Traumatic appendicitis is probably not real: an illustrative analysis of coincidental occurrences in nature
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* David N Naumann
* Tom Barker

## Abstract

There have been sporadic case reports describing ‘traumatic appendicitis’ (acute appendicitis occurring following injury) for almost a hundred years. Although this might seem to be an interesting and rare diagnosis for the journal reader, both appendicitis and trauma are very common, and their occurrence together may only give the illusion of causality. Indeed, such a diagnosis may not even exist. We provide an illustration of the statistical phenomenon of coincidental occurrences in nature using a computer simulation of traumatic appendicitis in the UK population. In our simulation, there are enough cases of traumatic appendicitis every 2 years to 3 years to account for the entire global literature on the topic. We suggest that unless there is a credible pathological process reported with demonstrable causality, further case reports of traumatic appendicitis need to have robust justification.

*   Appendicitis
*   Models, Statistical
*   Multiple Trauma
*   abdominal injuries

According to popular folklore, the famous magician Harry Houdini died following a perforated appendicitis—supposedly from a punch to the abdomen. Traumatic appendicitis is a recurring topic in medical literature, described in the literature as far ago as 1927.1 More recently, case reports every few years describe traumatic appendicitis following a diverse range of accidents and misadventures from cliff dives to camel kicks, as illustrated in table 1. Although ‘traumatic appendicitis’ might be an appealing diagnosis to beguile the surgical journal reader, both appendicitis and trauma are very common and will therefore occur in a population enough to give the illusion of causality. This logical fallacy of event A occurring before event B and therefore being the cause of event B is referred as post hoc ergo propter hoc (literally ‘after this, therefore because of this’).

View this table:
[Table 1](http://tsaco.bmj.com/content/8/1/e001093/T1)

Table 1 
Selection of English language case reports in the 20th century that describe ‘traumatic appendicitis’

Here we provide an illustration of the statistical phenomenon of coincidental occurrences in nature using traumatic appendicitis in the UK population. A computer model programmed using Perl V. 5.32 ([https://www.perl.org](https://www.perl.org)) was used to simulate the number of appendicitis and traumatic events and their temporal relationship in the UK population in a year. The model assumes a UK population of 67 100 000 people2 and a rate of appendicitis of 151 per 100 000.3 The incidence of trauma, especially of a trivial and reported nature, is unknown, so we ran the model for an incidence of trauma of 1:1 (ie, 1 trauma in 1 year), and subsequently in ratios of 1:10, 1:100, 1:1000, and 1:10 000.

## Model methodology

For each individual in the model, a random number between 1 and 100 000 was generated, and if that number was ≤151 then that individual had appendicitis in that year. Similarly, to test for trauma, a random number was generated between one and the trauma probability (1:1, 1:10, 1:100, 1:1000, and 1:10 000). If the number was one then that individual had a traumatic event that year. For individuals with both appendicitis and trauma events in the same year, two random numbers between 1 and 365 were generated (simulating the day of the year the appendicitis and the trauma occurred). If the day of the trauma fell within 3 days before the appendicitis in that year, that case was counted as a case of traumatic appendicitis. For individuals with appendicitis in the first 3 days of the year but no trauma before that, a further test was performed for trauma in that individual on the previous year using the methodology described earlier. A case of traumatic appendicitis was counted if the simulation produced a trauma at the end of the previous year with in 3 days of the appendicitis in the subsequent year. This model was then run 1000 times to produce summary statistics. The code used for the model is shown in online supplemental file 1.

### Supplementary data

[[tsaco-2023-001093supp001.pdf]](pending:yes)

## Model interpretation

Summary statistics for the data produced by the model are shown in table 2. At a trauma frequency of 1:10 000, there were 10.8% of runs that produced cases of traumatic appendicitis, and for a trauma frequency of 1:1000, it was 67.5% of runs. The incidence of major trauma and blunt abdominal trauma at the major trauma centres in one region of the UK has been reported as between 5401/6 000 000 (approximately 1 in 1,000) and 2793/6 000 000 (approximately 1 in 2000),4 which is within the range of the modelled statistics. However, given the trivial nature of some of the injuries reported in some cases reports, the relevant trauma frequency can be reasonably assumed to be much higher. At a trauma frequency of 1:100, the UK population alone would randomly generate enough cases of traumatic appendicitis every 2 years to 3 years to account for the entire global literature on this topic.

View this table:
[Table 2](http://tsaco.bmj.com/content/8/1/e001093/T2)

Table 2 
Predictive model of the number of expected diagnoses of ‘traumatic appendicitis’ according to the incidence of trauma per year in the UK and 1000 runs of the computer model.

Our model also demonstrates another common cognitive bias: the clustering illusion.5 Looking at the data for the 1:10 000 trauma frequency, results demonstrated that 89.2% of runs generate no cases of traumatic appendicitis, but in 10.8% of runs, there are clusters of up to three cases. Clustering is a normal phenomenon in small samples of random and pseudorandom data but is frequently interpreted to have significance due to a tendency for us to see patterns in random events. The prevalence, as well as a lack of awareness of these fallacies, is more relevant than ever in the data era and the age of the internet, and has been brought into sharp focus with COVID-19 and the relationship between vaccinations and potential adverse reactions.

While our model cannot not disprove the existence of traumatic appendicitis, it provides a plausible and demonstrable explanation for the phenomenon and an illustrative example of the post hoc fallacy. Unless a robust argument can be made for a legitimate pathological process, with demonstration of causality, justification is required for any further case reports about traumatic appendicitis. Those interested in scientific enquiry may wish to avoid perpetuation of logical fallacies in a world that needs more clarity, not less.

## Ethics statements

### Patient consent for publication

Not applicable.

### Ethics approval

Not applicable.

## Footnotes

*   Contributors TB designed and ran the computer model. DNN and TB wrote the manuscript and agreed on the final version.

*   Funding Open access funding was provided by the University of Birmingham.

*   Competing interests None declared.

*   Provenance and peer review Not commissioned; externally peer reviewed.

*   Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.

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