Adaptive stratified sampling design in two-phase studies for average causal effect estimation
Bibliographic record
Abstract
Causal inference using observational data often suffers from numerous confounding effects, with greatly distorted average causal effect (ACE) estimates if the confounders are ignored. Information on some confounders, such as genetic biomarkers and medical imaging, is prohibitively expensive to obtain in practice. Two-phase studies are resource-efficient solutions to this problem. In such studies, outcome, treatment, and inexpensive confounders are measured for a large number of subjects in the first phase; costly confounder measurements are then collected for a limited number of subjects in the second phase. An efficient statistical design is essential in controlling the cost arising in the second phase. In this paper, we propose an adaptive stratified sampling design (AdaStrat), which minimizes the variance of the ACE estimator with a given second-phase sample size. AdaStrat begins with gathering costly confounder measures for randomly selected pilot data, which are used to develop a stratification strategy and determine the sampling probabilities of strata. The resulting stratification and sampling strategy is applied to all first-phase subjects to determine the second-phase subjects with costly confounders measures. We rigorously show that AdaStrat produces a more efficient ACE estimator compared with the existing sampling designs with strata being prefixed. Finite sample properties of AdaStrat were evaluated through simulation studies, demonstrating its superiority against the fixed stratified sampling design (FixStrat), with relative efficiencies ranging from 20% to 30% in our simulation situations. The desired finite sample properties for AdaStrat were further confirmed through the application of the UK Biobank data.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.071 | 0.110 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".