Abstract:
Causal effect inference is essential in many areas, notably in healthcare and the medical sciences, for correctly understanding a cause and effect relationship between a treatment and an outcome. In order to perform causal inference, a strong and untestable assumption is usually invoked, stating that all of the covariates affecting both treatment and outcome (confounders) are observed. Violation of this assumption may cause bias in estimation of the causal effect, to which researchers may not be aware. Sensitivity analysis methods deal with possible hidden confounding and attempt to measure the bias under different possible models.
Existing sensitivity analysis methods typically assume that the confounder is completely hidden, and has a pre-specified limited effect on the treatment and outcome. We study the case where the confounder is partially observed via proxy variables, with no assumptions on its relation with the treatment and outcome. Researches that use the proxy variables notation generally focus on identification of the effect, rather than measuring the potential level of bias in its estimation, as sensitivity analysis methods do. We aim to bring the usage of proxy variables into the worlds of sensitivity analysis and create a flexible method for measuring the possible bias under such conditions.
Specifically, we make structural assumptions between the latent and proxy variables, and propose a flexible optimization-based method for inferring an interval estimate of the causal effect, an estimate that may be used to indicate the significance of the possible level of bias. Using numerical approximations of gradients, our approach can be applied using zeroth-order information alone and be easily modified to any effect estimator and structure function. The method is tested and analysed on both synthetic and real world data.
