A Causal Modeling Framework with Stochastic Confounders

The study of causal effects of an intervention or treatment on a specific outcome based on observational data is a fundamental problem in many applications. Examples include understanding the effects of massive wildfires on a person's mental health, of teaching methods on a student's employability, or of disease outbreaks on the global stock market. A critical problem of causal inference from observational data is confounding. A variable that affects both the treatment and the outcome is known as a confounder of the treatment effects on the outcome. Standard ways to measure observable confounders include propensity score matching and their variants (Rubin, 2005). However, if a confounder is hidden, the treatment effect on the outcome cannot be directly estimated without further assumptions (Pearl, 2009; Louizos et al., 2017). For example, household income, which cannot be easily measured, can affect both the therapy options available to a patient and the health condition after therapy of that patient.