Nested doubly robust estimating equations for causal analysis with an incomplete effect modifier
Bibliographic record
Abstract
Inference regarding exposure effects within subgroups of individuals and regarding the effect‐modifying role of some covariates plays a central role in research on stratified medicine. Large administrative databases offer an appealing basis for investigating these questions but causal inference can be challenging due to confounding and missing data. We consider the setting where subgroups are defined by the value of an incompletely observed potential effect modifier. We first formulate simple doubly inverse probability‐weighted estimating equations involving one weight to facilitate causal inference with complete data and another weight to adjust for the fact that the effect modifier is only partially observed. We then develop a nested doubly robust (NDR) estimating function which is shown to yield more efficient and robust estimators. In simulation studies, both approaches are shown to yield valid inference in finite samples, but the advantages of the NDR estimators are evident when one or more of the auxiliary models are misspecified. An application to a study of the effect of biological therapy on inflammation in a rheumatology cohort is given for illustration.
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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 | 0.038 | 0.098 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.005 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.007 | 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".