Covariate Measurement Error in the Cox Model: A Simulation Study

When a continuous covariate measured with error is used as a predictor in a survival analysis using the Cox proportional hazards model [Cox, D. R. (1972). Regression models and life tables (with discussion). J. R. Statist. Soc. Ser. B 34:187–220], the parameter estimate is usually biased. In a simulation study, we compared alternative approaches to account for additive measurement error in the Cox model for the scenario of one continuous covariate measured with error and one binary covariate measured without error. We considered both Gaussian and Gaussian-mixture distributions for the continuous covariate, and main effect and interaction models. We compared the bias reduction of the regression calibration approach [Carroll, R. J., Rupert, D., Stefanski, L. A. (1995). Measurement Error in Nonlinear Models. London: Chapman and Hall] and the fully parametric and semi-parametric likelihood-based approaches [Hu, P., Tsiatis, A. A., Davidian, M. (1998). Estimating the parameters in the Cox model when covariate variables are measured with error. Biometrics 54:1407–1419] to the results obtained when measurement error is ignored. These simulations support our analysis of the time to recurrence of major depression for elderly patients in a psychiatric clinical trial [Liu, K. S., Mazumdar, S., Stone, R. A., Dew, M. A., Houck, P. R., Reynolds, C. F. (2001). Accounting for covariate measurement error in a Cox model analysis of recurrence of depression. J. Psychiar. Res. 35:177–185] where the covariate measured with error was log transformed total rapid eye movement (REM) activity counts and the binary covariate was a treatment indicator. The likelihood-based estimates are virtually unbiased for the parameters in the main effects model under a standard Gaussian distribution when measurement error is small and equal between both treatment groups, and slightly biased otherwise. The regression calibration estimates are unstable for the interaction model when the continuous covariate has a large variance under a non-standard Gaussian distribution. For the Gaussian-mixture situation, the likelihood-based estimates typically are less biased than the estimates obtained using the other approaches, and the fully parametric estimates tend to be somewhat more biased than the semi-parametric estimates. The estimates for the interaction parameters are downwardly biased under all four approaches.