Heterogeneous survivor average causal effects
Treatment effect heterogeneity when outcomes are truncated by a terminal event
Extensive tools exist for studying treatment effect heterogeneity when outcomes are fully observed. Far fewer exist when a patient-centered outcome is truncated by a terminal event such as death — where, for participants who die during follow-up, the outcome is unobservable, undefined, or only partly observed.
Comparing survivors between arms does not solve this, because survival is itself affected by treatment and the two survivor groups are therefore different sets of people. Principal stratification provides a framework in which valid causal conclusions can be drawn: the estimand is defined on the always-survivors stratum, the participants who would survive under either arm.
This analysis estimates both the average causal effect and heterogeneous causal effects among always-survivors, using Bayesian Additive Regression Trees to flexibly specify separate mean models for the potential outcomes and for latent stratum membership. A regression tree is then fitted to the estimated conditional effects — the same “fit-the-fit” step used in the HTE analysis pipeline — to describe which patients the effect varies across.
What is in it
| Section | Contents |
|---|---|
| Introduction | Truncation by a terminal event, the principal stratification framework, and the always-survivors estimand |
| Functions | The two functions the analysis is built from, with their parameters and return values documented |
| Step 1 | Estimating the SACE and the conditional SACE with BART, via separate mean models for the potential outcomes and for latent stratum membership |
| Step 2 | The “fit-the-fit” approach — a classification and regression tree fitted to the estimated conditional effects, giving interpretable subgroups |
| ARDS ARMA data analysis | The methods applied to the ARDSNetwork ARMA trial of low tidal volume ventilation |
Relation to the HTE analysis pipeline
Both estimate a per-patient conditional effect with BART and then fit a tree to those estimates for interpretability. They differ in the estimand and in what that requires:
| HTE pipeline | This analysis | |
|---|---|---|
| Outcome | observed for every randomized patient | truncated by a terminal event |
| Estimand | conditional average treatment effect | conditional effect among always-survivors |
| Extra structure needed | none | principal stratification; latent stratum membership modelled |
Full methodological detail is in Chen, Harhay, Tong and Li, A Bayesian machine learning approach for estimating heterogeneous survivor causal effects: applications to a critical care trial, Annals of Applied Statistics, 2024.