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Sensitivity analysis: distributional assumptions and confounding assumptions.

Vanderweele TJ

Department of Health Studies, University of Chicago, 5841 South Maryland Avenue, MC 2007, Chicago, Illinois 60637, USA. vanderweele@uchicago.edu

In a presentation of various methods for assessing the sensitivity of regression results to unmeasured confounding, Lin, Psaty, and Kronmal (1998, Biometrics54, 948-963) use a conditional independence assumption to derive algebraic relationships between the true exposure effect and the apparent exposure effect in a reduced model that does not control for the unmeasured confounding variable. However, Hernán and Robins (1999, Biometrics55, 1316-1317) have noted that if the measured covariates and the unmeasured confounder both affect the exposure of interest then the principal conditional independence assumption that is used to derive these algebraic relationships cannot hold. One particular result of Lin et al. does not rely on the conditional independence assumption but only on assumptions concerning additivity. It can be shown that this assumption is satisfied for an entire family of distributions even if both the measured covariates and the unmeasured confounder affect the exposure of interest. These considerations clarify the appropriate contexts in which relevant sensitivity analysis techniques can be applied.

Published 16 May 2008 in Biometrics, 64(2): 645-9.
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