Table 1 Core assumptions for identifiability in causal inference

Stable unit treatment value assumption (SUTVA): The stable unit treatment value assumption states that there is no interference among units, that is, the treatment status of a unit does not affect the potential outcomes of other units and it also requires that there is only a single version of the treatment (no hidden variations in treatment; no multiple versions of treatment). Possible violations of the SUTVA include settings where units interact (e.g., schools, group interventions) or different treatment dosages exist or different modes of administration operate which can affect the potential outcomes.

Consistency: An individual’s potential outcome under the observed exposure history is precisely the observed outcome: If T = t, then Y_i^t = Y_i

Positivity: The probability of being assigned to each of the treatment levels is greater than zero for each level of a variable X: Pr(T = t|X = x) > 0

Assignment mechanism–ignorability: Also known as exchangeability, or unconfoundedness, this assumption states that treatment assignment is independent of the potential outcomes; this roughly translates to no unmeasured confounders and no informative censoring. Ignorability can be either unconditional or conditional.

 • Unconditional ignorability: In RCTs, where the treatment is randomly assigned, the potential outcomes will be independent of the treatment assignment. Formally, this is defined as (Y_i¹,Y_i⁰) ⊥ T. This stems from the main property of randomization, i.e., any measured or unmeasured confounder will be equally distributed across groups.

 • Conditional ignorability: In non-randomized settings, confounders are not bound to be equally distributed across treatment groups, and thus unconditional ignorability cannot hold. However, given a set of covariates X and assuming that no unmeasured confounder exist, conditional ignorability can be defined as (Y_i¹,Y_i⁰) ⊥ T | X_i.