Primary Submission Category: Design-Based Causal Inference
Stratified Sampling for Model-Assisted Estimation with Surrogate Outcomes
Authors: Reagan Mozer,
Presenting Author: Reagan Mozer*
In many randomized trials, outcomes such as essays or open-ended responses must be manually scored before impact analysis, a process that is costly and limiting. Model-assisted estimation combines surrogate outcomes from machine learning or large language models with a human-coded subset to obtain unbiased estimates, but existing approaches rely on simple random sampling and ignore systematic structure in prediction errors. We extend this framework by incorporating stratified sampling to more efficiently allocate human coding effort. We derive the exact variance of the stratified estimator, characterize conditions under which stratification improves precision, and identify a Neyman-type optimal allocation rule that oversamples strata with larger residual variance. Comprehensive simulation studies confirm that stratification consistently improves efficiency when surrogate prediction errors exhibit structured bias or heteroskedasticity. We present two empirical applications, including an education RCT and a large observational corpus, to illustrate practical implementation using ChatGPT-generated surrogate outcomes. Overall, this framework provides a practical design-based approach for leveraging surrogate outcomes and strategically allocating human coding effort to obtain unbiased estimates with greater efficiency.