propensity score

Used in matching method, propensity score is the probability of a unit being in the treatment group, given certain observed characteristics (vector of covariates ).

In observational studies for causal inference, propensity score are always unknown and therefore must be estimated, usually via binomial logistic regression:

• the dependent variable would be binary treatment assignment
• the independent variable would be variables believed to be confounders (covariates)

Usage

propensity score matching: the matching method involves matching treated units to control units on the basis of estimated propensity score. It can replace considering all covariates if the assignment mechanism is unconfounded.

*However, it is not recommended, because two units might have the same aggregate propensity score , but actually have different individual characteristics. propensity score matching rarely satisfies the strict balance test:

• Student t-test statistic for means between groups
• Multivariate bootstrap KS test for two distributions
• For both, higher p-value indicates more similarity between groups (more balance) ➡️ at least 0.15

There are better ways to perform matching (e.g., genetic matching)*.