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Using Surrogates in Covariate-adjusted Response-adaptive Randomization Experiments with Delayed Outcomes
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Proposes a multi-stage covariate-adjusted response-adaptive randomization design that uses immediately observed surrogate outcomes to improve ATE estimation when primary outcomes are delayed, with semiparametric efficiency results and a synthetic HIV case study.
Problem
CARA designs assume primary outcomes are immediately observable, but in clinical trials primary outcomes are often delayed or missing, which reduces efficiency of ATE estimation and hampers adaptive allocation.
Approach
Integrates delayed primary outcomes with immediately observed surrogate outcomes in a CARA design, modeling arm- and covariate-dependent delay nonparametrically, using surrogates to guide allocation, and deriving the semiparametric efficiency bound for the ATE with a design that attains it.
Key results
- Theoretical result: the proposed ATE estimator attains the semiparametric efficiency bound and is asymptotically normal under the design.
- In a synthetic HIV case study (calibrated to Tanzania RCT, true ATE 0.04), the proposed design yields smaller standard deviation than CARA using only primary outcomes and complete randomization, with vanishing bias for all three.
- The paper proves convergence of the adaptive allocation to the oracle optimal allocation under a sufficient-enrollment condition in non-delayed stages.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use surrogate outcomes to guide adaptive treatment allocation with delayed primary outcomes | CARA design · Synthetic HIV trial | standard deviation | Helped |
| Use surrogate outcomes to guide adaptive treatment allocation with delayed primary outcomes instead of complete randomization | CARA design · Synthetic HIV trial | standard deviation | Helped |
| Use surrogate outcomes in addition to delayed primary outcomes | CARA design · Synthetic HIV trial | estimation efficiency | Helped |
Limitations
- Assumes delay is independent of potential outcomes given arm and covariates; outcome-dependent delay not handled.
- Analysis restricted to discrete covariates and surrogates to avoid technical complexity.
- Evaluation only on a synthetic case study calibrated to one HIV trial.
Experimental setup
Datasets: HIV RCT data from Tanzania (Chamie et al.) used to calibrate a synthetic data-generating process
Benchmarks: synthetic HIV trial case study
Metrics: bias standard deviation of ATE estimator
Baselines: complete randomization CARA design using only primary outcomes
Builds on: covariate-adjusted response-adaptive randomization (CARA) semiparametric efficiency theory (Hahn 1998 style efficient influence function) principal surrogate criteria
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