Analysis of error-prone survival data under additive hazards models: measurement error effects and adjustments
Tóm tắt
Covariate measurement error occurs commonly in survival analysis. Under the proportional hazards model, measurement error effects have been well studied, and various inference methods have been developed to correct for error effects under such a model. In contrast, error-contaminated survival data under the additive hazards model have received relatively less attention. In this paper, we investigate this problem by exploring measurement error effects on parameter estimation and the change of the hazard function. New insights of measurement error effects are revealed, as opposed to well-documented results for the Cox proportional hazards model. We propose a class of bias correction estimators that embraces certain existing estimators as special cases. In addition, we exploit the regression calibration method to reduce measurement error effects. Theoretical results for the developed methods are established, and numerical assessments are conducted to illustrate the finite sample performance of our methods.
Tài liệu tham khảo
Breslow NE, Day NE (1980) Statistical methods in cancer research, vol 1., The design and analysis of case–control studies IARC, Lyon
Buzas JS (1998) Unbiased scores in proportional hazards regression with covariate measurement error. J Stat Plan Inference 67:247–257
Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM (2006) Measurement error in nonlinear models: a modern perspective, 2nd edn. Chapman & Hall/CRC, Boca Raton
Cox DR (1972) Regression models and life-tables (with Discussion). J R Stat Soc Ser B 34:187–220
Cox DR, Oakes D (1984) Analysis of survival data. Chapman & Hall/CRC, Boca Raton
Fuchs HJ, Borowitz DS, Christiansen DH, Morris EM, Nash ML, Ramsey BW, Rosenstein BJ, Smith AL, Wohl ME (1994) Effect of aerosolized recombinant human DNase on exacerbations of respiratory symptoms and on pulmonary function in patients with cystic fibrosis. N Engl J Med 331:637–642
Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, New York
Hu C, Lin DY (2004) Semiparametric failure time regression with replicates of mismeasured covariates. J Am Stat Assoc 99:105–118
Hu P, Tsiatis AA, Davidian M (1998) Estimating the parameters in the Cox model when covariates are measured with error. Biometrics 54:1407–1419
Huang Y, Wang CY (2000) Cox regression with accurate covariates unascertainable: a nonparametric-correction approach. J Am Stat Assoc 45:1209–1219
Jiang J, Zhou H (2007) Additive hazard regression with auxiliary covariates. Biometrika 94:359–369
Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley, Hoboken
Kulich M, Lin DY (2000) Additive hazards regression with covariate measurement error. J Am Stat Assoc 95:238–248
Li Y, Lin X (2003) Functional inference in frailty measurement error models for clustered survival data using the SIMEX approach. J Am Stat Assoc 98:191–203
Li Y, Ryan L (2004) Survival analysis with heterogeneous covariate measurement error. J Am Stat Assoc 99:724–735
Lin DY, Ying Z (1994) Semiparametric analysis of the additive risk model. Biometrika 81:61–71
Nakamura T (1992) Proportional hazards model with covariates subject to measurement error. Biometrics 48:829–838
Pollard D (1990) Empirical processes: theory and applications. IMS, Hayward
Prentice RL (1982) Covariate measurement errors and parameter estimation in a failure time regression model. Biometrika 69:331–342
Song X, Huang Y (2005) On corrected score approach for proportional hazards model with covariate measurement error. Biometrics 61:702–714
Sun L, Zhang Z, Sun J (2006) Additive hazards regression of failure time data with covariate measurement errors. Stat Neerlandica 60:497–509
van der Vaart AW (1998) Asymptotic statistics. Cambridge University Press, New York
Wang CY, Hsu L, Feng ZD, Prentice RL (1997) Regression calibration in failure time regression. Biometrics 53:131–145
Yan Y, Yi GY (2015) A class of functional methods for error-contaminated survival data under additive hazards models with replicate measurements. J Am Stat Assoc. doi:10.1080/01621459.2015.1034317
Yi GY, Lawless JF (2007) A corrected likelihood method for the proportional hazards model with covariates subject to measurement error. J Stat Plan Inference 137:1816–1828
Yi GY, Reid N (2010) A note on Mis-specified estimating functions. Stat Sinica 20:1749–1769
Zucker DM, Spiegelman D (2008) Corrected score estimation in the proportional hazards model with misclassified discrete covariates. Stat Med 27:1911–1933