A heuristic approach to the formulas for population attributable fraction
Bibliographic record
Abstract
BACKGROUND: As the definitional formula for population attributable fraction is not usually directly usable in applications, separate estimation formulas are required. However, most epidemiology textbooks limit their coverage to Levin's formula, based on the (dichotomous) distribution of the exposure of interest in the population. Few present or explain Miettinen's formula, based on the distribution of the exposure in the cases; and even fewer present the corresponding formulas for situations with more than two levels of exposure. Thus, many health researchers and public health practitioners are unaware of, or are not confident in their use of, these formulas, particularly when they involve several exposure levels, or confounding factors. METHODS/RESULTS: A heuristic approach, coupled with pictorial representations, is offered to help understand and interconnect the structures behind the Levin and Miettinen formulas. The pictorial representation shows how to deal correctly with several exposure levels, and why a commonly used approach is incorrect. Correct and incorrect approaches are also presented for situations where estimates must be aggregated over strata of a confounding factor.
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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 | 0.015 | 0.079 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.012 | 0.003 |
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".