Sensitivity analysis and distributional assumptions

In a presentation of various methods for assessing the sensitivity of regression results to unmeasured confounding, Lin et al. (1998) use a conditional independence assumption to derive algebraic relationships between the true exposure e¤ect and the apparent exposure e¤ect in a reduced model which does not control for the unmeasured confounding variable. However, Hernán and Robins (1999) have noted that if the measured covariates and the unmeasured confounder both a¤ect the exposure of interest then the principal conditional independence assumption which 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 satis…ed for an entire family of distributions even if both the measured covariates and the unmeasured confounder a¤ect the exposure of interest. These considerations clarify the appropriate context in which relevant sensitivity analysis techniques can be applied.