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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    ABSTRACT: Uncertainty concerning the measurement error properties of self-reported diet has important implications for the reliability of nutritional epidemiology reports. Biomarkers based on the urinary recovery of expended nutrients can provide an objective measure of short-term nutrient consumption for certain nutrients and, when applied to a subset of a study cohort, can be used to calibrate corresponding self-report nutrient consumption assessments. A nonstandard measurement error model that makes provision for systematic error and subject-specific error, along with the usual independent random error, is needed for the self-report data. Three estimation procedures for hazard ratio (Cox model) parameters are extended for application to this more complex measurement error structure. These procedures are risk set regression calibration, conditional score, and nonparametric corrected score. An estimator for the cumulative baseline hazard function is also provided. The performance of each method is assessed in a simulation study. The methods are then applied to an example from the Women's Health Initiative Dietary Modification Trial.
    Biometrics 10/2011; 68(2):397-407. DOI:10.1111/j.1541-0420.2011.01690.x · 1.57 Impact Factor
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    ABSTRACT: Fat and protein sources may influence whether low-carbohydrate diets are associated with type 2 diabetes (T2D). The objective was to compare the associations of 3 low-carbohydrate diet scores with incident T2D. A prospective cohort study was conducted in participants from the Health Professionals Follow-Up Study who were free of T2D, cardiovascular disease, or cancer at baseline (n = 40,475) for up to 20 y. Cumulative averages of 3 low-carbohydrate diet scores (high total protein and fat, high animal protein and fat, and high vegetable protein and fat) were calculated every 4 y from food-frequency questionnaires and were associated with incident T2D by using Cox models. We documented 2689 cases of T2D during follow-up. After adjustments for age, smoking, physical activity, coffee intake, alcohol intake, family history of T2D, total energy intake, and body mass index, the score for high animal protein and fat was associated with an increased risk of T2D [top compared with bottom quintile; hazard ratio (HR): 1.37; 95% CI: 1.20, 1.58; P for trend < 0.01]. Adjustment for red and processed meat attenuated this association (HR: 1.11; 95% CI: 0.95, 1.30; P for trend = 0.20). A high score for vegetable protein and fat was not significantly associated with the risk of T2D overall but was inversely associated with T2D in men aged <65 y (HR: 0.78; 95% CI: 0.66, 0.92; P for trend = 0.01, P for interaction = 0.01). A score representing a low-carbohydrate diet high in animal protein and fat was positively associated with the risk of T2D in men. Low-carbohydrate diets should obtain protein and fat from foods other than red and processed meat.
    American Journal of Clinical Nutrition 02/2011; 93(4):844-50. DOI:10.3945/ajcn.110.004333 · 6.77 Impact Factor
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    ABSTRACT: Purpose: Survival analysis is increasingly being used in perinatal epidemiology to assess time-varying risk factors for various pregnancy outcomes. Here we show how quantitative correction for exposure misclassification can be applied to a Cox regression model with a time-varying dichotomous exposure. Methods: We evaluated influenza vaccination during pregnancy in relation to preterm birth among 2267 non-malformed infants whose mothers were interviewed as part of the Slone Birth Defects Study during 2006 through 2011. The hazard of preterm birth was modeled using a time-varying exposure Cox regression model with gestational age as the time-scale. The effect of exposure misclassification was then modeled using a probabilistic bias analysis that incorporated vaccination date assignment. The parameters for the bias analysis were derived from both internal and external validation data. Results: Correction for misclassification of prenatal influenza vaccination resulted in an adjusted hazard ratio (AHR) slightly higher and less precise than the conventional analysis: Bias-corrected AHR 1.04 (95% simulation interval, 0.70-1.52); conventional AHR, 1.00 (95% confidence interval, 0.71-1.41). Conclusions: Probabilistic bias analysis allows epidemiologists to assess quantitatively the possible confounder-adjusted effect of misclassification of a time-varying exposure, in contrast with a speculative approach to understanding information bias.
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