Ignorability

Ignorability is a condition in statistics and causal inference that enables identification of causal effects from observational data where treatment assignment is not randomized. It typically means that the potential outcomes, Y(0) and Y(1), are independent of the treatment indicator T given a set of observed covariates X. In symbols: Y(0), Y(1) ⟂ T | X. If this holds, any differences in outcomes between treated and untreated units can be attributed to the treatment once X is accounted for.

This idea is usually paired with a positivity or overlap assumption: for all values of X, there is a positive probability of receiving each treatment, i.e., 0 < P(T=1|X) < 1. When both ignorability and overlap hold, the average treatment effect can be estimated from observational data by adjusting for X, using methods such as regression adjustment, propensity-score matching, or inverse probability weighting.

Strong ignorability is a term sometimes used to denote the combination of unconfoundedness (ignorability) and overlap. It reflects the requirement that all confounders of the treatment–outcome relationship are observed and that each unit has a nonzero chance of receiving each treatment level.

Ignorability also appears in missing data contexts. Here, a missingness mechanism is ignorable for likelihood-based inference if the data are missing at random (MAR) and the parameters governing the missingness mechanism are distinct from those of the data model. If ignorability fails, explicit modeling of the missingness process may be required.

Limitations include that ignorability is not testable from the data and relies on unverified assumptions about unobserved confounding. Sensitivity analyses and instrumental variable approaches are commonly used to assess robustness to potential violations.