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Foundations

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.

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Classic

1. 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.

Best for

Clean randomization, first experiments, binary or revenue outcomes.

Outputs

ATE via diff-in-means with classic inference (t-test, z-test, or bootstrap).

DGPs
Model Math

ATE definition, diff-in-means estimator, and inference for continuous or conversion outcomes.

Monitoring

Sample Ratio Mismatch (SRM) is the first alert for experiment health.

Assumptions
  • 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.
Data contract
user_idtreatmentoutcomeconfounders columns
Variance Reduction

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.

Best for

Randomized experiments with strong pre-period signals and noisy outcomes.

Outputs

CUPED-adjusted ATE with tighter confidence intervals than raw diff-in-means.

DGPs
Model Math

CUPED adjustment, optimal theta estimation, and adjusted treatment-effect estimator.

Monitoring

Sample Ratio Mismatch (SRM) checks assignment integrity before CUPED analysis.

Assumptions
  • 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.
Data contract
user_idtreatmentoutcomeconfounders columnsy_pre (or y_pre, y_pre_2)
Observational Client-level Study

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.

Best for

Non-randomized treatment settings with strong, rich confounders and sufficient overlap.

Outputs

Debiased ATE estimates with robust confidence intervals under unconfoundedness and overlap.

DGPs
Model Math

DML-IRM orthogonal score, cross-fitting, nuisance estimation, and robust ATE inference.

Refutation

Overlap and refutation diagnostics validate support and robustness in observational settings.

Assumptions
  • 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.
Data contract
user_idtreatmentoutcomeconfounders columns
Heterogeneous Effects

4. GATE

GATE extends the observational IRM workflow from one average effect to subgroup-level treatment effects. After fitting IRM, we project the orthogonal signal onto pre-defined client groups to measure how impact differs across segments.

We use this setup when subgroup definitions are chosen before treatment and we want interpretable, group-level heterogeneity instead of a single pooled estimate.

Best for

Observational studies where treatment effect heterogeneity matters and groups are defined before intervention.

Outputs

Group Average Treatment Effects for mutually exclusive client segments with subgroup-level uncertainty.

Model Math

Orthogonal IRM signal averaged within groups, with subgroup regression and robust inference.

Group Design
  • Groups must be pre-defined and aligned to the fitted observations through `user_id`.
  • The subgroup basis should be mutually exclusive and exhaustive.
  • Every estimable group needs at least one treated and one control observation.
Assumptions
  • SUTVA / consistency: observed outcomes correspond to the realized treatment, with no interference across units.
  • Unconfoundedness: conditional on observed covariates, treatment assignment is independent of potential outcomes.
  • Overlap / positivity holds for relevant covariates and within each estimable group.
  • Group membership must be pre-treatment, not defined by treatment, outcomes, or post-treatment covariates.
  • Cross-fitted nuisance models are accurate enough for the orthogonal score to behave like a stable pseudo-outcome.
Data contract
user_idtreatmentoutcomeconfounders columns
Multi-arm Observational Study

5. 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.

Best for

Multi-arm non-randomized interventions with rich covariates and sufficient overlap across arms.

Outputs

Pairwise and baseline-referenced treatment effects with orthogonalized robust inference.

DGPs
Model Math

Multi-treatment IRM score construction, cross-fitting, and robust effect inference across arms.

Refutation

Overlap and balance diagnostics ensure identification support across all treatment arms.

Assumptions
  • 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.
Data contract
user_idtreatment (multi-arm)outcomeconfounders columns
Panel Time Series

6. Synthetic Control

Synthetic Control estimates treatment effects for one treated unit by constructing a weighted combination of untreated units that matches pre-treatment dynamics.

We use this setup when treatment happens at a unit-time level and pre-treatment trajectories are rich enough to build a credible synthetic counterpart.

Best for

Single-treated-unit panel settings with strong untreated donor pools and informative pre-periods.

Outputs

Post-treatment effect path and aggregate ATTE from treated vs synthetic trajectories.

DGPs
Model Math

Augmented Synthetic Control formulation with bias correction and post-treatment effect aggregation.

Diagnostics

Placebo and pre-period fit checks validate synthetic control quality and support interpretation.

Assumptions
  • One treated unit and untreated donor units remain unaffected by treatment spillovers.
  • Pre-treatment outcomes are informative enough to approximate the treated counterfactual.
  • No structural break unrelated to treatment invalidates post-treatment comparisons.
Data contract
unit_idtimeis_treated_unitpost_treatmentoutcome