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1

Grouse, Lawrence. "Post hoc ergo propter hoc." Journal of Thoracic Disease 8, no. 7 (2016): E511—E512. http://dx.doi.org/10.21037/jtd.2016.04.49.

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2

Costello, E. Jane. "Post Hoc, Ergo Propter Hoc." American Journal of Psychiatry 174, no. 4 (2017): 305–6. http://dx.doi.org/10.1176/appi.ajp.2016.16111320.

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3

Hoyt, David B. "Post hoc ergo propter hoc." Journal of Trauma and Acute Care Surgery 74, no. 1 (2013): 8–16. http://dx.doi.org/10.1097/ta.0b013e31827dc6d3.

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4

Kassirer, Jerome P., and Richard I. Kopelman. "Post Hoc, Ergo Propter Hoc." Hospital Practice 22, no. 7 (1987): 69–73. http://dx.doi.org/10.1080/21548331.1987.11703268.

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5

North, Richard B. "Post Hoc Ergo Propter Hoc?" Neuromodulation: Technology at the Neural Interface 14, no. 5 (2011): 485. http://dx.doi.org/10.1111/j.1525-1403.2011.00401.x.

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6

Bullock, John D. "Post Hoc, Ergo Propter Hoc." Survey of Ophthalmology 45, no. 4 (2001): 355–57. http://dx.doi.org/10.1016/s0039-6257(00)00193-4.

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7

Srinivas, Titte R., Bing Ho, Joseph Kang, and Bruce Kaplan. "Post Hoc Analyses." Transplantation 99, no. 1 (2015): 17–20. http://dx.doi.org/10.1097/tp.0000000000000581.

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8

Bababekov, Yanik J., and David C. Chang. "Post Hoc Power." Annals of Surgery 269, no. 1 (2019): e11-e12. http://dx.doi.org/10.1097/sla.0000000000002914.

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9

Konjikušić, Snežana, Slađana Starčević, and Saša Mašić. "Post Hoc Analysis of Serbian hotel ratings." Industrija 47, no. 3 (2019): 7–22. http://dx.doi.org/10.5937/industrija47-22081.

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10

Curran-Everett, Douglas, and Henry Milgrom. "Post-hoc data analysis." Current Opinion in Allergy and Clinical Immunology 13, no. 3 (2013): 223–24. http://dx.doi.org/10.1097/aci.0b013e3283609831.

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11

Gillett, Raphael. "Post hoc power analysis." Journal of Applied Psychology 79, no. 5 (1994): 783–85. http://dx.doi.org/10.1037/0021-9010.79.5.783.

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12

Plate, Joost D. J., Alicia S. Borggreve, Richard van Hillegersberg, and Linda M. Peelen. "Post Hoc Power Calculation." Annals of Surgery 269, no. 1 (2019): e11. http://dx.doi.org/10.1097/sla.0000000000002910.

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13

Wallace, David K., and Michele Melia. "Post hoc Power Calculations." Ophthalmology 115, no. 11 (2008): 2098. http://dx.doi.org/10.1016/j.ophtha.2008.06.005.

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14

Sandborn, W., P. Rutgeerts, W. Reinisch, et al. "A post-hoc analysis." Inflammatory Bowel Diseases 17, suppl_1 (2011): S6. http://dx.doi.org/10.1093/ibd/17.supplement1.s6a.

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15

Raschke, Robert A. "Post Hoc Subgroup Analysis." Chest 145, no. 2 (2014): 435. http://dx.doi.org/10.1378/chest.13-2441.

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16

Ferreira, David, and Nicolas Meyer. "Post Hoc Bayesian Analyses." JAMA 321, no. 16 (2019): 1632. http://dx.doi.org/10.1001/jama.2019.1194.

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17

Aberegg, Scott K. "Post Hoc Bayesian Analyses." JAMA 321, no. 16 (2019): 1631. http://dx.doi.org/10.1001/jama.2019.1198.

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18

LeMaire, Scott A. "A Post Hoc Discussion About Post Hoc Power: Divergent Viewpoints on Controversial Methodology." Journal of Surgical Research 259 (March 2021): A1—A2. http://dx.doi.org/10.1016/j.jss.2021.01.002.

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19

Summers, Jesse S. "Post hoc ergo propter hoc: some benefits of rationalization." Philosophical Explorations 20, sup1 (2017): 21–36. http://dx.doi.org/10.1080/13869795.2017.1287292.

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20

Edmeads, John. "Headache and Head Injury...Post Hoc, or Propter Hoc?" Headache: The Journal of Head and Face Pain 28, no. 3 (1988): 228a—229. http://dx.doi.org/10.1111/j.1526-4610.1988.hed2803228a.x.

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21

Romney, M. G., C. Lowe, V. Leung, and E. Lloyd-Smith. "Nasal photodisinfection and chlorhexidine: post hoc ergo propter hoc?" Journal of Hospital Infection 90, no. 1 (2015): 83–84. http://dx.doi.org/10.1016/j.jhin.2015.01.022.

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22

James, Michelle A. "Insufficient Post Hoc Statistical Power." Journal of Bone and Joint Surgery 100, no. 14 (2018): e98. http://dx.doi.org/10.2106/jbjs.18.00256.

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23

de Roux-Serratrice, C., J. Serratrice, P. Champsaur, et al. "Vous avez dit post-hoc ?…" La Revue de Médecine Interne 26 (July 2005): S282—S283. http://dx.doi.org/10.1016/s0248-8663(05)81285-8.

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24

Friston, Karl, and Will Penny. "Post hoc Bayesian model selection." NeuroImage 56, no. 4 (2011): 2089–99. http://dx.doi.org/10.1016/j.neuroimage.2011.03.062.

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25

Uhlmann, Eric Luis. "Post hoc rationalism in science." Behavioral and Brain Sciences 34, no. 4 (2011): 214. http://dx.doi.org/10.1017/s0140525x11000410.

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AbstractIn advocating Bayesian Enlightenment as a solution to Bayesian Fundamentalism, Jones & Love (J&L) rule out a broader critique of rationalist approaches to cognition. However, Bayesian Fundamentalism is merely one example of the more general phenomenon of Rationalist Fundamentalism: the tendency to characterize human judgments as rational and optimal in a post hoc manner, after the empirical data are already known.
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26

Goligher, Ewan C., George Tomlinson, and Arthur S. Slutsky. "Post Hoc Bayesian Analyses—Reply." JAMA 321, no. 16 (2019): 1632. http://dx.doi.org/10.1001/jama.2019.1202.

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27

Borras, L., C. Damsa, P. Vidailhet, A. Andreoli, and F. Bianchi De Micheli. "Schizophrénies et traumatisme cranio-cérébral : post hoc, ergo propter hoc ?" Annales Médico-psychologiques, revue psychiatrique 162, no. 10 (2004): 788–93. http://dx.doi.org/10.1016/j.amp.2004.08.007.

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28

SARI, Halil İbrahim. "Testing Multistage Testing Configurations: Post-Hoc vs. Hybrid Simulations." International Journal of Psychology and Educational Studies 7, no. 1 (2020): 27–37. http://dx.doi.org/10.17220/ijpes.2020.01.003.

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29

Magini, Marina, Francesca Ingravallo, and Alberto Cicognani. "Danni cerebrali neonatali: la fallacia del post hoc ergo propter hoc." Pratica Medica & Aspetti Legali 1, no. 2 (2007): 71–76. http://dx.doi.org/10.7175/pmeal.v1i2.416.

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30

Finucane, Thomas E. "Post hoc ergo propter hoc: Complications and Death after Gastrostomy Placement." Journal of the American Medical Directors Association 13, no. 3 (2012): 197–98. http://dx.doi.org/10.1016/j.jamda.2011.10.003.

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31

Facharztmagazine, Redaktion. "Inotuzumab Ozogamicin: Neue Post-hoc-Daten." InFo Hämatologie + Onkologie 24, no. 1-2 (2021): 64. http://dx.doi.org/10.1007/s15004-021-8537-6.

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32

Dellinger, R. Phillip. "Post hoc analyses in sepsis trials." Critical Care Medicine 24, no. 5 (1996): 727–29. http://dx.doi.org/10.1097/00003246-199605000-00001.

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33

Redelmeier, Donald A., and Eldar Shafir. "Post Hoc Bias in Treatment Decisions." JAMA Network Open 7, no. 9 (2024): e2431123. http://dx.doi.org/10.1001/jamanetworkopen.2024.31123.

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ImportanceA goal of health care is to reduce symptoms and improve health status, whereas continuing dubious treatments can contribute to complacency, discourage the search for alternatives, and lead to shortfalls in care.ObjectiveTo test a potential bias in intuitive reasoning following a marginal improvement in symptoms after a dubious treatment (post hoc bias).Design, Setting, and ParticipantsSurveys eliciting treatment recommendations for hypothetical patients were sent to community members throughout North America recruited via an online survey platform in the early winter months of 2023 and 2024 and presented to health care professionals (pharmacists who were approached in person using a secret shopper technique) in the summer months of 2023.ExposureRespondents received randomized versions of surveys that differed according to whether vague symptoms improved or remained unchanged after a dubious treatment.Main Outcomes and MeasuresThe primary outcome was a recommendation to continue treatment.ResultsIn total, 1497 community members (mean [SD] age, 38.1 [12.5] years; 663 female [55.3%]) and 100 health care professionals were contacted. The first scenario described a patient with a sore throat who took unprescribed antibiotics; respondents were more likely to continue antibiotics after initial treatment if there was a marginal improvement in symptoms vs when symptoms remained unchanged (67 of 150 respondents [45%] vs 25 of respondents [17%]; odds ratio [OR], 3.98 [95% CI, 2.33-6.78]; P < .001). Another scenario described a patient with wrist pain who wore a copper bracelet; respondents were more likely to continue wearing the copper bracelet after initial care was followed by a marginal improvement in symptoms vs when symptoms remained unchanged (78 of 100 respondents [78%] vs 25 of 99 respondents [25%]; OR, 16.19 [95% CI, 5.32-19.52]; P < .001). A third scenario described a patient with fatigue who took unprescribed vitamin B12; respondents were more likely to continue taking vitamin B12 when initial treatment was followed by a marginal improvement in symptoms vs when symptoms remained unchanged (80 of 100 respondents [80%] vs 33 of 100 respondents [33%]; OR, 7.91 [95% CI, 4.18-14.97]; P < .001). Four further scenarios involving dubious treatments found similar results, including when tested on health care professionals.Conclusions and RelevanceIn this study of clinical scenarios, a marginal improvement in symptoms led patients to continue a dubious and sometimes costly treatment, suggesting that clinicians should caution patients against post hoc bias.
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34

Hui, Katrina. "The Illusion of Post Hoc Autonomy." AJOB Neuroscience 4, no. 4 (2013): 57–58. http://dx.doi.org/10.1080/21507740.2013.824043.

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35

DiSesa, Verdi J. "Giving post hoc a good name." Journal of Thoracic and Cardiovascular Surgery 152, no. 1 (2016): 277. http://dx.doi.org/10.1016/j.jtcvs.2016.03.037.

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36

Mullins, C. "Subgroup analysis versus post-hoc analysis." Clinical Therapeutics 23, no. 7 (2001): 1060. http://dx.doi.org/10.1016/s0149-2918(01)80091-6.

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37

Fogel, Joshua. "Post Hoc Power Analysis—Another View." Pharmacotherapy 21, no. 9 (2001): 1150. http://dx.doi.org/10.1592/phco.21.13.1150.34621.

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38

MARTENS, P. "Cola and dioxine: post hoc expertise." European Journal of Emergency Medicine 7, no. 2 (2000): 159. http://dx.doi.org/10.1097/00063110-200006000-00014.

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39

Carmichael, Zachariah, and Walter J. Scheirer. "Unfooling Perturbation-Based Post Hoc Explainers." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 6 (2023): 6925–34. http://dx.doi.org/10.1609/aaai.v37i6.25847.

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Monumental advancements in artificial intelligence (AI) have lured the interest of doctors, lenders, judges, and other professionals. While these high-stakes decision-makers are optimistic about the technology, those familiar with AI systems are wary about the lack of transparency of its decision-making processes. Perturbation-based post hoc explainers offer a model agnostic means of interpreting these systems while only requiring query-level access. However, recent work demonstrates that these explainers can be fooled adversarially. This discovery has adverse implications for auditors, regulators, and other sentinels. With this in mind, several natural questions arise - how can we audit these black box systems? And how can we ascertain that the auditee is complying with the audit in good faith? In this work, we rigorously formalize this problem and devise a defense against adversarial attacks on perturbation-based explainers. We propose algorithms for the detection (CAD-Detect) and defense (CAD-Defend) of these attacks, which are aided by our novel conditional anomaly detection approach, KNN-CAD. We demonstrate that our approach successfully detects whether a black box system adversarially conceals its decision-making process and mitigates the adversarial attack on real-world data for the prevalent explainers, LIME and SHAP. The code for this work is available at https://github.com/craymichael/unfooling.
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40

DiMaio, J. Michael, Kyle A. McCullough, and R. Jay Widmer. "A Post Hoc Analysis of ISCHEMIA." Journal of the American College of Cardiology 83, no. 5 (2024): 559–61. http://dx.doi.org/10.1016/j.jacc.2023.11.027.

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41

Snežana, MATIĆ-KEKIĆ, SAVIN Lazar, and DEDOVIĆ Nebojša. "HARVESTING OPTIMISATION AND POST-HOC ANALISYS." Contemporary Agriculture (2015) 64, no. 1-2 (2015): 30–37. https://doi.org/10.5281/zenodo.5810183.

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formulated model of linear programming, which minimizes the total harvest and transport time for the observed farm company, is necessary for achieving the maximum profit from combine harvester rentals. Interdependent field operations have been mutually connected. The calculated optimal operating time showed that more human labour and machinery were used than necessary. This was later used for the post-hoc analysis which determined the profit from the combine harvester rentals for the observed period.
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42

Baronti, Arianna, Francesco Gentile, Alice Chiara Manetti, et al. "Myocardial Infarction Following COVID-19 Vaccine Administration: Post Hoc, Ergo Propter Hoc?" Viruses 14, no. 8 (2022): 1644. http://dx.doi.org/10.3390/v14081644.

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Vaccination against coronavirus disease 2019 (COVID-19) is the safest and most effective strategy for controlling the pandemic. However, some cases of acute cardiac events following vaccine administration have been reported, including myocarditis and myocardial infarction (MI). While post-vaccine myocarditis has been widely discussed, information about post-vaccine MI is scarce and heterogenous, often lacking in histopathological and pathophysiological details. We hereby present five cases (four men, mean age 64 years, range 50–76) of sudden death secondary to MI and tightly temporally related to COVID-19 vaccination. In each case, comprehensive macro- and microscopic pathological analyses were performed, including post-mortem cardiac magnetic resonance, to ascertain the cause of death. To investigate the pathophysiological determinants of MI, toxicological and tryptase analyses were performed, yielding negative results, while the absence of anti-platelet factor 4 antibodies ruled out vaccine-induced thrombotic thrombocytopenia. Finally, genetic testing disclosed that all subjects were carriers of at least one pro-thrombotic mutation. Although the presented cases do not allow us to establish any causative relation, they should foster further research to investigate the possible link between COVID-19 vaccination, pro-thrombotic genotypes, and acute cardiovascular events.
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43

Brodtmann, A. "Vascular risk, depression, and stroke: Post hoc ergo propter hoc ... or not." Neurology 83, no. 19 (2014): 1688–89. http://dx.doi.org/10.1212/wnl.0000000000000968.

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44

Hays, Fred H., and Bruce B. Morgan. "LOCAL MARKET EFFECTS OF FINANCIAL SERVICES DEREGULATION: POST HOC ERGO PROPTER HOC?" Policy Studies Journal 16, no. 1 (1987): 116–33. http://dx.doi.org/10.1111/j.1541-0072.1987.tb00770.x.

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45

Retzlaff, Carl O., Alessa Angerschmid, Anna Saranti, et al. "Post-hoc vs ante-hoc explanations: xAI design guidelines for data scientists." Cognitive Systems Research 86 (August 2024): 101243. http://dx.doi.org/10.1016/j.cogsys.2024.101243.

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46

Juarros-Basterretxea, Joel, Gema Aonso-Diego, Álvaro Postigo, Pelayo Montes-Álvarez, Álvaro Menéndez-Aller, and Eduardo García-Cueto. "Post-hoc tests in one-way ANOVA: The case for normal distribution." Methodology 20, no. 2 (2024): 84–99. http://dx.doi.org/10.5964/meth.11721.

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When one-way ANOVA is statistically significant, a multiple comparison problem arises, hence post-hoc tests are needed to elucidate between which groups significant differences are found. Different post-hoc tests have been proposed for each situation regarding heteroscedasticity and sample size groups. This study aims to compare the Type I error (α) rate of 10 post-hoc tests in four different conditions based on heteroscedasticity and balance between-group sample size. A Montecarlo simulation study was carried out on a total of 28 data sets, with 10,000 resamples in each, distributed through four conditions. One-way ANOVA tests and post-hoc tests were conducted to estimate the α rate at a 95% confidence level. The percentage of times the null hypothesis was falsely refused is used to compare the tests. Three out of four conditions demonstrated considerable variability among sample sizes. However, the best post-hoc test in the second condition (heteroscedastic and balance group) did not depend on simple size. In some cases, inappropriate post-hoc tests were more accurate. Homoscedasticity and balance between-group sample size should be considered for appropriate post-hoc test selection.
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47

Mahajan, Anjali. "Post hoc tests in analysis of variance." Indian Journal of Occupational and Environmental Medicine 20, no. 2 (2016): 121. http://dx.doi.org/10.4103/0019-5278.197552.

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48

Seipp, Jendrik, Thomas Keller, and Malte Helmert. "Saturated Post-hoc Optimization for Classical Planning." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 13 (2021): 11947–53. http://dx.doi.org/10.1609/aaai.v35i13.17419.

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Saturated cost partitioning and post-hoc optimization are two powerful cost partitioning algorithms for optimal classical planning. The main idea of saturated cost partitioning is to give each considered heuristic only the fraction of remaining operator costs that it needs to prove its estimates. We show how to apply this idea to post-hoc optimization and obtain a heuristic that dominates the original both in theory and on the IPC benchmarks.
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49

van der Valk, F. M., D. F. van Wijk, and E. S. G. Stroes. "Serendipity of post-hoc surrogate marker research." European Heart Journal 33, no. 23 (2012): 2897–98. http://dx.doi.org/10.1093/eurheartj/ehs183.

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50

Rosa, M. J., K. Friston, and W. Penny. "Post-hoc selection of dynamic causal models." Journal of Neuroscience Methods 208, no. 1 (2012): 66–78. http://dx.doi.org/10.1016/j.jneumeth.2012.04.013.

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