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A Comparison of Methods to Estimate the Hazard Ratio Under Conditions of Time-varying Confounding and Nonpositivity

Naimi, Ashley I.a; Cole, Stephen R.a; Westreich, Daniel J.b; Richardson, David B.a

doi: 10.1097/EDE.0b013e31822549e8

In occupational epidemiologic studies, the healthy worker survivor effect refers to a process that leads to bias in the estimates of an association between cumulative exposure and a health outcome. In these settings, work status acts both as an intermediate and confounding variable and may violate the positivity assumption (the presence of exposed and unexposed observations in all strata of the confounder). Using Monte Carlo simulation, we assessed the degree to which crude, work-status adjusted, and weighted (marginal structural) Cox proportional hazards models are biased in the presence of time-varying confounding and nonpositivity. We simulated the data representing time-varying occupational exposure, work status, and mortality. Bias, coverage, and root mean squared error (MSE) were calculated relative to the true marginal exposure effect in a range of scenarios. For a base-case scenario, using crude, adjusted, and weighted Cox models, respectively, the hazard ratio was biased downward 19%, 9%, and 6%; 95% confidence interval coverage was 48%, 85%, and 91%; and root MSE was 0.20, 0.13, and 0.11. Although marginal structural models were less biased in most scenarios studied, neither standard nor marginal structural Cox proportional hazards models fully resolve the bias encountered under conditions of time-varying confounding and nonpositivity.

From the aDepartment of Epidemiology, Gillings School of Global Public Health, UNC-Chapel Hill, NC and bDepartment of Obstetrics and Gynecology and Duke Global Health Institute, Duke University

Submitted 21 October 2010; accepted 29 March 2011; posted 11 July 2011.

Supported in part by NIH grant R01CA117841 (D.B.R.), Fonds de Recherche en Santé du Québec through a Doctoral Research Award (A.I.N.), and NIH/NICHD grant K99-HD-06-3961 (D.J.W.).

Correspondence: Stephen R. Cole, Epidemiology, CB7415, University of North Carolina, Chapel Hill, NC 27599. E-mail:

© 2011 Lippincott Williams & Wilkins, Inc.