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Doubly Protected Estimation for Survival Outcomes Utilizing External Controls for Randomized Clinical Trials
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Proposes a doubly protected estimator for RMST difference that uses doubly robust efficient influence function estimation with density-ratio covariate-shift correction, plus DR-Learner-based detection of outcome drift to selectively borrow comparable external controls.
Problem
Estimating treatment effects for censored survival outcomes in small or imbalanced randomized trials by borrowing external controls, while avoiding bias from covariate shift and outcome drift between trial and external data.
Approach
Combines an efficient-influence-function doubly robust estimator (density ratio for covariate shift, censoring-weighted, RMST-based) with a DR-Learner pseudo-outcome for subject-level bias detection and penalized selection of comparable external controls, so only comparable external subjects are borrowed.
Key results
- Simulations (500 Monte Carlo reps): the proposed adaptive estimator keeps small bias under outcome drift and yields smaller SE than the trial-only AIPW benchmark, while the full-borrowing estimator is substantially biased under unmeasured confounding and lack of concurrency.
- Under Setting One (no outcome drift), all integrative estimators improve Root-MSE over the trial-only estimator, though the proposed selective estimator is less efficient than other integrative estimators.
- In the galcanezumab application, the adaptive estimator reaches PrSS >= 0.6 for detecting RMST difference < -0.1 at 6 months with 100 placebo patients versus at least 150 for the trial-only estimator.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add selective borrowing of comparable external controls | Doubly Protected Adaptive Integrative Analysis · Simulation Settings Two and Three | bias | Helped |
| borrow all external controls without selective drift detection | ACW, PSRWE, and TransCox · Simulation Settings Two and Three | bias | Hurt |
| integrate external controls when there is no outcome heterogeneity | Integrative estimators · Simulation Setting One | Root-MSE | Helped |
| use selective borrowing with bias detection rather than full borrowing | Doubly Protected Adaptive Integrative Analysis · Simulation Setting One | efficiency | Hurt |
| use selective borrowing rather than full borrowing | Doubly Protected Adaptive Integrative Analysis · Simulation Settings Two and Three | type-I error | Helped |
| use selective borrowing rather than full borrowing | Doubly Protected Adaptive Integrative Analysis · Simulation Settings Two and Three | coverage probability | Helped |
| use selective borrowing rather than trial-only estimation | Doubly Protected Adaptive Integrative Analysis · Simulation Settings One to Three | power | Mixed |
| augment EVOLVE-1 placebo controls with REGAIN placebo controls using selective borrowing | Doubly Protected Adaptive Integrative Analysis · Galcanezumab episodic migraine application | PrSS: PrSS ≥ 0.6; 100 vs at least 150 | Helped |
| selectively borrow comparable controls rather than use trial-only estimation | Doubly Protected Adaptive Integrative Analysis · Galcanezumab episodic migraine application | PrSS | Helped |
| use selective borrowing when comparable external controls are available | Doubly Protected Adaptive Integrative Analysis · Trial population; asymptotic variance | variance | Helped |
Surprising findings
- The naive full-borrowing estimator controls type-I error only when no outcome drift is present and inflates type-I error under unmeasured confounding and lack of concurrency.
- Type-I error control is challenging for small samples under unmeasured confounding, a limitation shared by Bayesian dynamic borrowing.
Limitations
- Selection based on RMST differences may exclude external controls that are only partially comparable (invariant in parts of the survival function).
- Type-I error inflation for small samples in the presence of unmeasured confounding.
- Bootstrap variance with only 50 replicates used for inference in simulations.
Experimental setup
Datasets: EVOLVE-1 (galcanezumab phase 3 trial, episodic migraine) REGAIN (galcanezumab phase 3 trial, chronic migraine placebo arm) simulated data
Benchmarks: simulation studies (five external-control settings) EVOLVE-1/REGAIN galcanezumab migraine data
Metrics: bias standard error root MSE type-I error coverage probability power probability of study success
Baselines: trial-only AIPW estimator full-borrowing estimator (acw) propensity score-integrated estimator (psrwe) TransCox transfer learning Cox regression
Builds on: DR-Learner augmented inverse probability weighting double machine learning adaptive lasso
Closest papers by meaning
- Assessing the robustness of heterogeneous treatment effects in survival analysis under informative censoring (NeurIPS 2026 · similarity 0.86)
- Heterogeneous Treatment Effect in Time-to-Event Outcomes: Harnessing Censored Data with Recursively Imputed Trees (ICML 2025 · similarity 0.86)
- Orthogonal Survival Learners for Estimating Heterogeneous Treatment Effects from Time-to-Event Data (NeurIPS 2025 · similarity 0.86)
- Using Surrogates in Covariate-adjusted Response-adaptive Randomization Experiments with Delayed Outcomes (NeurIPS 2024 · similarity 0.85)
- Enhancing Statistical Validity and Power in Hybrid Controlled Trials: A Randomization Inference Approach with Conformal Selective Borrowing (ICML 2025 · similarity 0.84)
- Adaptive Data-Borrowing for Improving Treatment Effect Estimation using External Controls (NeurIPS 2025 · similarity 0.84)
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