Bounds on Causal Effects Based on Expectations in Ordered-Outcome Models

Bounding causal effects under unmeasured confounding is particularly challenging when the outcome variable is ordinal. When the goal is to assess whether an intervention leads to a better outcome, ordinal causal effects offer a more appropriate analytical framework. In contrast, the average causal effect (ACE), defined as the difference in expected outcomes, is more suitable for capturing population-level effects. In this paper, we derive sharp bounds for causal effects with ternary outcomes using an expectation-based framework, under both general conditions and monotonicity assumptions. We conduct numerical simulations to evaluate the width of the bounds under various scenarios. Finally, we demonstrate our method’s practical utility by applying it to the CDC Diabetes Health Indicators Dataset to assess the causal effect of health behaviors on diabetes risk.