Causal Sensitivity Analysis: f-sensitivity through entropic value at risk computation

Abstract

The field of causal inference provides a variety of estimators that can be used to find the effect of a treatment on an outcome based on observational data. However, many of these estimators require the unconfoundedness assumption, stating that all relevant confounders are observed within the data. This assumption is quite strict and many real-life problems would violate it, due to confounders being too expensive, immoral, or abstract to observe. To weaken this assumption, causal sensitivity analysis attempts to quantify the level of hidden confounding and use it to create a possible bound on the causal effect. This study compares a well-established Marginal Sensitivity Model (MSM) with a newly proposed f-sensitivity model. Given f-sensitivity is relatively new, the current approaches for computation can be inefficient or non-deterministic. A new method of computing the f-sensitivity bound is proposed, which can lead to closed-form solutions in some estimator-specific cases. The differences between the MSM and f-sensitivity models are outlined and illustrated with examples, from which a set of guiding questions is created for researchers to decide between the two sensitivity models. All of the code required to reproduce this study is located in this GitHub repository.