Studying noncollapsibility of the odds ratio with marginal structural and logistic regression models
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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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 | 0.113 | 0.368 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.004 | 0.006 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".