Second-hop exposure to retracted literature in 600 recent papers
Direct citation of retracted work is rare and well studied. Citation of work that itself cites retracted work is neither. Two independent random samples of 300 papers each — 600 in total, drawn with no selection on citation behaviour — were traced through both hops.
Sample
| Exposure | Seed 42 | Seed 7 | n | % of 600 | 95% CI (Wilson) |
|---|---|---|---|---|---|
| Level 1 — cites retracted work | 2 | 6 | 8 | 1.3 | 0.7 – 2.6 |
| Level 2 — cites a paper that does | 52 | 59 | 111 | 18.5 | 15.6 – 21.8 |
| Depends on work already retracted when cited | 25 | 28 | 53 | 8.8 | 6.8 – 11.4 |
| No flagged dependency | 248 | 241 | 489 | 81.5 | 78.2 – 84.4 |
Rows are not mutually exclusive — a paper can be exposed at both levels, and the already-retracted row is a subset of the two above it. Intervals are Wilson score intervals computed from the counts.
The two samples agree to within two percentage points on both headline rows. The direct-citation count moved from 2 to 6 between them, which is why it is reported as a count rather than a rate: at that magnitude a single paper swings the percentage.
Method
Two samples of 300 works were drawn from OpenAlex with its sample parameter under seeds 42 and 7, filtered to from_publication_date:2024-01-01,type:article,has_doi:true — journal articles with a DOI, published since January 2024. Nothing about how a paper cites entered the selection.
For each paper, its referenced_works were resolved from OpenAlex, then the reference lists of those references. Both sets were intersected with the Retraction Watch database, published openly by Crossref, matched by DOI. Retraction Watch's RetractionNature field separates retractions from expressions of concern and corrections; reinstatements are excluded outright.
Timing compares the citing paper's publication date against the notice date. A citation made more than 90 days after the notice is reported as post-retraction; within 90 days it is reported as ambiguous rather than assigned, because publication lag means the authors may not have been able to know. Retraction notices, duplicate preprint/published versions and self-citations are removed before counting, and each exclusion is reported in every response.
Score definition
Each hit is weighted: 12 for a direct citation, 4 for an indirect one; multiplied by 0.35 if the notice is a concern rather than a retraction; multiplied by 3.0 if the citation postdates the notice, or 1.3 if it falls inside the 90-day window. The total is divided by the number of references, floored at 10 so a short bibliography with one hit is not flattered by a small denominator, then scaled and capped at 100. It is a sort key for triage, not a measurement, and it is published so it can be argued with.
Caveats
- Exposure is not contamination. A retracted work in the chain may be cited in passing, or in a section irrelevant to the claim you care about — including papers citing a retraction in order to criticise it. GhostCite reads metadata, never full text, so it cannot tell the difference.
- Coverage bounds everything. 62,030 of 62,389 registry DOIs resolve to an OpenAlex work, and second-hop reference lists exist only where OpenAlex has them. Retraction Watch is curated by humans and lags real retractions. Every number here is a floor.
- Notice dates are uneven. Where either the notice date or the citing paper's date is missing, the hit is reported as unknown timing rather than being assigned to a side of the line.
- The score is a heuristic. It weights severity and timing on a scale we chose.
- A clean result is not evidence that a paper is sound. Absence of a finding is not a finding of absence.
Data & replication
Per-paper output for both samples is committed under data/findings, and the pooled figures above are regenerated from those two files by api/scripts/pool_findings.py. The score formula and every exclusion rule are set out in docs/methodology.md. Both source datasets are CC0.