Assessing causal effects in the presence of unobserved confounding is a
challenging problem. Existing studies leveraged proxy variables or multiple
treatments to adjust for the confounding bias. In particular, the latter
approach attributes the impact on a single outcome to multiple treatments,
allowing estimating latent variables for confounding control. Nevertheless,
these methods primarily focus on a single outcome, whereas in many real-world
scenarios, there is greater interest in studying the effects on multiple
outcomes. Besides, these outcomes are often coupled with multiple treatments.
Examples include the intensive care unit (ICU), where health providers evaluate
the effectiveness of therapies on multiple health indicators. To accommodate
these scenarios, we consider a new setting dubbed as multiple treatments and
multiple outcomes. We then show that parallel studies of multiple outcomes
involved in this setting can assist each other in causal identification, in the
sense that we can exploit other treatments and outcomes as proxies for each
treatment effect under study. We proceed with a causal discovery method that
can effectively identify such proxies for causal estimation. The utility of our
method is demonstrated in synthetic data and sepsis disease.Comment: Preprint, under revie