Causal Inference inside an RCT – STATA-First Edition

0 Glossary of Key Abbreviations

Short-form	Stands for	Meaning in this document
R	Randomised assignment	The arm a participant is assigned to by the randomisation algorithm (sometimes noted Z).
D	Delivered (received) treatment	What the participant actually gets; equals R only if compliance is perfect.
ACE	Average Causal Effect	Generic label for “true” causal effect; equals ATE/ATT/ATU when R = D for everyone.
ATE	Average Treatment Effect	Mean effect in the entire target population.
ATT / ATU	Effect on the Treated / Untreated	Mean effect restricted to those who did / did not receive treatment.
ITT	Intention-to-Treat	Primary estimator that compares arms exactly as randomised, ignoring crossover.
PP / AT	Per-Protocol / As-Treated	Analyses restricted by compliance (PP) or re-labelled by actual D (AT); lose randomisation protection.
CACE	Complier Average Causal Effect (also called LATE)	The causal effect among participants who would comply with their assignment, estimated with an IV approach when R ≠ D.

Exchangeability – Randomisation balances both measured & unmeasured baseline risk.
Positivity – By design, every participant has a non-zero chance of landing in each arm.
No-Interference (part of SUTVA) – Each patient’s assignment rarely affects another’s outcome; use cluster randomisation if it might.
Consistency (second part of SUTVA) – The protocol specifies one clear version of each arm; monitor adherence to keep it that way.

Result ➜ The standard ITT contrast is already a causal estimator.

If every subject receives exactly what they were assigned (R = D):

ACE  =  ATE  =  ATT  =  ATU

So you only need to report the ITT contrast.

* assume variable treat = 1 treatment arm, 0 control
ttest outcome, by(treat)          // mean difference + CI

regress outcome i.treat baseline_outcome age sex
margins, dydx(treat)               // adjusted mean diff = ATE

Adding baseline prognostic covariates shrinks the standard error; it is not for confounder control in an RCT.

cci events_treat total_treat  events_ctrl total_ctrl  // crude RD & RR

logit event i.treat age sex

margins treat, predict(pr)            // get arm-specific risks
lincom _b[1.treat]/(1-_b[1.treat]) / (_b[0.treat]/(1-_b[0.treat])) , eform

Margins calculate arm-level predicted probabilities; the lincom line converts those risks into a marginal OR.

Goal	Recommended estimator / Stata tool
Effectiveness (policy)	ITT – as above; remains primary.
Efficacy in compliers	CACE via two-stage least squares (IV): ivregress 2sls outcome (D = R) covariates ; estat firststage to diagnose instrument strength.
Supportive PP / AT	Restrict or relabel using keep if or replace treat = D – report as sensitivity only.

Pitfall	Why it matters	Stata-first fix
Adjusting for too many baseline covariates “for balance”	Up-weights noise → wider CIs	Limit to ≤ 5 strong prognostic factors; pre-specify.
Using conditional OR as final result	Mis-matches causal estimand	Always run margins to obtain marginal effect.
Multiple versions of treatment emerge	Breaks Consistency	Add arm indicator for version or stratify analysis.
>15 % event rate yet reporting OR	Odds mislead at common events	Prefer RD/RR: riskrr (user package) or cci above.

Write the estimand sentence (e.g., “ATE of 30-day mortality for Drug X vs placebo in adults with septic shock”).
Check adherence – if < 90 %, plan CACE alongside ITT.
Pre-select covariates for precision only.
Decide risk vs odds scale before looking at results.
Use margins for all marginal effects; bootstrap (vce(bootstrap)) if you need robust CIs after complex modelling.

Randomisation makes all four identifiability assumptions hold by design.
With perfect compliance, ITT delivers the single average causal effect you need.
Covariate adjustment in an RCT targets precision, not confounding.
For binary outcomes, translate conditional logistic results into marginal metrics using margins.
Non-compliance? Keep ITT for policy, add CACE (IV) for efficacy, and treat PP/AT as secondary.