Non-parametric Maximum Likelihood Estimation for Cox Regression with Subject-Specific Measurement Error
Many epidemiological studies have been conducted to identify an association between nutrient consumption and chronic disease risk. To this problem, Cox regression with additive covariate measurement error has been well developed in the literature. However, researchers are concerned with the validity...
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| Published in | Scandinavian journal of statistics Vol. 35; no. 4; pp. 613 - 628 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Oxford, UK
Blackwell Publishing Ltd
01.12.2008
Blackwell Publishing Blackwell Danish Society for Theoretical Statistics |
| Series | Scandinavian Journal of Statistics |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0303-6898 1467-9469 |
| DOI | 10.1111/j.1467-9469.2008.00605.x |
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| Abstract | Many epidemiological studies have been conducted to identify an association between nutrient consumption and chronic disease risk. To this problem, Cox regression with additive covariate measurement error has been well developed in the literature. However, researchers are concerned with the validity of the additive measurement error assumption for self-report nutrient data. Recently, some study designs using more reliable biomarker data have been considered, in which the additive measurement error assumption is more likely to hold. Biomarker data are often available in a subcohort. Self-report data often encounter with a variety of serious biases. Complications arise primarily because the magnitude of measurement errors is often associated with some characteristics of a study subject. A more general measurement error model has been developed for self-report data. In this paper, a non-parametric maximum likelihood (NPML) estimator using an EM algorithm is proposed to simultaneously adjust for the general measurement errors. |
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| AbstractList | . Many epidemiological studies have been conducted to identify an association between nutrient consumption and chronic disease risk. To this problem, Cox regression with additive covariate measurement error has been well developed in the literature. However, researchers are concerned with the validity of the additive measurement error assumption for self‐report nutrient data. Recently, some study designs using more reliable biomarker data have been considered, in which the additive measurement error assumption is more likely to hold. Biomarker data are often available in a subcohort. Self‐report data often encounter with a variety of serious biases. Complications arise primarily because the magnitude of measurement errors is often associated with some characteristics of a study subject. A more general measurement error model has been developed for self‐report data. In this paper, a non‐parametric maximum likelihood (NPML) estimator using an EM algorithm is proposed to simultaneously adjust for the general measurement errors. Many epidemiological studies have been conducted to identify an association between nutrient consumption and chronic disease risk. To this problem, Cox regression with additive covariate measurement error has been well developed in the literature. However, researchers are concerned with the validity of the additive measurement error assumption for self-report nutrient data. Recently, some study designs using more reliable biomarker data have been considered, in which the additive measurement error assumption is more likely to hold. Biomarker data are often available in a subcohort. Self-report data often encounter with a variety of serious biases. Complications arise primarily because the magnitude of measurement errors is often associated with some characteristics of a study subject. A more general measurement error model has been developed for self-report data. In this paper, a non-parametric maximum likelihood (NPML) estimator using an EM algorithm is proposed to simultaneously adjust for the general measurement errors. Many epidemiological studies have been conducted to identify an association between nutrient consumption and chronic disease risk. To this problem, Cox regression with additive covariate measurement error has been well developed in the literature. However, researchers are concerned with the validity of the additive measurement error assumption for self-report nutrient data. Recently, some study designs using more reliable biomarker data have been considered, in which the additive measurement error assumption is more likely to hold. Biomarker data are often available in a subcohort. Self-report data often encounter with a variety of serious biases. Complications arise primarily because the magnitude of measurement errors is often associated with some characteristics of a study subject. A more general measurement error model has been developed for self-report data. In this paper, a non-parametric maximum likelihood (NPML) estimator using an EM algorithm is proposed to simultaneously adjust for the general measurement errors. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2008. |
| Author | WANG, C. Y. |
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| CitedBy_id | crossref_primary_10_1080_01621459_2014_896805 crossref_primary_10_1515_ijb_2018_0028 crossref_primary_10_1093_biostatistics_kxr051 crossref_primary_10_1002_bimj_201500238 crossref_primary_10_1002_bimj_201000180 |
| Cites_doi | 10.1007/978-1-4757-2545-2 10.1111/j.0006-341X.2000.00106.x 10.1002/sim.4780080905 10.1111/1467-9868.00247 10.1111/j.0006-341X.2005.454_1.x 10.1136/bmj.311.7011.986 10.1093/aje/kwg091 10.1093/jnci/88.23.1738 10.2307/2533670 10.1080/01621459.1999.10474195 10.1093/oxfordjournals.aje.a116086 10.1093/biomet/69.2.331 10.1214/aos/1176324462 10.1080/01621459.1997.10474051 10.2307/2532348 10.2307/3315770 10.1093/aje/153.4.394 10.1201/9781420010138 10.2307/2533103 10.2307/2529620 10.1093/biomet/88.2.447 10.1080/01621459.2000.10474321 10.1111/j.2517-6161.1977.tb01600.x 10.1111/1467-9868.00317 10.1080/01621459.1995.10476485 10.1111/j.2517-6161.1972.tb00899.x 10.1111/j.1541-0420.2006.00632.x |
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| Keywords | Biometrics Parameter estimation Error estimation Non parametric estimation Multivariate analysis Covariate Epidemiology biomarker data Parametric method Hypothesis test Statistical test Medical science Measurement error Chronic disease Statistical association Parametric estimation Statistical method Statistical regression Experimental design Maximum likelihood corrected score calibration sample EM algorithm Application Biased estimation |
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| References | Xie, S. X., Wang, C. Y. & Prentice, R. L. (2001). A risk set calibration method for failure time regression using a covariate reliability sample. J. Roy. Statist. Soc. Ser. B Stat. Methodol. 63, 855-870. Breslow, N. E. (1974). Covariance analysis of censored survival data. Biometrics 30, 89-99. Tsiatis, A. A., DeGruttola, V. & Wulfsohn, M. S. (1995). Modeling the relationship of survival to longitudinal data measured with error. Applications to survival and CD4 count in patients with AIDS. J. Amer. Statist. Assoc. 90, 27-37. Rosner, B., Willett, W. C. & Spiegelman, D. (1989). Correction of logistic regression relative risk estimates and confidence intervals for systematic within-person measurement error. Stat. Med. 8, 1051-1070. Tsiatis, A. A. & Davidian, D. (2001). A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error. Biometrika 88, 447-458. Prentice, R. L., Pettinger, M. & Anderson, G. L. (2005). Statistical issues arising in the Women's Health Initiative (with discussion). Biometrics 61, 899-941. Murphy, S. A., Rossini, A. J. & Van Der Vaart, A. W. (1997). Maximum likelihood estimation in the proportional odds model. J. Amer. Statist. Assoc. 92, 968-976. Kipnis, V., Subar, A. F., Midthune, D., Freedman, L. S., Ballard-Barbash, R., Troiano, R., Bingham, S., Schoeller, D. A., Schatzkin, A. & Carroll, R. J. (2003). The structure of dietary measurement error: results of the OPEN biomarker study. Am. J. Epidemiol. 158, 14-21. Chen, H. Y. & Little, R. J. A. (1999). Proportional hazards regression with missing covariates. J. Amer. Statist. Assoc. 94, 896-908. Wang, C. Y., Hsu, L., Feng, Z. D. & Prentice, R. L. (1997). Regression calibration in failure time regression. Biometrics 53, 131-145. Van Der Vaart, A. W. & Wellner, J. A. (1996). Weak convergence and empirical processes. Springer-Verlag, New York. Cox, D. R. (1972). Regression models and life tables (with discussion). J. Roy. Statist. Soc. Ser. B Stat. Methodol. 34, 187-220. Dafni, U. G. & Tsiatis, A. A. (1998). Evaluating surrogate markers of clinical outcome measured with error. Biometrics 54, 1445-1462. Willett, W. C. (1990). Nutritional epidemiology. Oxford University Press, Oxford. Murphy, S. A. (1995). Asymptotic theory for the frailty model. Ann. Statist. 23, 182-198. Freedman, L. S., Carroll, R. J. & Wax, Y. (1991). Estimating the relationship between dietary intake obtained from a food frequency questionnaire and true average intake. Am. J. Epidemiol. 134, 310-320. Carroll, R. J., Freedman, L. S., Kipnis, V. & Li, L. (1998). A new class of measurement error models, with applications to estimating the distribution of usual intake. Canad. J. Statist. 26, 467-477. Nakamura, T. (1992). Proportional hazards models with covariates subject to measurement error. Biometrics 48, 829-838. Carroll, R. J., Ruppert, D., Stefanski, L. A. & Crainiceanu, C. M. (2006). 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L. & Lissner, L. (1995). Dietary underreporting by obese individuals - is it specific or non-specific? Br. Med. J. 311, 986-989. Nielsen, G. G., Gill, R. D., Andersen, P. K. & Sørensen, T. I. A. (1992). A counting process approach to maximum likelihood estimation in frailty models. Scand. J. Statist. 19, 25-43. Prentice, R. L. (1996). Dietary fat and breast cancer: measurement error and results from analytic epidemiology. J. Natl. Cancer Inst. 88, 1738-1747. Huang, Y. & Wang, C. Y. (2000). Cox regression with accurate covariates unascertainable: a nonparametric-correction approach. J. Amer. Statist. Assoc. 95, 1209-1219. Prentice, R. L. (1982). Covariate measurement errors and parameter estimation in a failure time regression model. 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| References_xml | – reference: Rosner, B., Willett, W. C. & Spiegelman, D. (1989). Correction of logistic regression relative risk estimates and confidence intervals for systematic within-person measurement error. Stat. Med. 8, 1051-1070. – reference: Kipnis, V., Subar, A. F., Midthune, D., Freedman, L. S., Ballard-Barbash, R., Troiano, R., Bingham, S., Schoeller, D. A., Schatzkin, A. & Carroll, R. J. (2003). The structure of dietary measurement error: results of the OPEN biomarker study. Am. J. Epidemiol. 158, 14-21. – reference: Nakamura, T. (1992). Proportional hazards models with covariates subject to measurement error. Biometrics 48, 829-838. – reference: Prentice, R. L. (1996). Dietary fat and breast cancer: measurement error and results from analytic epidemiology. J. Natl. Cancer Inst. 88, 1738-1747. – reference: Willett, W. C. (1990). Nutritional epidemiology. Oxford University Press, Oxford. – reference: Carroll, R. J., Freedman, L. S., Kipnis, V. & Li, L. (1998). A new class of measurement error models, with applications to estimating the distribution of usual intake. Canad. J. Statist. 26, 467-477. – reference: Xie, S. X., Wang, C. Y. & Prentice, R. L. (2001). A risk set calibration method for failure time regression using a covariate reliability sample. J. Roy. Statist. Soc. Ser. B Stat. Methodol. 63, 855-870. – reference: Tsiatis, A. A. & Davidian, D. (2001). A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error. Biometrika 88, 447-458. – reference: Cox, D. R. (1972). Regression models and life tables (with discussion). J. Roy. Statist. Soc. Ser. B Stat. Methodol. 34, 187-220. – reference: Dafni, U. G. & Tsiatis, A. A. (1998). Evaluating surrogate markers of clinical outcome measured with error. Biometrics 54, 1445-1462. – reference: Freedman, L. S., Carroll, R. J. & Wax, Y. (1991). Estimating the relationship between dietary intake obtained from a food frequency questionnaire and true average intake. Am. J. Epidemiol. 134, 310-320. – reference: Chen, H. Y. & Little, R. J. A. (1999). Proportional hazards regression with missing covariates. J. Amer. Statist. Assoc. 94, 896-908. – reference: Murphy, S. A. (1995). Asymptotic theory for the frailty model. Ann. Statist. 23, 182-198. – reference: Nielsen, G. G., Gill, R. D., Andersen, P. K. & Sørensen, T. I. A. (1992). A counting process approach to maximum likelihood estimation in frailty models. Scand. J. Statist. 19, 25-43. – reference: Tsiatis, A. A., DeGruttola, V. & Wulfsohn, M. S. (1995). Modeling the relationship of survival to longitudinal data measured with error. Applications to survival and CD4 count in patients with AIDS. J. Amer. Statist. Assoc. 90, 27-37. – reference: Wang, C. Y. & Pepe, M. S. (2000). Expected estimating equations to accommodate covariate measurement error. J. Roy. Statist. Soc. Ser. B Stat. Methodol. 62, 509-524. – reference: Dempster, A. P., Laird, N. M. & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. Ser. B Stat. Methodol. 39, 1-38. – reference: Murphy, S. A., Rossini, A. J. & Van Der Vaart, A. W. (1997). Maximum likelihood estimation in the proportional odds model. J. Amer. Statist. Assoc. 92, 968-976. – reference: Prentice, R. L., Pettinger, M. & Anderson, G. L. (2005). Statistical issues arising in the Women's Health Initiative (with discussion). Biometrics 61, 899-941. – reference: Wang, C. Y., Hsu, L., Feng, Z. D. & Prentice, R. L. (1997). Regression calibration in failure time regression. Biometrics 53, 131-145. – reference: Breslow, N. E. (1974). Covariance analysis of censored survival data. Biometrics 30, 89-99. – reference: Carroll, R. J., Ruppert, D., Stefanski, L. A. & Crainiceanu, C. M. (2006). Nonlinear measurement error models: a modern perspective, 2nd edn. Chapman and Hall, London. – reference: Van Der Vaart, A. W. & Wellner, J. A. (1996). Weak convergence and empirical processes. Springer-Verlag, New York. – reference: Wang, C. Y. (2000). Weighted normality-based estimator in correcting correlation coefficient estimation between incomplete nutrient measurements. Biometrics 56, 106-112. – reference: Prentice, R. L. (1982). Covariate measurement errors and parameter estimation in a failure time regression model. Biometrika 69, 331-342. – reference: Huang, Y. & Wang, C. Y. (2000). Cox regression with accurate covariates unascertainable: a nonparametric-correction approach. J. Amer. Statist. Assoc. 95, 1209-1219. – reference: Heitman, B. L. & Lissner, L. (1995). Dietary underreporting by obese individuals - is it specific or non-specific? Br. Med. J. 311, 986-989. – reference: Sugar, E. A., Wang, C. Y. & Prentice, R. L. (2007). Methods for logistic regression with flexible measurement error. 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| Title | Non-parametric Maximum Likelihood Estimation for Cox Regression with Subject-Specific Measurement Error |
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