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An Exact Corrected Log‐Likelihood Function for Cox's Proportional Hazards Model under Measurement Error and Some Extensions

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  • Thomas Augustin

Abstract

. This paper studies Cox's proportional hazards model under covariate measurement error. Nakamura's [Biometrika 77 (1990) 127] methodology of corrected log‐likelihood will be applied to the so‐called Breslow likelihood, which is, in the absence of measurement error, equivalent to partial likelihood. For a general error model with possibly heteroscedastic and non‐normal additive measurement error, corrected estimators of the regression parameter as well as of the baseline hazard rate are obtained. The estimators proposed by Nakamura [Biometrics 48 (1992) 829], Kong et al. [Scand. J. Statist. 25 (1998) 573] and Kong & Gu [Statistica Sinica 9 (1999) 953] are re‐established in the special cases considered there. This sheds new light on these estimators and justifies them as exact corrected score estimators. Finally, the method will be extended to some variants of the Cox model.

Suggested Citation

  • Thomas Augustin, 2004. "An Exact Corrected Log‐Likelihood Function for Cox's Proportional Hazards Model under Measurement Error and Some Extensions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 43-50, March.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:1:p:43-50
    DOI: 10.1111/j.1467-9469.2004.00371.x
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    References listed on IDEAS

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    1. Christopher J. Flinn & James J. Heckman, 1982. "Models for the Analysis of Labor Force Dynamics," NBER Working Papers 0857, National Bureau of Economic Research, Inc.
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    1. Yingyao Hu & Geert Ridder, 2012. "Estimation of nonlinear models with mismeasured regressors using marginal information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 347-385, April.
    2. Muff, Stefanie & Ott, Manuela & Braun, Julia & Held, Leonhard, 2017. "Bayesian two-component measurement error modelling for survival analysis using INLA—A case study on cardiovascular disease mortality in Switzerland," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 177-193.
    3. Buzas, Jeffrey S., 2009. "A note on corrected scores for logistic regression," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2351-2358, November.
    4. Liang Li & Bo Hu & Tom Greene, 2009. "A Semiparametric Joint Model for Longitudinal and Survival Data with Application to Hemodialysis Study," Biometrics, The International Biometric Society, vol. 65(3), pages 737-745, September.
    5. Yih-Huei Huang & Chi-Chung Wen & Yu-Hua Hsu, 2015. "The Extensively Corrected Score for Measurement Error Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 911-924, December.
    6. Hans Schneeweiss & Thomas Augustin, 2006. "Some recent advances in measurement error models and methods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 183-197, March.
    7. Yanlin Tang & Xinyuan Song & Grace Yun Yi, 2022. "Bayesian analysis under accelerated failure time models with error-prone time-to-event outcomes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 139-168, January.
    8. Li-Pang Chen & Grace Y. Yi, 2021. "Semiparametric methods for left-truncated and right-censored survival data with covariate measurement error," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 481-517, June.

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