-74.
36. Wilcox AJ, Dunson D, Baird DD.The timing of the "fertile window" in the menstrual cycle: day specific estimates from a prospective study. BMJ (Clinical Research Ed.) 2000; 321(7271):1259-1262.
37. Bland JM, Altman DG.Measuring agreement in method comparison studies. Statistical Methods in Medical Research 1999; 8(2):135-160.
38. McIntyre J, Stefanski LA.Density estimation with replicate heteroscedastic measurements. Annals of the Institute of Statistical Mathematics 2011; 63(1):81-99.
39. Dias T, Mahsud-Dornan S, Thilaganathan B, Papageorghiou A, Bhide A.First-trimester ultrasound dating of twin pregnancy: are singleton charts reliable?. BJOG: An International Journal of Obstetrics and Gynaecology 2010; 117(8):979-984.