Counterfactual inference with latent variable and its application in mental health care

This paper deals with the problem of modeling counterfactual reasoning in scenarios where, apart from the observed endogenous variables, we have a latent variable that affects the outcomes and, consequently, the results of counterfactuals queries. This is a common setup in healthcare problems, including mental health. We propose a new framework where the aforementioned problem is modeled as a multivariate regression and the counterfactual model accounts for both observed and a latent variable, where the latter represents what we call the patient individuality factor ( $$ ). In mental health, focusing on individuals is paramount, as past experiences can change how people see or deal with situations, but individuality cannot be directly measured. To the best of our knowledge, this is the first counterfactual approach that considers both observational and latent variables to provide deterministic answers to counterfactual queries, such as: what if I change the social support of a patient, to what extent can I change his/her anxiety? The framework combines concepts from deep representation learning and causal inference to infer the value of $$ and capture both non-linear and multiplicative effects of causal variables. Experiments are performed with both synthetic and real-world datasets, where we predict how changes in people's actions may lead to different outcomes in terms of symptoms of mental illness and quality of life. Results show the model learns the individually factor with errors lower than 0.05 and answers counterfactual queries that are supported by the medical literature. The model has the potential to recommend small changes in people's lives that may completely change their relationship with mental illness.