0. Introduction to Causal Inference
Get to know notation and intuition of Causal Inference with the Potential Outcome Framework. Learn what calculation of effect could be done.
Read the full article1. Classic RCT
The Randomized Controlled Trial (RCT) is widely considered the gold standard for establishing causal relationships. By randomly assigning subjects to treatment and control groups, we ensure that both groups are identical in all aspects except for the treatment itself.
We call it classic because we do not have pre-treatment data of your units.
Clean randomization, first experiments, binary or revenue outcomes.
ATE via diff-in-means with classic inference (t-test, z-test, or bootstrap).
ATE definition, diff-in-means estimator, and inference for continuous or conversion outcomes.
- Unconfoundedness: random assignment breaks correlation with potential outcomes.
- Overlap: each unit has a non-zero probability of assignment to every arm.
- SUTVA: no interference and consistent treatment definitions.
2. CUPED
Controlled-experiment Using Pre-Experiment Data (CUPED) is a powerful variance reduction technique. By leveraging data from before the experiment started, we can reduce the variance of our metric and detect smaller effects with the same sample size.
We use CUPED when pre-treatment outcomes are available for the same units and are predictive of post-treatment outcomes.
Randomized experiments with strong pre-period signals and noisy outcomes.
CUPED-adjusted ATE with tighter confidence intervals than raw diff-in-means.
CUPED adjustment, optimal theta estimation, and adjusted treatment-effect estimator.
Sample Ratio Mismatch (SRM) checks assignment integrity before CUPED analysis.
- Unconfoundedness: assignment remains independent of potential outcomes.
- Overlap: each unit has non-zero assignment probability.
- SUTVA: no interference and consistent treatment definition.
- Pre-treatment outcomes are measured before treatment and predictive of post-period outcomes.
3. Unconfoundedness
Unconfoundedness is the assumption that we have measured all variables that influence both the treatment assignment and the outcome. This allows us to estimate causal effects from observational data by adjusting for these measured confounders.
We use this setup when treatment is not randomized and we rely on rich confounders plus overlap checks for valid identification.
Non-randomized treatment settings with strong, rich confounders and sufficient overlap.
Debiased ATE estimates with robust confidence intervals under unconfoundedness and overlap.
DML-IRM orthogonal score, cross-fitting, nuisance estimation, and robust ATE inference.
Overlap and refutation diagnostics validate support and robustness in observational settings.
- Unconfoundedness: all confounders affecting treatment and outcome are observed.
- Overlap: each unit has non-zero treatment probability conditional on covariates.
- SUTVA: no interference and consistent treatment definitions.
- Nuisance models are sufficiently accurate for orthogonalized estimation.
4. Multi Unconfoundedness
Multi Unconfoundedness extends observational identification to multiple treatment arms. We estimate causal contrasts across arms by adjusting for observed confounders and modeling generalized propensity scores.
We use this setup when assignment is non-random and treatment has three or more levels.
Multi-arm non-randomized interventions with rich covariates and sufficient overlap across arms.
Pairwise and baseline-referenced treatment effects with orthogonalized robust inference.
Multi-treatment IRM score construction, cross-fitting, and robust effect inference across arms.
Overlap and balance diagnostics ensure identification support across all treatment arms.
- Multi-arm unconfoundedness: all confounders affecting arm assignment and outcomes are observed.
- Overlap: each unit has positive probability for every treatment arm.
- SUTVA: no interference and consistent treatment definitions across arms.
- Nuisance models for outcome and generalized propensity are sufficiently accurate.