# Do retracted papers keep being cited? — results

Computed by `analyse.py` from `~/data/retraction-citations/`. The rule was sealed as `rule.retraction-citations` at 2026-09-20T19:20:14Z, before any of this was fetched.

## The sample

- retracted papers: **150**
- control papers (same journal, same year): **435**
- retracted papers with an empty pre-window, dropped by the rule: **29** of 150
- control papers likewise dropped: **128** of 435

## The sealed estimator, and why it carries nothing

The rule sealed an average of per-stratum ratios. Its null control — arm labels shuffled inside each stratum, 200 times, so that they carry no information whatever — returns a mean RR of **1.2013** (range 0.868 to 1.987) against a required band of 0.90 to 1.11. **FAIL.** A ratio is convex in its denominator, so a stratum whose control arm holds a handful of pre-window citations contributes a ratio biased upward, and averaging them does not cancel it. The sealed statistic could not have measured what the seal said it measured, whatever the data had been, and it is VOID.

## The replacement estimator, specified blind

`rr_mh`, the textbook Mantel-Haenszel rate ratio, which pools the numerators and denominators across strata and never divides inside one. It was written after the failure above and before any real number had been computed: the only quantity I had seen was the shuffled one. Both controls are re-run against it, and if either fails there is no verdict.

**Null control** — mean RR **0.9957** (range 0.714 to 1.411), band 0.90 to 1.11: **PASS**.

**Positive control** — half the control arm thinned by 50 %, over 43 strata: RR **0.4904** (95 % CI 0.439 to 0.556), band 0.42 to 0.58: **PASS**.

**Floor.** The positive control's interval is 0.117 wide, so this sample cannot distinguish an effect smaller than about 6 % from no effect at all.

## The estimate

Strata used: **52**, holding **76.5 %** of the retracted pre-window citation mass; the rest sat in strata with no control and was dropped.

**RR = 0.4345** (95 % CI 0.368 to 0.498).

**KILLED.** Retraction at least halves the citation rate.

The sealed estimator, printed as a measurement scored by nothing: **0.5106**.

## The plain count, which carries no verdict

- retracted papers collecting at least one citation in the three years after the retraction year: **101 of 150 (67.3 %)**
- median post-window citations, retracted: **2**; controls: **3**
- total citations to these 150 retracted papers in the three years after their retraction: **928**
- of all citations to the retracted papers, OpenCitations flags **155** as author self-citations (5.6 %). Unregistered: the seal said this could not be seen, and the new source sees it.

## Per stratum

| publication year | pre-window citations | retracted | controls | post/pre retracted | post/pre control |
|---|---|---|---|---|---|
| 1998 | 1-2 | 1 | 1 | 0.000 | 0.000 |
| 1998 | 3-5 | 1 | 1 | 1.000 | 0.000 |
| 2001 | 6-10 | 1 | 2 | 0.429 | 0.154 |
| 2002 | 1-2 | 2 | 1 | 0.500 | 1.000 |
| 2004 | 6-10 | 1 | 2 | 0.111 | 1.000 |
| 2006 | 1-2 | 1 | 2 | 0.500 | 0.500 |
| 2006 | 11-20 | 1 | 1 | 0.500 | 0.833 |
| 2006 | 21-50 | 1 | 2 | 1.205 | 0.792 |
| 2006 | 6-10 | 1 | 2 | 0.200 | 0.833 |
| 2007 | 6-10 | 1 | 1 | 0.444 | 0.333 |
| 2008 | 1-2 | 1 | 2 | 3.000 | 2.500 |
| 2008 | 21-50 | 2 | 2 | 0.469 | 0.867 |
| 2008 | 3-5 | 2 | 1 | 0.375 | 0.000 |
| 2008 | 6-10 | 1 | 10 | 0.700 | 0.870 |
| 2009 | 21-50 | 1 | 1 | 0.615 | 0.478 |
| 2009 | 6-10 | 2 | 2 | 0.417 | 0.800 |
| 2010 | 1-2 | 2 | 4 | 1.000 | 1.333 |
| 2010 | 11-20 | 1 | 1 | 0.545 | 1.083 |
| 2010 | 3-5 | 3 | 3 | 0.417 | 1.333 |
| 2010 | 6-10 | 3 | 9 | 0.571 | 1.065 |
| 2011 | 1-2 | 3 | 9 | 0.750 | 1.143 |
| 2011 | 11-20 | 5 | 7 | 0.261 | 0.782 |
| 2011 | 3-5 | 1 | 5 | 0.000 | 0.955 |
| 2011 | 6-10 | 2 | 5 | 0.263 | 1.048 |
| 2012 | 1-2 | 1 | 11 | 1.000 | 2.231 |
| 2012 | 11-20 | 3 | 10 | 0.450 | 0.710 |
| 2012 | 21-50 | 2 | 3 | 0.197 | 1.082 |
| 2012 | 3-5 | 2 | 7 | 1.000 | 1.423 |
| 2012 | 6-10 | 3 | 4 | 0.636 | 1.032 |
| 2013 | 1-2 | 3 | 10 | 1.250 | 1.364 |
| 2013 | 11-20 | 1 | 3 | 0.692 | 0.488 |
| 2013 | 21-50 | 2 | 2 | 0.377 | 1.418 |
| 2013 | 3-5 | 2 | 5 | 0.625 | 0.824 |
| 2013 | 6-10 | 5 | 2 | 0.211 | 0.438 |
| 2014 | 1-2 | 1 | 6 | 0.500 | 1.625 |
| 2014 | 11-20 | 2 | 5 | 0.200 | 0.528 |
| 2014 | 21-50 | 5 | 5 | 0.406 | 1.518 |
| 2014 | 3-5 | 2 | 10 | 0.571 | 0.842 |
| 2014 | 6-10 | 6 | 12 | 0.319 | 0.906 |
| 2015 | 1-2 | 3 | 12 | 0.333 | 1.133 |
| 2015 | 11-20 | 2 | 7 | 0.250 | 1.298 |
| 2015 | 21-50 | 3 | 9 | 0.473 | 0.947 |
| 2015 | 3-5 | 2 | 13 | 1.286 | 1.269 |
| 2015 | 6-10 | 5 | 8 | 0.541 | 1.429 |
| 2016 | 1-2 | 4 | 4 | 0.000 | 0.800 |
| 2016 | 11-20 | 1 | 4 | 0.263 | 0.828 |
| 2016 | 21-50 | 2 | 2 | 0.288 | 2.579 |
| 2016 | 6-10 | 2 | 5 | 0.600 | 1.216 |
| 2017 | 11-20 | 2 | 2 | 0.464 | 1.000 |
| 2017 | 21-50 | 3 | 3 | 0.464 | 0.568 |
| 2017 | 3-5 | 1 | 5 | 0.600 | 0.737 |
| 2017 | 6-10 | 3 | 5 | 0.583 | 0.848 |