Studying noncollapsibility of the odds ratio with marginal structural and logistic regression models
Why this work is in the frame
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Bibliographic record
Abstract
One approach to quantifying the magnitude of confounding in observational studies is to compare estimates with and without adjustment for a covariate, but this strategy is known to be defective for noncollapsible measures such as the odds ratio. Comparing estimates from marginal structural and standard logistic regression models, the total difference between crude and conditional effects can be decomposed into the sum of a noncollapsibility effect and confounding bias. We provide an analytic approach to assess the noncollapsibility effect in a point-exposure study and provide a general formula for expressing the noncollapsibility effect. Next, we provide a graphical approach that illustrates the relationship between the noncollapsibility effect and the baseline risk, and reveals the behavior of the noncollapsibility effect for a range of different exposure and covariate effects. Various observations about noncollapsibility can be made from the different scenarios with or without confounding; for example, the magnitude of effect of the covariate plays a more important role in the noncollapsibility effect than does that of the effect of the exposure. In order to explore the noncollapsibility effect of the odds ratio in the presence of time-varying confounding, we simulated an observational cohort study. The magnitude of noncollapsibility was generally comparable to the effect in the point-exposure study in our simulation settings. Finally, in an applied example we demonstrate that collapsibility can have an important impact on estimation in practice.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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 it