Population attributable fraction: comparison of two mathematical procedures to estimate the annual attributable number of deaths
Bibliographic record
Abstract
OBJECTIVE: The purpose of this paper was to compare two mathematical procedures to estimate the annual attributable number of deaths (the Allison et al procedure and the Mokdad et al procedure), and derive a new procedure that combines the best aspects of both procedures. The new procedure calculates attributable number of deaths along a continuum (i.e. for each unit of exposure), and allows for one or more neutral (neither exposed nor nonexposed) exposure categories. METHODS: Mathematical derivations and real datasets were used to demonstrate the theoretical relationship and practical differences between the two procedures. Results of the comparison were used to develop a new procedure that combines the best features of both. FINDINGS: The Allison procedure is complex because it directly estimates the number of attributable deaths. This necessitates calculation of probabilities of death. The Mokdad procedure is simpler because it estimates the number of attributable deaths indirectly through population attributable fractions. The probabilities of death cancel out in the numerator and denominator of the fractions. However, the Mokdad procedure is not applicable when a neutral exposure category exists. CONCLUSION: By combining the innovation of the Allison procedure (allowing for a neutral category) and the simplicity of the Mokdad procedure (using population attributable fractions), this paper proposes a new procedure to calculate attributable numbers of death.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.132 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.008 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".