Survival Analysis with Error-Prone Time-Varying Covariates: A Risk Set Calibration Approach

Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts 02115, USA.
Biometrics (Impact Factor: 1.57). 03/2011; 67(1):50-8. DOI: 10.1111/j.1541-0420.2010.01423.x
Source: PubMed


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).

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    • "These include regression calibration (Prentice, 1982; Wang et al., 1997), risk set regression calibration (Xie et al., 2001), parametric, semiparametric and nonparametric likelihood procedures (Hu et al., 1998), conditional scores (Tsiatis and Davidian, 2001), parametric corrected scores (Nakamura, 1992), and nonparametric corrected scores procedures (Huang and Wang, 2000, 2006; Hu and Lin, 2002, 2004; Gorfine et al., 2004; Song and Huang, 2005). There has also been consideration of more general error models (Hu and Lin, 2002; Liao et al., 2011) under the assumption that a `validation' subsample is available where the covariate of interest is precisely measured. In our setting, the precisely measured covariate is not obtainable. "
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