# Supplementary analyses

Generated 2026-07-31 04:42. Source: authoritative Crossref GitLab CSV.
Retractions 66013; machine-attributed 9161; comparison 56852.

## Issue 4. Regime analysis restricted by minimum possible follow-up
Snapshot date 2026-07-29. A minimum follow-up of k months keeps only articles published on or before
the snapshot date minus k months, so every retained article had at least k months in which it could have
been investigated and retracted.

| Cut-point | Min follow-up (months) | n before | n on or after | Paper mill % before | Paper mill % on or after (95% CI) | Median lag before | Median lag on or after |
|---|---|---|---|---|---|---|---|
| 2022-11-30 | 0 | 8194 | 967 | 71.3 | 69.6 (66.62-72.41) | 501 | 402 |
| 2022-11-30 | 12 | 8194 | 955 | 71.3 | 70.47 (67.5-73.28) | 501 | 405 |
| 2022-11-30 | 18 | 8194 | 949 | 71.3 | 70.92 (67.95-73.72) | 501 | 406 |
| 2022-11-30 | 24 | 8194 | 797 | 71.3 | 84.32 (81.63-86.68) | 501 | 456 |
| 2023-07-01 | 0 | 8526 | 635 | 71.89 | 60.79 (56.94-64.51) | 502 | 390 |
| 2023-07-01 | 12 | 8526 | 623 | 71.89 | 61.96 (58.08-65.69) | 502 | 397 |
| 2023-07-01 | 18 | 8526 | 617 | 71.89 | 62.56 (58.68-66.29) | 502 | 397 |
| 2023-07-01 | 24 | 8526 | 465 | 71.89 | 82.8 (79.1-85.95) | 502 | 442 |
| 2024-01-01 | 0 | 8766 | 395 | 72.31 | 44.56 (39.73-49.49) | 503 | 283 |
| 2024-01-01 | 12 | 8766 | 383 | 72.31 | 45.95 (41.03-50.96) | 503 | 298 |
| 2024-01-01 | 18 | 8766 | 377 | 72.31 | 46.68 (41.71-51.73) | 503 | 298 |
| 2024-01-01 | 24 | 8766 | 225 | 72.31 | 77.78 (71.9-82.72) | 503 | 369 |
| 2024-07-01 | 0 | 8984 | 177 | 72.51 | 0.56 (0.1-3.13) | 497 | 137 |
| 2024-07-01 | 12 | 8984 | 165 | 72.51 | 0.61 (0.11-3.35) | 497 | 137 |
| 2024-07-01 | 18 | 8984 | 159 | 72.51 | 0.63 (0.11-3.48) | 497 | 136 |
| 2024-07-01 | 24 | 8984 | 7 | 72.51 | 0 (0-35.43) | 497 | 399 |

## Issue 5. Expanded generative-AI terminology search
Word-boundary regular expressions applied to the Title and Notes fields of all 66013 retractions.
Distinct records matching at least one term: **716**, of which **318** are machine-attributed.
Every match is listed in tables\t22_ai_term_matches.csv with a snippet and two blank columns for manual adjudication.

| Term | Records matching |
|---|---|
| ChatGPT | 8 |
| GPT (word boundary) | 1 |
| LLM (word boundary) | 0 |
| large language model | 3 |
| language model | 5 |
| generative AI | 0 |
| AI-generated | 1 |
| artificial intelligence | 700 |
| Bard / Gemini / Copilot / Claude | 4 |
| SCIgen | 0 |
| tortured phrase | 0 |
| paraphrasing tool | 0 |

Note: the Notes field is not the full text of the retraction notice, so this is a search of available
database metadata, not of notice texts.

## Issue 6. Mantel-Haenszel adjusted analysis of paper-mill co-coding
Strata: retraction year x publisher group (six largest publishers plus Other). Contributing strata: 23.

| Estimate | Value |
|---|---|
| Crude risk ratio | 7.783 |
| Mantel-Haenszel adjusted risk ratio | 1.431 |
| Mantel-Haenszel adjusted odds ratio (95% CI) | 2.311 (2.15-2.484) |
| Cochran Q for heterogeneity (df) | 248.2 (7) |

Q far exceeding df indicates the association differs across strata, so the adjusted summary should not be read as a common effect.

## Issue 7. Notice-level aggregation
Every retraction notice is summarised by the median, minimum and maximum lag of its constituent articles
and by the proportion carrying a paper-mill flag, rather than by selecting one arbitrary record.

| Measure | Value |
|---|---|
| Machine-attributed notices | 8127 |
| Comparison notices | 53010 |
| Machine notices covering more than one article | 2 |
| Median articles per multi-article notice | 518 |
| Median within-notice lag spread (max minus min), days | 4210 |
| Median of notice-level median lags, machine | 475 |
| Median of notice-level median lags, comparison | 471 |
| Location, notice level | delta 0.0351, z 5.099, p 3.4e-7 |
| Dispersion, notice level | MAD 214.1 vs 767.1, ratio 0.279, t -88.142, p < 1e-15 |

