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A Unified Framework for the Transportability of Population-Level Causal Measures
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Proposes a unified framework for transporting first-moment population causal measures (RD, RR, OR, NNT, etc.) from an RCT to a target population under covariate shift, with identification, weighting/G-formula/doubly robust estimators, asymptotics, simulations and a CRASH-3/Traumabase case study.
Problem
Generalizing RCT treatment effects to a target population is mostly done for the risk difference, while clinically important absolute and relative measures (RR, OR, NNT) are non-collapsible or nonlinear and lack transport estimators.
Approach
A general definition of first-moment causal measures as functions of the mean potential outcomes, with identification under exchangeability in mean and in effect measure, and classical (weighted HT, G-formula) plus semiparametric (one-step, estimating equation) estimators built from the efficient influence function; shows one-step and EE estimators coincide for RD but diverge for nonlinear measure
Key results
- Under a non-linear outcome model (N=50,000, 3,000 reps), G-formula estimators are biased while estimating-equation estimators remain unbiased across measures.
- Estimating-equation estimators are shown to be (weakly) doubly robust: consistent if either the outcome regressions or the density ratio are correct.
- On the CRASH-3/Traumabase data, all estimators suggest a slight beneficial effect of tranexamic acid, but the treatment appears to have little to no impact in the target population.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use estimating-equation estimators instead of G-formula estimators | Estimators under exchangeability in mean · Synthetic Experiment 1, nonlinear response | bias | Helped |
| use one-step estimation instead of estimating equations for non-RD measures | Estimators under exchangeability in mean · Synthetic Experiment 1, nonlinear response | accuracy | Hurt |
| rely on exchangeability in mean when it is violated, while exchangeability in effect measure holds | Estimators introduced under exchangeability in mean · Synthetic Experiment 2, RR and OR | convergence | Hurt |
| use the exchangeability-in-effect-measure estimators | Estimators under exchangeability in effect measure · Synthetic Experiment 2 | bias | Helped |
| transport treatment effects from CRASH-3 to Traumabase | Estimators under exchangeability in mean · CRASH-3 and Traumabase | treatment effect | No clear effect |
Surprising findings
- One-step and estimating-equation approaches give the same estimator for the risk difference but different estimators for nonlinear measures such as RR and OR.
- Under exchangeability in effect measure, RR and OR estimators fail to converge in the simulations, while RD estimators still converge despite violation of strong transportability.
Limitations
- Concerns about OS estimators: no general double robustness result; must be checked case by case.
- Exchangeability in effect measure requires access to control outcomes in the target population, and few estimators exist for it since most rely on CATE estimation.
- Real-data results lack a known true effect, so performance cannot be verified directly.
Experimental setup
Datasets: CRASH-3 trial Traumabase registry
Benchmarks: synthetic simulations CRASH-3 and Traumabase combined dataset
Metrics: bias estimator comparison across causal measures confidence intervals via stratified bootstrap
Baselines: weighted Horvitz-Thompson weighted G-formula transported G-formula one-step estimator
Builds on: Horvitz-Thompson estimator G-formula efficient influence function cross-fitting
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