Matching & Weighting

No randomization? The observational fallback: find untreated units that look like treated ones on everything that matters, and compare outcomes within those matched pairs. The treated user who started 6 months ago, has 3 devices, churned once — pair them with a non-treated twin, not with 'average control'.

Matching in raw features gets unwieldy fast (too many dimensions, no 'near' in high-D). Propensity scores collapse it: fit a model P(treated | X), then match or weight on that single number. Matching on the propensity score is provably equivalent to matching on all covariates that drive treatment — under the assumptions that make the method honest at all.