Omitting continuous covariates in binary regression models: implications for sensitivity and mediation analysis (original) (raw)
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2009
In observational studies, the estimation of a treatment effect on an outcome of in terest is often done by controlling on a set of pre-treatment characteristics (covariates). This yields an unbiased estimator of the treatment effect when the assumption of un confoundedness holds, that is, there are no unobserved covariates affecting both the treatment assignment and the outcome. This is in general not realistically testable. It is, therefore, important to conduct an analysis about how sensitive the inference is with respect to the unconfoundedness assumption. In this paper we propose a procedure to conduct such a Bayesian sensitivity analysis, where the usual parameter uncertainty and the uncertainty due to the unconfoundedness assumption can be compared. To measure departures from the assumption we use a correlation coefficient which is in tuitively comprehensible and ensures that the results of sensitivity analyses made on different evaluation studies are comparable. Our proced...
Simple yet sharp sensitivity analysis for unmeasured confounding
Journal of Causal Inference, 2022
We present a method for assessing the sensitivity of the true causal effect to unmeasured confounding. The method requires the analyst to set two intuitive parameters. Otherwise, the method is assumption free. The method returns an interval that contains the true causal effect and whose bounds are arbitrarily sharp, i.e., practically attainable. We show experimentally that our bounds can be tighter than those obtained by the method of Ding and VanderWeele, which, moreover, requires to set one more parameter than our method. Finally, we extend our method to bound the natural direct and indirect effects when there are measured mediators and unmeasured exposure–outcome confounding.