Point: Risk Ratio Equations for Natural Direct and Indirect Effects in Causal Mediation Analysis of a Binary Mediator and a Binary Outcome—A Fresh Look at the Formulas
Bibliographic record
Abstract
In this article, we review the formulas for the natural direct and indirect effects' risk ratios introduced by Ananth and VanderWeele (Am J Epidemiol. 2011;174(1):99-108) for causal mediation analysis of a binary mediator and a binary outcome. In particular, we show that the closed-form equations Ananth and VanderWeele provided do not correspond to the log-binomial model specified by these authors for the mediator variable, but rather to a logistic model. We then provide risk ratio equations for natural direct and indirect effects that truly pertain to a log-binomial model. We conclude with a discussion on the practical implications of the binary mediator model's specification by analysts. The related impact can be negligible or not, depending on the rareness of the mediator.
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How this classification was reachedexpand
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 | 0.006 | 0.045 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.003 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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) | 0.000 | 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 teacher head, 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".