Survival Analysis with Error-Prone Time-Varying Covariates: A Risk Set Calibration Approach
Article first published online: 10 MAY 2010
© 2010, The International Biometric Society
Volume 67, Issue 1, pages 50–58, March 2011
How to Cite
Liao, X., Zucker, D. M., Li, Y. and Spiegelman, D. (2011), Survival Analysis with Error-Prone Time-Varying Covariates: A Risk Set Calibration Approach. Biometrics, 67: 50–58. doi: 10.1111/j.1541-0420.2010.01423.x
- Issue published online: 14 MAR 2011
- Article first published online: 10 MAY 2010
- Received November 2009. Revised February 2010. Accepted February 2010.
- Cox proportional hazards model;
- Measurement error;
- Risk set regression calibration;
- Time-varying covariates
Summary Occupational, environmental, and nutritional epidemiologists are often interested in estimating the prospective effect of time-varying exposure variables such as cumulative exposure or cumulative updated average exposure, in relation to chronic disease endpoints such as cancer incidence and mortality. From exposure validation studies, it is apparent that many of the variables of interest are measured with moderate to substantial error. Although the ordinary regression calibration (ORC) approach is approximately valid and efficient for measurement error correction of relative risk estimates from the Cox model with time-independent point exposures when the disease is rare, it is not adaptable for use with time-varying exposures. By recalibrating the measurement error model within each risk set, a risk set regression calibration (RRC) method is proposed for this setting. An algorithm for a bias-corrected point estimate of the relative risk using an RRC approach is presented, followed by the derivation of an estimate of its variance, resulting in a sandwich estimator. Emphasis is on methods applicable to the main study/external validation study design, which arises in important applications. Simulation studies under several assumptions about the error model were carried out, which demonstrated the validity and efficiency of the method in finite samples. The method was applied to a study of diet and cancer from Harvard's Health Professionals Follow-up Study (HPFS).