Using data on patients with a Veterans Affairs (VA) emergency department visit for a mental health condition, Costantini et al. (2025) finds that:
…longer waiting times make it more likely that patients miss their follow-up mental health visit, consequently increasing the probability that they permanently disengage from care. A 1 standard deviation increase in wait time between the emergency department visit and follow-up appointment date (11.7 days) increases two-year mortality by about 1.5 percent.
You can read the full paper here.