{"paper_id":"600c7719-5905-4373-bd67-030f6ae10902","body_text":"p. 1 of all 74 \nCover page 1 \n 2 \nExploratory Data Analysis Recognizing Geometrical Patterns in Meta-analysis 3 \n 4 \nKeiichiro Kimoto, M.Sc.1, 2 *, Munekazu Yamakuchi, M.D., Ph.D.1, Kazunori Takenouchi, M.D., Ph.D. 1, 5 \nTeruto Hashiguchi, MD, Ph.D.1 6 \n 7 \n1 Department of Laboratory and Vascular Medicine, Kagoshima University Graduate School of Medical and 8 \nDental Sciences, 8-35-1 Sakuragaoka, Kagoshima 890-8520, Japan 9 \n2 Present Affiliation: External Advisor for Data Strategy Research Institute, Yokohama, Japan 10 \n 11 \n*Corresponding author: Keiichiro Kimoto 12 \nDepartment of Laboratory and Vascular Medicine, Kagoshima University Graduate School of Medical and 13 \nDental Sciences, 8-35-1 Sakuragaoka, Kagoshima 890-8520, Japan. 14 \nE-mail address: k1974142@kadai.jp 15 \nPhone: /Fax: +81-99-275-5437/+81-99-275-2629 16 \nWord count (text section): 2492 (summary text: 252, main text: 2240) 17 \n  18 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \nNOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.\n\n  p. 2 of all 74 \n 19 \nText 20 \nSummary text 21 \nHistorically, Sir Isaac Newton, with a great perspective of geometry, analysed an elliptical 22 \norbit derived from Kepler's primary astronomical data analysis, and the sir elicited the theory of 23 \ngravitation. Namely, secondary analysis with geometry was an essential step in physics. Then, with a 24 \ngeometrical perspective, a re-analysis of a chart in the figure is also practical in biomedicine? 25 \nNowadays, some image-checking AI detects research misconduct but not for useful, latent findings1. 26 \nTaking our concept one step further, we focused on a geometrical meaning of the confidence interval 27 \nerror bar. As an exploratory data analysis know-how in a figure of meta-regression analysis, we 28 \nconceived a method based on recognising geometrical patterns (layered hyperbolic shapes) suspected of 29 \noverlapping subgroups. Here we show the result that we applied our ideas to the traveller's thrombosis 30 \n(economy class syndrome) and coronavirus disease 2019 (COVID-19), both of which were suspected of 31 \nhaving overlooked information from many controversy2-21. Our analysis implied two S-curve types of 32 \nrisk increasing during a flight in the traveller's thrombosis. Also, our analysis demonstrated overlooked 33 \ncyclic patterns on the onset of thrombosis. This result suggests a strong relationship between travel and 34 \nstarting oral contraceptives (e.g., honeymoon and starting birth control oral contraceptives), which 35 \nmeans that risk diversification might allow more safe use of oral contraceptives. In the COVID-19, our 36 \nanalysis demonstrated unrecognised scatter plot patterns on cardiac biomarkers, which may serve 37 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 3 of all 74 \nstudies for pathophysiology in COVID-19 patients. Regarding the above findings, pattern recognition of 38 \nhyperbolic shapes can contribute to a significant discovery in data mining. 39 \n 40 \nMain text 41 \nRecently, software improvements have allowed us to make a beautiful chart, but the understanding 42 \nchart is required22. As readers of a scientific article, we took the idea of \"reading a chart carefully\" one step 43 \nfurther and made a question that \"something new exploratory data analysis (data mining) method assisted us 44 \nto find important knowledge from previously published figures?\". In addition, although statistics based on 45 \nprobability theory have applied the mathematical method to biomedicine (e.g., P-value), we turned our 46 \nattention to the viewpoint of geometry regarding its importance in history. 47 \nSubsequently, we were interested in a research field, traveller's thrombosis, in which many 48 \ncontroversies seemed to be associated with something overlooked (Supplementary discussion 1: history of 49 \ntraveller's thrombosis). In the literature review, we focused on a figure that showed a result of meta-50 \nregression analysis (Chandra et al., Ann Intern Med. 2009;151(3):180-90., Figure 3)7. In this figure, we saw a 51 \ngeometrical shape (layered hyperbolic shapes) that seemed to be formed by overlapping two subgroups (Fig. 1 52 \na-d, Fig. 2, a). 53 \nThrough those trains of thought, we conceived a methodological process based on our basic concept 54 \nthat approaching biomedical data from geometry was essential for exploratory data analysis. As know-how, 55 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 4 of all 74 \nhere we propose a kind of pattern recognition, which is searching for layered hyperbolic patterns in a figure 56 \nshowing a result of meta-regression analysis. 57 \nTo validate our ideas, we worked on consecutive exploratory data analyses, such as Analysis 1 (1A, 58 \n1B) and Analysis 2, setting a working hypothesis that the shape formed by multiple subgroups for (overall 59 \nstudy framework is shown in Extended Data Fig. 1). 60 \n 61 \nNumerical Experiment 62 \nConsidering theoretical consideration and numerical experiment, we constructed three mathematical 63 \nformulas for fitting hyperbolic patterns to data (see Fig. 1 & Methods). The numerical experiment indicated 64 \nthat a U-shaped curve formed by the end of the confidence limit could be approximated by a parabola (Fig. 1, 65 \nc). 66 \n 67 \nAnalysis 1A (dataset: Chandra et al.)7 68 \nTo assess eligibility for regression analysis, we reviewed a dataset, which was consisted of four 69 \nstudy data gathered by Chandra et al.7 for meta-regression analysis (Martinelli et al., 2003; Parkin et al., 2006; 70 \nCannegieter et al., 2006; Kuipers et al., 2007)23-26. In this assessment, two study data (Martinelli et al., 2003; 71 \nCannegieter et al., 2006)23,25 were judged inappropriate and excluded. Also, the odds ratio reported by Parkin 72 \net al.24 was suspected to be affected by a miscalculation, but qualitatively, it could only be used (see Extended 73 \nData Fig. 1 & Methods). 74 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 5 of all 74 \nIn a part of the original dataset (Parkin et al., 2006 & Kuipers et al., 2007)24,26, layered hyperbolic 75 \npatterns appeared and applied regression analysis with the above three formulas. The inflexion points of the S-76 \ncurves (centres of distributions) were 7.1 hours and 11.8 hours, respectively (Fig. 2, b). 77 \nNotably, we observed an overlooked cyclic pattern in the figure reported by Cannegieter et al25 78 \nduring the data review process. The cycle was 27.4 days (Extended Data Fig. 2). They did not mention this 79 \nwave pattern, and this notable oversight allowed to be accounted for by an inappropriate 3-dimensional graph 80 \nthat disrupted human visual recognition (Fig. 2, c, d, & Extended Data Fig. 2). 81 \n 82 \nAnalysis 1B (dataset: Philbrick et al.)4 83 \nConsidering that only a few data were available for the first analysis, to validate the first result, we 84 \nperformed a similar analysis using another dataset, which was gathered by Philbrick et al. for a systematic 85 \nreview. As a preparation, we conducted a data review to confirm eligibility for regression analysis (see 86 \nExtended Data Fig. 1). Then, only S-curves were applied because the dataset did not contain risk ratio data, 87 \nand hyperbolic shapes could not be fitted (for the details, see Methods). In this analysis, we found that two 88 \ninflexion points of S-curves were divided similarly to the first analysis (< 10 hours, > 10 hours) in the 89 \nstratified datasets by pulmonary embolism (PE) and deep vein thrombosis (DVT). The inflexion point of PE 90 \nwas about 9.2 hours, and the point of DVT was about 12.1 hours, respectively (Extended Data Fig. 3). 91 \nAdditionally, we found that unrecognised periodic pattern in the data reported by Clérel and 92 \nCaillard27 during the data review, which was suspected to be the effect of circadian rhythm (Extended Data 93 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 6 of all 74 \nFig. 4). We also found a post-travel cyclic pattern in the Kelman et al.28 same cases as Cannegieter et al25. The 94 \nwave was less clear than the wave observed in the data reported by Cannegieter et al25. In the waveform, there 95 \nwas a raw-risk period just before 90 days. In this data, there was an uptrend (Extended Data Fig. 5). 96 \nFurthermore, we found a correlation between the stepped stages of increasing PE patients and the 97 \nissuance of the guidelines29-32 for preventive hormone replacement therapy (HRT) to a menopause woman in a 98 \nfigure reported by Clérel and Caillard27 (Extended Data Fig. 6). 99 \n 100 \nAnalysis 2 (dataset: COVID-19)33 101 \nConsidering the above two analysis results, we decided to apply our ideas to the current complex 102 \nCOVID-19 pandemic problem to find some overlooked things because there was some controversy about the 103 \nCOVID-19 related thrombosis. This situation was similar to that of the traveller's thrombosis. 104 \n(Supplementary discussion 2: research situations of COVID-19 related thrombosis), and we started this 105 \nanalysis under the inspiration from the famous mathematician Polya who stated that solving a similar problem 106 \nhelped us solve a more difficult problem34. 107 \nOne of us (KK) searched for the layered hyperbolic pattern using a search engine and extracted a 108 \nfigure reported by Matsushita et al.33 (Fig. 3, a-c). After evaluating eligibility (see Extended Data Fig. 1), 109 \npatterns that allowed to be fitted hyperbolic shapes appeared (Fig. 3, d-f, & g-i). 110 \nConsidering the cause of these patterns, we found the matching between grouping the data by 111 \nhyperbolic patterns and grouping by data cut-off days (Extended Data Fig. 7). We calculated weighted 112 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 7 of all 74 \naverages of age by grouping. In the earlier days group, non-severe was 46.5, severe was 57.7, and middle age 113 \n(45-64). In the late date group, non-severe was 40.9, and severe was 68.6, which were mature age (25-44) and 114 \nelderly (> 65), respectively. 115 \nSurprisingly, we found unrecognized patterns during the data review process in a figure reported by 116 \nGuo et al.35, which showed a relationship between N-terminal pro-brain natriuretic peptide (NT-proBNP) and 117 \nTroponin T (TnT). There were three clusters of subgroup patterns, and each cluster could be fitted parabola 118 \n(Fig. 4 a, b, Extended Data Fig. 8 & Extended Data Fig. 9). 119 \nThe third subgroup pattern was similar to the pattern of ST-elevating myocardial infarction in the 120 \nfigure report by Budnik et al36. That study was a comparative study between Takotsubo cardiomyopathy (also 121 \nknown as stress cardiomyopathy or broken heart syndrome) and ST-elevating myocardial infarction. This tiled 122 \nparabola appeared in another study on COVID-19 patients37, and the pattern had already appeared in other 123 \nstudies38,39 before the pandemic. However, those patterns were not recognised by each author. 124 \nAdditionally, In the case of dropping points to the horizontal axis (troponin axis), the histogram on 125 \nthe troponin axis results in bimodality. The above results matched the patterns reported by other studies 126 \n(Extended Data Fig. 8)37,40,41. 127 \nFurthermore, by mounting the data of high-sensitivity C-Reactive protein (hsCRP) onto the third 128 \nsubgroup and constructing a parabolic cylinder, we found a pattern that might further be subdivided into two 129 \nsubgroups on the side surface of this parabolic cylinder (Fig. 4, c, d, & Extended Data Fig. 10). 130 \n 131 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 8 of all 74 \nDiscussion 132 \nUsing pattern recognition of hyperbolic shape as a key to discoveries in exploratory data analysis, 133 \nwe started research for traveller's Thrombosis and COVID-19, and as a result, our concept of the geometrical 134 \nviewpoint allowed us to discover many unrecognised patterns. Therefore, approaching data from geometry 135 \nand exploring data focusing on hyperbolic patterns can be a practical option for researchers. 136 \nIn traveller's thrombosis, we obtained consistent results from two analyses (7.1 hours and 11.8 hours 137 \nvs 9.2 hours and 12.1 hours) (Fig. 2, b, Extended Data Fig. 3). The discrepancy between the value of 7.1 138 \nhours and 8.5 hours seems to be explained by the miscalculation found in the data review process (see 139 \nMethods). Although many researchers have led controversial discussions based on a single curve, our results 140 \nimplied two S-curves. We hypothesised two high-risk periods and two types of high-risk groups, which may 141 \nhave to be considered with the \"factor V Leiden paradox\"42 (Supplementary discussion 3: two high-risk 142 \nperiods and two types of high-risk groups?). 143 \nAnother noteworthy point is the cyclic patterns (wave) (Fig. 2, c, d) and the raw-risk period just 144 \nbefore 90 days in Kelman et al.27 (Extended Data Fig. 5). In Cannegieter et al.24, the cyclic pattern 145 \ndisappeared around 90 days, consistent with that the high-risk period in oral contraceptive (OC) use was the 146 \nfirst three months (90 days)42. Also, the above raw-risk period explains extended-use type OC, which has a 147 \nplanned drug withdrawal, such as 84 active days and seven placebo days43-45. In addition, the uptrend in the 148 \ndata by Kelman et al.27 could be explained by depot agent type OC administrated 90 days cycle46. So, our 149 \nfindings imply that the 28 days cycle OC is attributable to the cyclic pattern, and both cycle type and 150 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 9 of all 74 \nextended-use type OC use is triggered by travel. An opposition may arise considering that both of relative risk 151 \nreported by Martinelli et al.22 and Cannegieter et al.24 were low (Fig. 2, b), but it seems to be explained by 152 \nbias derived from using their partner as control (Supplementary discussion 4: OC users and bias by their 153 \npartner). 154 \nA halfway cycle (17.9 days) in Kelman et al.28 was explained by a mixture of the 28 days OC cycle 155 \nand a type of HRT cycle (sequential type; daily estrogen dosing and 10–14 days progestogen)46. Also, another 156 \nproblem is that the wave in Cannegieter et al. was clear (thrombosis onset: March 1999-March 2000)25. 157 \nHowever, the wave in Kelman et al. (1981-1999)28 was not clear despite the exposures in Cannegieter et al. 158 \n(air travel, train, bus, and 48.5% car trip)25 was more complex than Kelman et al. (only air travel)28, was 159 \nanswered by the history of HRT. In Kelman et al.28, there might be both young women taking OC and 160 \nmenopausal women receiving HRT, but only OC users might remain after the HERS study reported risk of 161 \nHRT (1998)31, which was assisted by the growth of thrombosis onset slowed at the HERS study31 (Extended 162 \nData Fig. 6). Also, the above cars might be honeymoon cars. Although it was not decreasing, the result might 163 \nbe caused by some woman's desire for joyful travel to Paris with HRT. 164 \nOur thought on pharmacoepidemiology in the real world, starting OC or HRT was triggered by 165 \ntravel and decision making of HRT connected to travel, which means that well-planned usage based on risk 166 \ndiversification may allow more safe use of OC and HRT. 167 \nIn appreciation of our ideas to COVID-19, the dataset grouping by Matsushita et al.32 matched the 168 \ngrouping by data cut-off dates (Extended Data Fig. 7), and age structure diverged from middle age to mature 169 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 10 of all 74 \nand elderly, which was consistent with the hypothesis that COVID-19 spread from the seafood market. 170 \nMiddle-aged people might go into the workforce for manual labour treating fish containers, mature people 171 \nmight want to select IT jobs, and elderly people might stay in the house. 172 \nInterestingly, our analysis of the data by Guo et al.34 showed three clusters of subgroups, and one of 173 \nthose formed the tilted parabola. Also, the patterns matched the other studies (Fig. 4 a, b, Extended Data Fig. 174 \n8 & Extended Data Fig. 9)36-41. Considering the study by Budnik et al.36, those subgroups may have different 175 \nbiological mechanisms. 176 \nAdditionally, we found patterns on the side surface of this parabolic cylinder (Fig. 4, c, d, & 177 \nExtended Data Fig. 10). A paradoxical result on troponin was obtained just before the pandemic48, and 178 \nMeisel et al. mentioned that the CRP to troponin ratio (CRP/troponin) could serve to differentiate between 179 \nmyopericarditis and acute myocardial ischemia (AMI), although not the study on COVID-19 patients. In 180 \nCOVID-19, Caro-Codón et al. reported interesting behaviour of CRP35. Also, a meta-analysis by Lagunas-181 \nRangel reported that the lymphocyte‐to‐C‐reactive protein ratio (LCR) level, which was not a simple 182 \nmeasurement value but a ratio, might be related to an inflammatory process47. 183 \nThe above studies might imply complex data structures in 2-dimensional and 3-dimensional scatter 184 \nplots consisting of biomarker values, and our findings may serve cardiac biomarkers' research field. 185 \nSupplementary, we explain the misuse of linear regression analysis in the study by Guo et al.35 186 \n(Supplementary discussion 5: misuse of linear regression analysis). 187 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 11 of all 74 \nAlthough many studies on visualization of meta-analysis have been conducted48, our simple idea 188 \n(hyperbolic pattern) has not been proposed. As named “error”, researchers usually view an error bar 189 \nnegatively. Also, in the wheel's history, an invention of carriages, which was achieved by arranging the 190 \nwheels in parallel, appeared in ancient times, but the idea of the bicycle, which was innovatively arranging 191 \nwheels vertically, had not been conceived before the 19th century49,50. Those mental blocks might have made 192 \nit hard to imagine that vertical error bars provided information on a horizontal axis. 193 \nEvaluating our ideas, we discovered many oversights which were entirely beyond the initial scope. 194 \nAppearing overlapped hyperbolic patterns may show poor data review and analysis. Currently, pattern 195 \nrecognition based on Artificial Intelligence (AI) detects cancer sites from images. Considering our discoveries 196 \nby an analogy that Newton's theory enabled the prediction of a planet's orbit, implementing our idea (a kind of 197 \nmathematical model or theory) in an AI system might assist another discovery of clinical issues. 198 \n  199 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 12 of all 74 \n 200 \nMain references 201 \n1 Van Noorden, R. Journals adopt AI to spot duplicated images in manuscripts. Nature, 202 \ndoi:10.1038/d41586-021-03807-6 (2021). 203 \n2 Adi, Y., Bayliss, S., Rouse, A. & Taylor, R. S. The association between air travel and deep vein 204 \nthrombosis: systematic review & meta-analysis. BMC Cardiovasc Disord 4, 7, doi:10.1186/1471-205 \n2261-4-7 (2004). 206 \n3 Kuipers, S. et al. Travel and venous thrombosis: a systematic review. J Intern Med 262, 615-634, 207 \ndoi:10.1111/j.1365-2796.2007.01867.x (2007). 208 \n4 Philbrick, J. T., Shumate, R., Siadaty, M. S. & Becker, D. M. Air travel and venous 209 \nthromboembolism: a systematic review. J Gen Intern Med 22, 107-114, doi:10.1007/s11606-006-210 \n0016-0 (2007). 211 \n5 Spencer, F. A. 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Intern Emerg Med 15, 1375-1387, doi:10.1007/s11739-020-02432-x 249 \n(2020). 250 \n21 Rothman, K. J. Thrombosis after travel. PLoS Med 3, e300, doi:10.1371/journal.pmed.0030300 251 \n(2006). 252 \n22 Cairo, A.     (W. W. Norton & Company, New York, 2019).  253 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 15 of all 74 \n23 Martinelli, I. et al. Risk of venous thromboembolism after air travel: interaction with thrombophilia 254 \nand oral contraceptives. Arch Intern Med 163, 2771-2774, doi:10.1001/archinte.163.22.2771 (2003). 255 \n24 Parkin, L., Bell, M. L., Herbison, G. P., Paul, C. & Skegg, D. C. Air travel and fatal pulmonary 256 \nembolism. Thromb Haemost 95, 807-814 (2006). 257 \n25 Cannegieter, S. C., Doggen, C. J., van Houwelingen, H. C. & Rosendaal, F. R. Travel-related 258 \nvenous thrombosis: results from a large population-based case control study (MEGA study). PLoS 259 \nMed 3, e307, doi:10.1371/journal.pmed.0030307 (2006). 260 \n26 Kuipers, S. et al. The absolute risk of venous thrombosis after air travel: a cohort study of 8,755 261 \nemployees of international organisations. PLoS Med 4, e290, doi:10.1371/journal.pmed.0040290 262 \n(2007). 263 \n27 Clérel, M. & Caillard, G. [Thromboembolic syndrome from prolonged sitting and flights of long 264 \nduration: experience of the Emergency Medical Service of the Paris Airports]. Bull Acad Natl Med 265 \n183, 985-997; discussion 997-1001 (1999). 266 \n28 Kelman, C. W. et al. Deep vein thrombosis and air travel: record linkage study. BMJ 327, 1072, 267 \ndoi:10.1136/bmj.327.7423.1072 (2003). 268 \n29 Guidelines for counseling postmenopausal women about preventive hormone therapy. American 269 \nCollege of Physicians. Ann Intern Med 117, 1038-1041, doi:10.7326/0003-4819-117-12-1038 270 \n(1992). 271 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 16 of all 74 \n30 Smith, S. C. et al. AHA consensus panel statement. Preventing heart attack and death in patients 272 \nwith coronary disease. The Secondary Prevention Panel. J Am Coll Cardiol 26, 292-294, 273 \ndoi:10.1016/0735-1097(95)90846-g (1995). 274 \n31 Hulley, S. et al. Randomized trial of estrogen plus progestin for secondary prevention of coronary 275 \nheart disease in postmenopausal women. Heart and Estrogen/progestin Replacement Study (HERS) 276 \nResearch Group. JAMA 280, 605-613, doi:10.1001/jama.280.7.605 (1998). 277 \n32 Rossouw, J. E. et al. Risks and benefits of estrogen plus progestin in healthy postmenopausal 278 \nwomen: principal results From the Women's Health Initiative randomized controlled trial. JAMA 279 \n288, 321-333, doi:10.1001/jama.288.3.321 (2002). 280 \n33 Matsushita, K. et al. The Relationship of COVID-19 Severity with Cardiovascular Disease and Its 281 \nTraditional Risk Factors: A Systematic Review and Meta-Analysis. Glob Heart 15, 64, 282 \ndoi:10.5334/gh.814 (2020). 283 \n34 Polya, G. How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library).  284 \n(Princeton University Press, 1957). 285 \n35 Guo, T. et al. Cardiovascular Implications of Fatal Outcomes of Patients With Coronavirus Disease 286 \n2019 (COVID-19). JAMA Cardiol 5, 811-818, doi:10.1001/jamacardio.2020.1017 (2020). 287 \n36 Budnik, M. et al. Simple markers can distinguish Takotsubo cardiomyopathy from ST segment 288 \nelevation myocardial infarction. Int J Cardiol 219, 417-420, doi:10.1016/j.ijcard.2016.06.015 289 \n(2016). 290 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 17 of all 74 \n37 Wang, Y. et al. Cardiac Injury and Clinical Course of Patients With Coronavirus Disease 2019. 291 \nFront Cardiovasc Med 7, 147, doi:10.3389/fcvm.2020.00147 (2020). 292 \n38 Sugawa, S., Masuda, I., Kato, K. & Yoshimura, M. Increased Levels of Cardiac Troponin I in 293 \nSubjects with Extremely Low B-type Natriuretic Peptide Levels. Sci Rep 8, 5120, 294 \ndoi:10.1038/s41598-018-23441-z (2018). 295 \n39 Satyan, S., Light, R. P. & Agarwal, R. Relationships of N-terminal pro-B-natriuretic peptide and 296 \ncardiac troponin T to left ventricular mass and function and mortality in asymptomatic hemodialysis 297 \npatients. Am J Kidney Dis 50, 1009-1019, doi:10.1053/j.ajkd.2007.08.017 (2007). 298 \n40 Caro-Codón, J. et al. Characterization of NT-proBNP in a large cohort of COVID-19 patients. Eur J 299 \nHeart Fail 23, 456-464, doi:10.1002/ejhf.2095 (2021). 300 \n41 Demir, O. M. et al. Impact and Determinants of High-Sensitivity Cardiac Troponin-T Concentration 301 \nin Patients With COVID-19 Admitted to Critical Care. Am J Cardiol 147, 129-136, 302 \ndoi:10.1016/j.amjcard.2021.01.037 (2021). 303 \n42 van Langevelde, K., Flinterman, L. E., van Hylckama Vlieg, A., Rosendaal, F. R. & Cannegieter, S. 304 \nC. Broadening the factor V Leiden paradox: pulmonary embolism and deep-vein thrombosis as 2 305 \nsides of the spectrum. Blood 120, 933-946, doi:10.1182/blood-2012-02-407551 (2012). 306 \n43 Wiegratz, I. et al. Effect of extended-cycle regimen with an oral contraceptive containing 30 mcg 307 \nethinylestradiol and 2 mg dienogest on bleeding patterns, safety, acceptance and contraceptive 308 \nefficacy. Contraception 84, 133-143, doi:10.1016/j.contraception.2011.01.002 (2011). 309 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 18 of all 74 \n44 Loudon, N. B., Foxwell, M., Potts, D. M., Guild, A. L. & Short, R. V. Acceptability of an oral 310 \ncontraceptive that reduces the frequency of menstruation: the tri-cycle pill regimen. Br Med J 2, 311 \n487-490, doi:10.1136/bmj.2.6085.487 (1977). 312 \n45 Legro, R. S. A Review of Extended-Cycle Oral Contraception. (Morrisville, North Carolina, USA, 313 \n2003). 314 \n46 Humans, I. W. G. o. t. E. o. C. R. t. Combined estrogen-progestogen contraceptives and combined 315 \nestrogen-progestogen menopausal therapy. IARC Monogr Eval Carcinog Risks Hum 91, 1-528 316 \n(2007). 317 \n47 Lagunas-Rangel, F. A. Neutrophil-to-lymphocyte ratio and lymphocyte-to-C-reactive protein ratio 318 \nin patients with severe coronavirus disease 2019 (COVID-19): A meta-analysis. J Med Virol 92, 319 \n1733-1734, doi:10.1002/jmv.25819 (2020). 320 \n48 Kossmeier, M., Tran, U. S. & Voracek, M. Charting the landscape of graphical displays for meta-321 \nanalysis and systematic reviews: a comprehensive review, taxonomy, and feature analysis. BMC 322 \nMed Res Methodol 20, 26, doi:10.1186/s12874-020-0911-9 (2020). 323 \n49 Brunner, B. in The Smart Set (online magazine)    (Drexel University, Philadelphia, 2017). 324 \n50 Japanese Wikipedia contributors     (Wikipedia (Japanese site), 2021). 325 \n  326 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 19 of all 74 \n 327 \nMethods 328 \n1. Numerical experiment 329 \nUnavoidably, this study conducted a numerical experiment to determine what curve approximates an 330 \nedge of a confidence limit (Fig. 1, c). 331 \nGenerally, a dose-response relationship often indicates an S-curve. Considering the distribution of a 332 \npopulation at thrombosis risk and the cumulative thrombosis onset, each of those is monomodal distribution 333 \nand the S-shaped curve, respectively. So, we decided to use the sigmoid function, which is generally used in 334 \ncurve fitting to dose-response data, as the formula for the S-curve fitting. 335 \nContrastively, the curve expressing the end of a confidence interval (confidence limit) is a sum of 336 \nthe S-shaped curve and U-shaped curve because the width of the confidence interval narrows near the centre 337 \nof distribution due to many cases around the points. Similarly, the confidence interval widens at the 338 \ndistribution edge due to the small number of cases (see Fig. 1, d). 339 \nBased on the above consideration, we selected the parabola as a candidate for the U-shaped curve 340 \nbecause this curve was mathematically easy to handle (just junior high school level mathematics). So, we 341 \nexamined the validity of using parabola. However, mathematical proof of our conjecture was difficult because 342 \nnormal distribution was continuous probability distribution. So, we used a kind of discrete probability 343 \ndistribution, binomial distribution, to prove our conjecture experimentally because normal distribution could 344 \nbe approximated by binominal distribution. This idea was thinking in reverse of the usual statistical technique. 345 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 20 of all 74 \nTo generate binomial distribution data, we used the \"BINOM.DIST\" function, which is a function 346 \nfor calculating the probability of binomial distribution in a kind of spreadsheet software, Microsoft Excel○R 347 \n(Microsoft Corporation, Redmond, Washington, US). 348 \n 349 \n2. Equations for regression analysis 350 \nThe equations for the S-shaped curve, the upper end of the confidence limit, and the lower end of the 351 \nconfidence limit, those equations are the following (1), (2), and (3), respectively. Note that in the below 352 \nequations, the coefficient L is generally set as 1. So we used this equation under the condition as L=1 unless 353 \nthere is some reason. 354 \n 355 \n𝑦 = {\n𝐾1\n1+e𝐿(𝑥−𝑀) + 𝐾2}      (1) 356 \n𝑦 = {\n𝐾1\n1+e𝐿(𝑥−𝑀) + 𝐾2} + (𝑎𝑥2 + 𝑏𝑥+ 𝑐)    (2) 357 \n𝑦 = {\n𝐾1\n1+e𝐿(𝑥−𝑀) + 𝐾2} − (𝑎𝑥2 + 𝑏𝑥+ 𝑐)    (3) 358 \n 359 \nAlso, a complete square of the quadratic function that represents the parabola is the following equation (4). 360 \n 361 \n𝑎𝑥2 + 𝑏𝑥+ 𝑐 = 𝑎 (𝑥 +\n𝑏\n2𝑎)\n2\n−\n𝑏2−4𝑎𝑐\n4𝑎     (4) 362 \n 363 \nBesides, the point P is the apex of the parabola is the following (5). 364 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 21 of all 74 \n 365 \nP (−\n𝑏\n2𝑎 , −\n𝑏2−4𝑎𝑐\n4𝑎 )       (5) 366 \n 367 \nThe following equations are the formula that expresses the outline of the distribution obtained by differential 368 \ncalculation on the S-shaped curve (6). 369 \n 370 \n𝑑𝑦\n𝑑𝑥 = −\n𝐾1𝐿𝑒𝐿(𝑥−𝑀)\n{𝑒𝐿(𝑥−𝑀)+1}\n2      (6) 371 \n 372 \n3. Analysis tools in this study 373 \nReading values from the published figures were performed using the public domain software ImageJ 374 \nin the public domain (https://imagej.net/Welcome). Regression analysis was performed using Python (Python 375 \nSoftware Foundation, Delaware, USA https://www.python.org/psf/records/incorporation/). At this time, 376 \nPython's functional modules NumPy (NumFOCUS sponsored open-source project, https://numpy.org/), 377 \nPandas (NumFOCUS sponsored open-source project, https://pandas.pydata.org/), SciPy (NumFOCUS 378 \nsponsored open-source project, https://www.scipy.org/) and Matplotlib (NumFOCUS sponsored open-source 379 \nproject, https://matplotlib.org/) were also used. Additionally, a function as \"Chart option\" of Microsoft 380 \nExcel○R , which was shown in the \"Trendline Options\" section contained in \"Format Trendline,\" was used. In 381 \nthe case of symbolic formula manipulation was required, formula manipulation software wxMaxima (Project 382 \nMaxima maintained by 27 volunteers, https://maxima.sourceforge.io/) was used. 383 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 22 of all 74 \n 384 \n4. Analysis 1A (dataset: Chandra et al.)7 385 \n1) Data review to validate eligibility for regression analysis 386 \na. The process of data review in this analysis 387 \nAs the first step, we performed data mapping. In the figure of meta-regression analysis reported by 388 \nChandra et al.7, it was not described what the data points correspond to the four original papers (Martinelli et 389 \nal., 2003; Parkin et al., 2006; Cannegieter et al., 2006 and Kuipers et al., 2007)23-26. So, we measured the 390 \npositions of each point and compared them with the original descriptions in the papers. In the second step, we 391 \nperformed a data review, which was an examination of the accuracy of cited values, and appropriately from 392 \nthe viewpoint of biomedicine. Our re-calculation confirmed the odds ratio (OR), confidence interval of the 393 \nOR, and adjusted OR. In examining the values, we did not confirm Chandra et al.7 and the four authors23-26 394 \nbecause Chandra et al. described that each author did not respond to inquiry7. As a final step, we performed 395 \nregression analysis using the eligible data for using regression analysis. 396 \n 397 \nb. Data review 398 \nThe data review showed some problems in the research reported by Cannegieter et al. and Martinelli 399 \net al.23,25, and we excluded those data in the regression analysis. Also, there was a point to notice in the data 400 \nreported by Parkin et al.24 (see Extended Data Fig. 1). 401 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 23 of all 74 \nIn confirming the accuracy of the values, there were no problems with the two studies (Kuipers et al. 402 \nand Cannegieter et al.)25,26, but there were problems in the other two studies (Martinelli et al. and Parkin et 403 \nal.)23,24. 404 \nIn Martinelli et al.23, the problem was gender imbalance and unadjusted OR. In addition, although 405 \nthere were no explanations for the odds ratio described in the text cited by Chandra et al7, the above OR was 406 \npresumed to be an unadjusted value, judging from the context. Comprehensively, judging from both 407 \ncalculation results and the original article, the odds ratio cited by Chandra et al.7 was strongly suspected of 408 \nbeing an unadjusted value. 409 \nIn Parkin et al.24, there was a discrepancy between the OR and the described OR calculated by us. 410 \nAlso, it was suspected that cells in the cross table were mistaken (e.g., in the table of Fig. 1a, the cell for 411 \ncontrol and the cell for total were mistaken). However, the error bar's length was relatively small since the 412 \ntotal number of cases was notably smaller than other studies. So, qualitatively, it could only be used to group 413 \ndata to find hyperbolic patterns. 414 \nIn confirming from the viewpoint of the biomedicine side, there were no problems with two studies 415 \n(Kuipers et al. and Parkin et al.)24,26, but there were problems in the other two studies (Martinelli et al. and 416 \nCannegieter et al.)23,25. In Martinelli et al.23, judging from the subtitle, \"interaction with thrombophilia and 417 \noral contraceptives,\" oral contraceptive (OC) bias was suspected. Initially, the study aimed to evaluate the 418 \ninteraction between OC use and travel. Considering the above, the OR had to be considered a value that 419 \ncontained a strong bias (see also Supplementary discussion 4: OC users and bias by their partner). In 420 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 24 of all 74 \nCannegieter et al.25, the data contained car travel, and the other studies contained only air travel. So exposure 421 \nfactors were different, and there was a problem from the viewpoint of comparability (e.g., air pressure, 422 \ndehydration, and time difference). Also, Chandra et al.7 showed two types of analysis results, including 423 \nCannegieter et al.25 and not. Besides, the cyclic pattern could be explained by OC use was observed (see Fig. 424 \n2, c & d). Also, Cannegieter et al.25 did not adjust the OR by sex and OC use. So, it was strongly suspected 425 \nthat there was a strong bias derived from the different types of exposure factors and OC. 426 \nJudging from the above two types of data reviews, we excluded the data reported by two studies 427 \n(Martinelli et al. and Parkin et al.)23,24. In the data reported by Kuipers et al.26, there was no problem. The 428 \ndata reported by Parkin et al.24 seemed to be used only for the purpose described above. 429 \nInterestingly, in four studies used in meta-regression analysis by Chandra et al.7, all the first authors' 430 \nnames seem to be women's names (\"Suzanne\" Cannegieter25, \"Saskia\" Kuipers26, \"Ida\" Martinelli23, \"Lianne\" 431 \nParkin24). 432 \n 433 \n2) Regression Analysis 434 \nFor the data judged as eligible, hyperbolic patterns were visually searched, and each data point was 435 \ngrouped into two groups. Then, a non-linear regression analysis using the formulas above was performed. In 436 \nthe fitting of the U-shaped curve, since there were many unknown coefficients for the number of data (there 437 \nare seven unknowns, K1, K2, M, a, b, and c. in the equations (2) and (3)), the S-curve was fitted first, and the 438 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 25 of all 74 \nremaining unknown coefficients (a, b, c) were fitted to the residuals of the S-curve fitting (see equation (2) 439 \nand (3)). 440 \n 441 \n3) Additional analysis 442 \nAs described above, the cyclic pattern in the data reported by Cannegieter et al.25 was observed, and 443 \nwe performed additional analysis. To conduct an appropriate non-linear regression analysis, we made an 444 \nequation by combining two types of equations. The exponential decay equation was usually used to express 445 \nradioactive decay in physics and clearance in medicine. The other was a trigonometric function (sine function) 446 \nto express waveforms. The equation is shown in as below equation (7). Also, this scientific model (model 447 \nformula) was used to estimate the ratio of patients by integral calculation. 448 \n 449 \n𝑦 =  𝑁1𝑒−𝜆1(𝑡−𝑏) + 𝑁2𝑒−𝜆2(𝑡−𝑏) Asin{𝐵(𝑡 − 𝑏)}   (7) 450 \n 451 \nThe data reported as a bar graph was weekly data (see Fig. 2, c and Extended Data Fig. 2). So, the 452 \nweek was converted into the number of days before the analysis, such as; the day getting off the vehicle was 453 \nset as days 0, the first week was set as days 4, the second week was set as days 4 + 7, and the third week was 454 \nset as days 4 + 7 × two, and the Nth week was set as days 4 + 7 × N. 455 \nSupplementary, according to the original description by Cannegieter et al.25, 68 patients developed 456 \nthrombosis in the first week, and \"233\" patients developed thrombosis within eight weeks after travelling. 457 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 26 of all 74 \nHowever, there was a slight discrepancy in the values read from the bar graph. The value in our measurement 458 \nwithin eight weeks after travelling was \"234\", but the effect of only one patient was allowed to be regarded as 459 \nsmall (the description of 68 patients was the same.). 460 \nCannegieter et al. described the number of patients who travelled with their partners to evaluate the 461 \neffect of OC (Cannegieter et al., PLoS Med. 2006 Aug;3(8):e307., Table 2)25. We found some mismatches for 462 \nthe number of patients in the table, and the overall discrepancy was only one person by offset, and 463 \nCannegieter et al. described that there were derived from missing value25. The mismatch between our 464 \nmeasurement and description might be related to the described explanation. 465 \n 466 \n5. Analysis 1B (dataset: Philbrick et al.)4 467 \n1) Dataset search and data review 468 \na. Dataset search 469 \nTo validate the result of analysis 1A, we searched another dataset from meta-analysis or systematic 470 \nreview on the traveller's thrombosis. To conduct this search, we used PubMed® setting the following search 471 \nkeywords: \"economy class syndrome [Title] \" OR \"traveler's [Title] AND thrombosis [Title]\" OR \"traveler's 472 \n[Title] AND thromboembolism [Title]\" OR \"flight [Title] AND thrombosis [Title]\" OR \"flight [Title] AND 473 \nthromboembolism [Title]\" OR \"flight-related [Title] AND thrombosis [Title]\" OR \"flight-related [Title] AND 474 \nthromboembolism [Title]\" OR \"travel [Title] AND thrombosis [Title]\" OR \"travel [Title] AND 475 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 27 of all 74 \nthromboembolism [Title]\" OR \"travel-related [Title] AND thrombosis [Title]\" OR \"travel-related [Title] AND 476 \nthromboembolism [Title]\" (Filters: Meta-Analysis, Systematic Review). 477 \nAs a result, we obtained the eight articles (da Silva LF et al. J Vasc Bras. 2021 10;20:e20200164; 478 \nBenhaberou-Brun Perspect Infirm. 2010 7(3):16-7; Chandra et al. Ann Intern Med. 2009 151(3):180-90; 479 \nKuipers et al. J Intern Med. 2007 262(6):615-34; Philbrick et al. J Gen Intern Med. 2007 22(1):107-14; Hsieh 480 \net al. J Adv Nurs. 2005 51(1):83-98; Ansari et al. J Travel Med. 2005;12(3):142-54; Adi et al. BMC 481 \nCardiovasc Disord. 2004 19;4:7). 482 \nSubsequently, we selected articles containing available abstracts on PubMed® online, confirming the 483 \ncontents. As a candidate for our analysis, we selected a systematic review reported by Philbrick et al.4. The 484 \nstudy was taken up by the ACP Journal Club of the American College of Physicians5 and another journal 485 \nclub10. So, it seemed to be a highly reputed study. Therefore, we regarded that the dataset contained in the 486 \nresearch was suitable for validation. 487 \nAlso, the research contained two lists of tables, one of which was a cohort studies dataset, and the 488 \nother was the case-control studies. However, the case-control studies had many different exposure factors. So, 489 \nwe decided to use only the cohort studies dataset. 490 \n 491 \nb. Data review 492 \nIn the data review process, we reviewed the table containing ten cohort studies27,28,51-58 and found 493 \nseven eligible cohort studies27,51,54-58 for regression analysis. In Gajic et al. and Kelman et al., the only 494 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 28 of all 74 \ndistances were described28,52, and Hughes et al. reported duration data for not per one flight (e.g., mean 39.4 495 \nh)53, so time data for regression analysis was unavailable. 496 \nAdditionally, although Philbrick et al. described that incidence per million was 0.5 in table 2 of their 497 \narticle4, the number was incorrect because it was based on only 1998. In the original description, Clérel & 498 \nCaillard mentioned that \"According to the number of the passengers landing in the Aeroports de Paris, the 499 \nincidence during 1998 is 0.5 per million passengers\"27. 500 \n 501 \n2) Regression Analysis 502 \nFor the seven studies, data stratified by Pulmonary Embolism (PE) and Deep Vein Thrombosis 503 \n(DVT), regression analysis was performed using an S-shaped curve formula (see equation (1)). In the case of 504 \ncurve-fitting on DVT data, we cancelled the setting of coefficient L=1 to increase the degree of freedom of the 505 \nS-curve (Extended Data Fig. 3, b). To show the error bar in the figure (Extended Data Fig. 3), we did not 506 \nuse the values of confidence limits described in the report by Philbrick et al.4, but values were re-calculated 507 \nfrom the number of cases using Wilson's method because data review result described above showed the error 508 \nof values at the citation. 509 \nIn the seven studies, not OR or relative risk (RR), only the data indicating the incidence rate of 510 \nthrombosis was available. So, the hyperbolic pattern did not appear in the figure theoretically, and we 511 \nperformed only the S-shaped curve fitting. This mechanism is explanted from the following calculation on a 512 \nconfidence interval of a ratio. 513 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 29 of all 74 \nThe formula for a 95% confidence limit of a ratio using binomial approximation is expressed by the 514 \nfollowing formula: P is a ratio, and N is the number of trials. 515 \n 516 \n𝑃 − 1.96 √𝑃(1−𝑃)\n√𝑁 ≤ 𝑃 ≤ 𝑃 + 1.96 √𝑃(1−𝑃)\n√𝑁     (8) 517 \n 518 \nIn the above equation, the fraction's numerator is not a constant value and does not depend on only the N, 519 \nwhich is associated with a data point's position in a population (see Fig. 1). 520 \nIn this regression analysis, converting time categories to time points was necessary, so we performed 521 \nthis in three directions. The first one was taking the midpoint if the category was not the end of a category 522 \nsequence (e.g., 10-15 h could be converted to 12.5 h). The second one was taking the midpoint between the 523 \ntime point of 0 and the lower limit of the category if the category was the lower end of a category sequence 524 \n(e.g., <3 h could be converted to 1.5 h). The third one was taking the sum of the value of the upper limit and 525 \nthe value of the midpoint between the time point of 0 and the lower limit of the category sequence if the 526 \ncategory was the upper side of a category sequence (e.g., > 12 h could be converted to 12 h + 1.5 h =13.5 h). 527 \nDetails of conversions are shown below (the original time category is shown in brackets). 528 \nBelcaro et al. [10-15 h]: 12.5 h (Belcaro, G. et al., Angiology. 2001;52(6):369-74.)51; Clérel et al. 529 \n[12.7 h]: 12.7 h (Clérel, M., & Caillard, G., Bull Acad Natl Med. 1999;183(5):985-97.)27; Jacobson et al. [11 530 \nh]: 11 h; Lapostolle et al. [<3 h, 3-6 h, 6-9 h, 9-12 h,> 12 h]: 1.5 h, 4.5 h, 7.5 h, 10.5 h, 13.5 h (12 + 1.5 = 13.5 531 \nh) (Jacobson, B.F. et al., S Afr Med J. 2003;93(7):522-8.)54; Pérez-Rodríguez et al. [<6 h, 6-8 h,> 8 h]: 3 h, 7 532 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 30 of all 74 \nh, 11 h (8 + 3 = 11 h) (Pérez-Rodríguez, E. et al., Arch Intern Med. 2003;163(22):2766-70.)56; Schwarz et al. 533 \n2002 [> 8 h]: 12 h (midpoint of 0-8 h is 4 h and 8 + 4 = 12 hours) (Schwarz, T. et al., Blood Coagul 534 \nFibrinolysis. 2002;13(8):755-7.)57; Schwarz et al. 2003 [> 8 h]: 12 h (midpoint of 0-8 h is 4 h and 8 + 4 = 12 535 \nhours) (Schwarz, T. et al., Arch Intern Med. 2003 2003;163(22):2759-64.)58. 536 \n 537 \n3) Additional analysis 538 \na. Regression analysis (data: Kelman et al.28) 539 \nIn the review process, a cyclic pattern was observed. So, we worked on regression analysis. 540 \nConsidering that onset of thrombosis tends to increase again, an equation upward-sloping curve was added to 541 \nequation (7). The equation is the following (9). 542 \n 543 \n𝑦 =  𝑁1𝑒−𝜆1(𝑡−𝑏) + 𝑁2𝑒−𝜆2(𝑡−𝑏) Asin{𝐵(𝑡 − 𝑏)} + (𝑎𝑥2 + 𝑏𝑥+ 𝑐)  (9) 544 \n 545 \nb. Analysis by using correlogram (data: Clérel & Caillard27) 546 \nWe considered using the \"correlogram\" in this study because it was more practical than observing 547 \nthe original data's fluctuation. Periodic fluctuation patterns may be unclear when looking at the original data 548 \nalone, but potential patterns can be obtained using a correlogram, a data visualization method for analyzing 549 \ntime-series data. Also, as the correlation coefficient plotted on the correlogram, we decided to use Spearman's 550 \nrank correlation coefficient instead of Pearson's product-moment correlation coefficient, which is easily 551 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 31 of all 74 \naffected by outliers. Also, we performed a non-linear regression analysis using a mathematical formula (10) 552 \nthat includes two sine functions. 553 \n 554 \n𝑦 =  𝑛1 sin{𝑎1(𝑥 − 𝑏1)} + 𝑛2 sin{𝑎2(𝑥 − 𝑏2)}     (10) 555 \n 556 \nIn correlogram creation, firstly, a combination of data (data X1, data X1) was created by arranging 557 \nthe original time series data (data X1) and a new combination (data X1, data X1') was created by shifting one 558 \nof them. Secondary, the correlation coefficient (also called the auto-correlation coefficient) between the 559 \noriginal time-series data (data X1) and the sifted time-series data (data X1'), except at the ends of two types of 560 \ntime-series data where some correspondence could not be formed. By repeating shifting the time string data 561 \nand calculating the correlation coefficient, the locus of the correlation coefficient becomes the shape of waves. 562 \nFirstly (original waves of time strings are overlapped), the correlation coefficient is 1, and the value of the 563 \ncorrelation coefficient gradually decreases as the distance of the overlap increases. Finally (the wave is 564 \ninverted), the correlation coefficient is -1. 565 \nIn this study, since the risk of developing thrombosis is expected to increase as travel time increases 566 \nby cumulative exposure to environmental risk factors, it was necessary to investigate whether the fluctuations 567 \nin the number of patients really reflect the periodicity by confirming the fluctuation of the percentage of onset 568 \npatients to the total number of passengers to examine whether the fluctuation reflects the increase or decrease 569 \nin the number of passengers. However, this confirmation could not be made because data on the total number 570 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 32 of all 74 \nof passengers was not available. So, we focused on a method that suppressed the influence of the height of the 571 \nwave and evaluated only curved shapes. Therefore, we decided to draw a correlogram that reduced wave 572 \nheight by the property of the correlation coefficient, which fluctuates only between -1 and 1. 573 \nHowever, Pearson's product-moment correlation coefficient has a weakness: it is easily affected by 574 \noutliers. Also, as the progress of shifting the one side of the data string against the original data, their 575 \ncorrespondence decreases. In other words, the number of data that can be used to calculate the correlation 576 \ncoefficient gradually decreases. This problem may cause considerable variation between the calculated 577 \ncorrelation coefficients. Also, the thrombosis onset was recorded in 1-hour increments, and the length of the 578 \ndata was limited to 24 hours (24 data points). Therefore, instead of Pearson's product-moment correlation 579 \ncoefficient, we decided to create a correlogram using Spearman's rank correlation coefficient. 580 \n 581 \n6. Analysis 2 (dataset: COVID-19)33 582 \n1) Dataset search and data review 583 \nc. Dataset search 584 \nTo apply our idea to COVID-19 problems, one of the authors (KK) searched hyperbolic patterns 585 \nusing a search service Google (https://www.google.com/) provided by Google Inc., which allows displaying 586 \nsearch results as \"images.\" The search keyword was \"COVID-19 AND Meta-analysis\". In the case of 587 \ndisplaying bubble charts instead of the error bars, the size of the bubble chart (inversely proportional to the 588 \nlength of the error bars) was converted in mind. Consequently, we selected a suspicious study reported by 589 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 33 of all 74 \nMatsushita et al. (Matsushita, K. et al., Glob Heart. 2020;15(1):64.)33 that included eight research papers in 590 \nFigure 559-66. 591 \n 592 \nd. Data review 593 \nAs in the case of Analysis 1, we reviewed to evaluate numerical accuracy and appropriateness from 594 \nthe viewpoints of biomedicine. Since Matsushita et al.33 originally made web Figure 5 and excluded 17 595 \nstudies35,67-82 from avoiding duplication of studies in Wuhan city in the making of Figure 5, we inspected both 596 \nof studies in Figure 5 (8 studies) and only in web Figure 5 (17 studies). 597 \nBased on the results shown below, considering the issue of comparability, we excluded the data 598 \nreported by Yuan et al.65 and Wang L. et al63. Also, we re-calculated age difference using data reported by 599 \nGuan et al. 61 (see Extended Data Fig. 1). 600 \nAs a side note, the numbers assigned to each point in figure 3 were the same numbers described in 601 \nthe original figure by Matsushita et al.33, and the correspondence relationship is the following (Fig. 3): No.2: 602 \nCao et al. (Cao, J. et al., Intensive Care Med. 2020;46(5):851-853.)59, No.7: Deng et al. (Deng, Y. et al., Chin 603 \nMed J (Engl). 2020;133(11):1261-1267.)60, No.8: Guan et al. (Guan, W.J. et al., N Engl J Med. 604 \n2020;382(18):1708-1720.)61, No.19: Wang D. et al. (Wang, D. et al., JAMA. 2020;323(11):1061-1069.)62, 605 \nNo.20: Wang L. et al. (Wang, L. et al., J Infect. 2020;80(6):639-645.)63, No.21: Wu et al. (Wu, C. et al., JAMA 606 \nIntern Med. 2020;180(7):934-943.)64, No.23: Yuan et al. (Yuan, M. et al., PLoS One. 2020;15(3):e0230548)65, 607 \nNo.25: Zhou et al. (Zhou, F. et al., Lancet. 2020;395(10229):1054-1062.)66. 608 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 34 of all 74 \n 609 \n(i) No.8 Guan et al. (Guan, W.J. et al., N Engl J Med. 2020;382(18):1708-1720.)61 610 \nWe found a matter of consideration in the data reported by Guan et al61. Initially, features of that 611 \ndata differed from the other studies, which contained only cases reported from Wuhan city. In contrast, the 612 \ndata reported by Guan et al.61 contained cases outside of Wuhan city. Also, regarding the situation of the early 613 \npandemic, there were concerns about the presence of patients who could not take appropriate medication, 614 \nespecially in non-urban areas. Also, Matsushita et al.33 did not use the data divided into the severe and non-615 \nsevere groups by Guan et al.61 but used the data divided into yes and no by Guan et al.61 using \"Presence of 616 \nPrimary Composite End Point\", which means entry to the intensive care unit (ICU), use of mechanical 617 \nventilation, or death. 618 \nSince Cao et al. (Wuhan University Zhongnan Hospital in Wuhan; affiliation of Dr Jianlei Cao: 619 \nDepartment of Cardiology)59 and Wang et al. (Zhongnan Hospital of Wuhan University in Wuhan; affiliation 620 \nof Dawei Wang, MD: Department of Critical Care Medicine)62 also used ICU admission as a criterion for 621 \nsevere or non-severe, we examined the rate of severely ill patients and resulted in 21.4% (18/84) and 35.3% 622 \n(36/102), respectively. However, in the case of using the \"Presence of Primary Composite End Point\", the 623 \npercentage was only 6.5% (67/1032). Whereas, in the original categorisation by Guan et al.61, the percentage 624 \nwas 18.7% (173/926). Therefore, we prioritised the original classification of severe or non-severe by Guan et 625 \nal61. 626 \n 627 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 35 of all 74 \n(ii) No. 9 Guo et al. (Guo et al. JAMA Cardiol. 2020;5(7):811- 818)35 (only in eFigure5) 628 \nWe read this paper carefully, a report from Wuhan city published in March 2020. Although this 629 \ndocument may significantly influence the studies on COVID-19 (according to the JAMA Cardiology website, 630 \nthe article was cited more than 1,500 as of 20th September 2021), we found that misuse of linear regression 631 \nanalysis in Guo et al. on a figure (see Extended Data Fig. 8 & Supplementary discussion 5: misuse of linear 632 \nregression analysis)35. 633 \nAdditionally, three subgroup patterns appeared in a figure reported by Guo et al., although they did 634 \nnot mention it. Precautionary, we considered whether the subgroups in the Guo et al.35 affected the meta-635 \nanalysis on the web Figure 5. The data in other studies allowed to be expected to have the same subgroups 636 \nbecause the patient data described by Guo et al.71 and other studies were reported from China (most of them 637 \nwere in Wuhan City). 638 \n 639 \n(iii) No. 20 Wang L. et al. (Wang, D. et al., JAMA. 2020;323(11):1061-1069.)63 640 \nIn confirming from the viewpoint of the biomedicine side, it was found that a significant matter of 641 \nconsideration on eligibility, patient population reported by Wang L. et al. was limited to over age 6063. The 642 \ntitle was \"Coronavirus disease 2019 in elderly patients: Characteristics and prognostic factors based on 4-643 \nweek follow-up\", and Matsushita et al. 33 had to pay attention to the word \"elderly\". 644 \n 645 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 36 of all 74 \n(iv) No.23 Yuan M. et al. (Yuan M. et al., PLoS One. 2020;15(3):e0230548.)65 646 \nIn confirming the accuracy of values, we found a mixture of values derived from different 647 \ncalculation types in Figure 5: Odds Ratio (OR), hazard ratio, and a value derived from the imputation of 0.5 648 \nfor the zero cells in the cross table. The zero cells appeared in the study reported by Yuan et al65. Yuan M. et 649 \nal. studied 27 patients who confirmed novel coronavirus infected pneumonia (NCIP) during the early phase of 650 \nthe pandemic to evaluate radiologic characteristics65. In other words, the difficulty of patient enrollment might 651 \ncause a small sample size, which seemed to be a concern from the viewpoint of comparability (c.f., Guan W. 652 \net al., n=109961; Zhou F. et al., n=19166; Wang D. et al., n=13862; Wu C. et al. n=20164; Cao J. et al., n=10259; 653 \nDeng Y. et al., n=22560). 654 \n 655 \n(v) The term \"Cardiovascular disease (CVD).\" 656 \nThere was an inconsistency in the studies on \"Cardiovascular disease (CVD).\" For example, vascular 657 \ndiseases such as arrhythmia and arteriosclerosis are also classified as CVD, but in the studies reported by 658 \nGuan et al.61 and Zhou et al.66, the term \"Coronary heart disease\" was used. Also, \"Cardiac disease\" was used 659 \nby Yuan et al.65, \"Heart disease\" was used by Deng et al.60, and \"Cardiovascular disease\" was used by Wang L 660 \net al63. 661 \n 662 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 37 of all 74 \n2) Regression analysis 663 \nConsidering the problem of comparability, we re-calculated OR and visually grouped it into two 664 \nhyperbolic patterns. In the case of S-shaped curve fitting, since there were many unknown coefficients for the 665 \nnumber of data (3 unknown coefficients of K1, K2, and M), the regression analysis was performed after setting 666 \nthe zero point value. In the fitting of upper and lower curves, since there were many unknown coefficients 667 \n(K1, K2, M, a, b, c), we firstly obtained the coefficient of M (see equation (1)) by the curve fitting of the S-668 \nshaped curve, and then performed curve fitting of parabolas. After substituting M for x value of apex in 669 \nequation (4) (see equations (4) & (5)), regression analysis was performed on the data in the middle row of 670 \nFigure 3 (Fig. 3, d-f). Finally, the S-shaped curve and the parabola were merged (Fig. 3, g-i). 671 \n 672 \n3) Calculation of weighted average 673 \nIn earlier days group, the median age and the number of cases are tabulated by severe and non-674 \nsevere cases as follows. Guan W. et al. (severe n=173 [age: 52] vs non-severe n=926 [age: 45])61, Zhou F. et 675 \nal. (non-survival n=54 [age: 69] vs survival n=137 [age: 52])66, Wang D. et al. (ICU n=36 [age: 66] vs non-676 \nICU n=102 [age: 51])62, Wu C. et al. (ARDS n=84 [age: 58.5] vs non-ARDS n=117 [age: 48])64, and whole of 677 \nearlier days group (severe n = 347 vs non-severe n = 1282). 678 \nThe weighted average of severe and non-severe in the earlier days group was calculated from these 679 \nvalues by the following formulas. In the earlier days group, the weighted average of severe and non-severe 680 \nwere 57.7 and 46.5, respectively. 681 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 38 of all 74 \n 682 \n𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠 𝑖𝑛 𝑒𝑎𝑟𝑙𝑖𝑒𝑟 𝑑𝑎𝑦𝑠 𝑔𝑟𝑜𝑢𝑝 (𝑠𝑒𝑣𝑒𝑟𝑒) = 173 + 54 + 36 + 84 =  𝟑𝟒𝟕 683 \n𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑚𝑒𝑎𝑛 𝑜𝑓 𝑒𝑎𝑟𝑙𝑖𝑒𝑟 𝑑𝑎𝑦𝑠 𝑔𝑟𝑜𝑢𝑝 (𝑠𝑒𝑣𝑒𝑟𝑒) = 173\n𝟑𝟒𝟕 × 52 + 54\n𝟑𝟒𝟕 × 69 + 36\n𝟑𝟒𝟕 × 66 + 84\n𝟑𝟒𝟕 × 58.5684 \n≅  57.7 685 \n 686 \n𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠 𝑖𝑛 𝑒𝑎𝑟𝑙𝑖𝑒𝑟 𝑑𝑎𝑦𝑠 𝑔𝑟𝑜𝑢𝑝(𝑛𝑜𝑛 − 𝑠𝑒𝑣𝑒𝑟𝑒) = 926 + 137 + 102 + 117 =  𝟏𝟐𝟖𝟐 687 \n𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑚𝑒𝑎𝑛 𝑜𝑓 𝑒𝑎𝑟𝑙𝑖𝑒𝑟 𝑑𝑎𝑦𝑠 𝑔𝑟𝑜𝑢𝑝 (𝑛𝑜𝑛 − 𝑠𝑒𝑣𝑒𝑟𝑒)688 \n= 926\n𝟏𝟐𝟖𝟐 × 45 + 137\n𝟏𝟐𝟖𝟐 × 52 + 102\n𝟏𝟐𝟖𝟐 × 51 + 117\n𝟏𝟐𝟖𝟐 × 48 ≅  46.5 689 \n 690 \nIn later days group, the median age and the number of cases are tabulated by severe and non-severe 691 \ncases as follows. Cao J. et al. (ICU n=18 [age: 66] vs non-ICU n=84 [age: 31])59, Deng Y. et al. (Death n=109 692 \n[age: 69] vs survival n=116 [age: 48])60, and whole of later days group (severe n = 127 vs non-severe n = 693 \n200). 694 \nThe weighted average of severe and non-severe in the late date group was calculated from these 695 \nvalues by the following formulas. In the late date group, the weighted average of severe and non-severe were 696 \n68.6 years and 40.9, respectively. 697 \n 698 \n𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠 𝑖𝑛 𝑙𝑎𝑡𝑒 𝑑𝑎𝑡𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑠𝑒𝑣𝑒𝑟𝑒) = 18 + 109 =  𝟏𝟐𝟕 699 \n𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑚𝑒𝑎𝑛 𝑜𝑓 𝑙𝑎𝑡𝑒 𝑑𝑎𝑡𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑠𝑒𝑣𝑒𝑟𝑒) = 18\n𝟏𝟐𝟕 × 66 + 109\n𝟏𝟐𝟕 × 69 ≅  68.6 700 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 39 of all 74 \n𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠 𝑖𝑛 𝑙𝑎𝑡𝑒 𝑑𝑎𝑡𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑛𝑜𝑛 − 𝑠𝑒𝑣𝑒𝑟𝑒) = 84 + 116 =  𝟐𝟎𝟎 701 \n𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑚𝑒𝑎𝑛 𝑜𝑓 𝑙𝑎𝑡𝑒 𝑑𝑎𝑡𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑛𝑜𝑛 − 𝑠𝑒𝑣𝑒𝑟𝑒) = 84\n𝟐𝟎𝟎 × 31 + 116\n𝟐𝟎𝟎 × 48 ≅  40.9 702 \n 703 \n4) Additional analysis: Regression analysis on the parabolic cylinder 704 \nOne of the authors (KK) found a way to fit an appropriate curve to the data reported by Guo et al., 705 \nperforming trial and error with his mathematical intuition (Fig. 4). Firstly, he calculated the centre of gravity 706 \nof the data by each subgroup cluster (centre of gravity: the average of the values on the horizontal axis x and 707 \nthe average of the values on the vertical axis y). Second, he obtained equations of three straight lines passing 708 \nthrough the origin and centres of gravity. Thirdly, he obtained the equation of a straight line passing through 709 \neach centre of gravity and intersecting the straight lines obtained above. Fourthly, he re-set new origin as each 710 \ncentre of gravity and regarded the above two crossed lines as a small cartesian coordinate system. Finally, he 711 \napplied parabola fitting with Excel○R in each new cartesian coordinate system. In this curve fitting, he used the 712 \ndata of distance between each data point and the straight line obtained secondary, and the data of distance 713 \nbetween each data point and the straight line obtained firstly (see \"distance from a point to a line\" in a high 714 \nschool textbook). 715 \n 716 \n5) Making example data 717 \nTo explain the misuse of linear regression analysis in Guo et al.35, we made the following data to 718 \nshow the example. It allows being used in R by copying and pasting the following. 719 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 40 of all 74 \n 720 \nValue_X<-721 \nc(0.04 ,0.08 ,0.12 ,0.16 ,0.2 ,0.24 ,0.28 ,0.32 ,0.36 ,0.4 ,0.44 ,0.48 ,0.52 ,0.56 ,0.6 ,0.64 ,0.68 ,0.72 ,0.76 ,0.8 ,0722 \n.84 ,0.88 ,0.92 ,0.96 ,1 ,1.04 ,1.08 ,1.12 ,1.16 ,1.2 ,1.24 ,1.28 ,1.32 ,1.36 ,1.4 ,1.44 ,1.48 ,1.52 ,1.56 ,1.6 ,1.64 ,723 \n1.68 ,1.72 ,1.76 ,1.8 ,1.84 ,1.88 ,1.92 ,1.96 ,2 ,2.04 ,2.08 ,2.12 ,2.16 ,2.2 ,2.24 ,2.28 ,2.32 ,2.36 ,2.4 ,2.44 ,2.48 724 \n,2.52 ,2.56 ,2.6 ,2.64 ,2.68 ,2.72 ,2.76 ,2.8 ,2.84 ,2.88 ,2.92 ,2.96 ,3 ,3.04 ,3.08 ,3.12 ,3.16 ,3.2 ,3.24 ,3.28 ,3.32 725 \n,3.36 ,3.4 ,3.44 ,3.48 ,3.52 ,3.56 ,3.6 ,3.64 ,3.68 ,3.72 ,3.76 ,3.8 ,3.84 ,3.88 ,3.92 ,3.96 ,4) 726 \n 727 \nValue_Y<-728 \nc(2.01742 ,2.02749 ,2.04454 ,2.02009 ,2.03445 ,2.04749 ,2.03641 ,1.99047 ,1.98671 ,2.06711 ,2.09772 ,2.005729 \n39 ,1.86985 ,2.01679 ,2.12183 ,1.94453 ,1.86497 ,1.87444 ,2.09483 ,1.91073 ,1.69244 ,1.70968 ,1.81376 ,2.0730 \n4219 ,1.69059 ,1.75939 ,1.95321 ,1.8417 ,1.58169 ,1.75585 ,1.73497 ,1.47847 ,1.9115 ,1.44962 ,1.85063 ,1.3731 \n2298 ,1.28437 ,1.74621 ,1.27232 ,1.32763 ,1.575 ,1.56609 ,1.5933 ,1.76707 ,1.11264 ,1.06188 ,1.40139 ,0.94732 \n084 ,1.0756 ,1.38507 ,1.33408 ,1.54375 ,1.60257 ,1.02029 ,0.98612 ,1.79094 ,0.97916 ,0.81212 ,1.1484 ,1.51733 \n68 ,1.70236 ,1.38945 ,1.69072 ,1.75042 ,1.67571 ,1.38623 ,1.81503 ,1.80665 ,1.41073 ,2.3175 ,2.24852 ,1.75734 \n95 ,2.81818 ,1.93654 ,2.36998 ,2.0987 ,2.19539 ,2.44747 ,2.57255 ,3.24637 ,2.78881 ,3.51638 ,2.68107 ,2.87735 \n259 ,4.3749 ,3.13393 ,3.92099 ,4.1223 ,3.78584 ,4.9666 ,5.4888 ,5.70712 ,4.84752 ,5.1409 ,6.31637 ,5.53198 736 \n,6.89257 ,7.86387 ,7.98237 ,8.64705) 737 \n 738 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 41 of all 74 \n7. Statement of our intention for data review results 739 \nTo clarify our stance, we mention this statement of intention for results. In this article, we pointed 740 \nout many overlooking and errors. However, we have no intention to attack previous works because our 741 \nanalysis results owing to their original works, including original research articles, reported valuable data and 742 \narticles of meta-analysis synthesised valuable datasets. Since just a scientist had better reconfirm the previous 743 \nstudies with no preconception with being grateful to the researchers of those studies, we carefully reviewed 744 \nthe data reported by previous studies. We highly respect previous works, which have the intention to solve 745 \nmedical issues, although some articles contained technical errors. 746 \n  747 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 42 of all 74 \n 748 \nMethods references 749 \n51 Belcaro, G., Geroulakos, G., Nicolaides, A. N., Myers, K. A. & Winford, M. Venous 750 \nthromboembolism from air travel: the LONFLIT study. Angiology 52, 369-374, 751 \ndoi:10.1177/000331970105200601 (2001). 752 \n52 Gajic, O. et al. Long-haul air travel before major surgery: a prescription for thromboembolism? 753 \nMayo Clin Proc 80, 728-731, doi:10.1016/S0025-6196(11)61525-5 (2005). 754 \n53 Hughes, R. J. et al. Frequency of venous thromboembolism in low to moderate risk long distance air 755 \ntravellers: the New Zealand Air Traveller's Thrombosis (NZATT) study. Lancet 362, 2039-2044, 756 \ndoi:10.1016/s0140-6736(03)15097-0 (2003). 757 \n54 Jacobson, B. F. et al. The BEST study--a prospective study to compare business class versus 758 \neconomy class air travel as a cause of thrombosis. S Afr Med J 93, 522-528 (2003). 759 \n55 Lapostolle, F. et al. Severe pulmonary embolism associated with air travel. N Engl J Med 345, 779-760 \n783, doi:10.1056/NEJMoa010378 (2001). 761 \n56 Pérez-Rodríguez, E. et al. Incidence of air travel-related pulmonary embolism at the Madrid-Barajas 762 \nairport. Arch Intern Med 163, 2766-2770, doi:10.1001/archinte.163.22.2766 (2003). 763 \n57 Schwarz, T. et al. Deep vein and isolated calf muscle vein thrombosis following long-haul flights: 764 \npilot study. Blood Coagul Fibrinolysis 13, 755-757, doi:10.1097/00001721-200212000-00013 765 \n(2002). 766 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 43 of all 74 \n58 Schwarz, T. et al. Venous thrombosis after long-haul flights. Arch Intern Med 163, 2759-2764, 767 \ndoi:10.1001/archinte.163.22.2759 (2003). 768 \n59 Cao, J. et al. Clinical features and short-term outcomes of 18 patients with corona virus disease 769 \n2019 in intensive care unit. Intensive Care Med 46, 851-853, doi:10.1007/s00134-020-05987-7 770 \n(2020). 771 \n60 Deng, Y. et al. Clinical characteristics of fatal and recovered cases of coronavirus disease 2019 in 772 \nWuhan, China: a retrospective study. Chin Med J (Engl) 133, 1261-1267, 773 \ndoi:10.1097/CM9.0000000000000824 (2020). 774 \n61 Guan, W. J. et al. Clinical Characteristics of Coronavirus Disease 2019 in China. N Engl J Med 382, 775 \n1708-1720, doi:10.1056/NEJMoa2002032 (2020). 776 \n62 Wang, D. et al. Clinical Characteristics of 138 Hospitalized Patients With 2019 Novel Coronavirus-777 \nInfected Pneumonia in Wuhan, China. JAMA 323, 1061-1069, doi:10.1001/jama.2020.1585 (2020). 778 \n63 Wang, L. et al. Coronavirus disease 2019 in elderly patients: Characteristics and prognostic factors 779 \nbased on 4-week follow-up. J Infect 80, 639-645, doi:10.1016/j.jinf.2020.03.019 (2020). 780 \n64 Wu, C. et al. Risk Factors Associated With Acute Respiratory Distress Syndrome and Death in 781 \nPatients With Coronavirus Disease 2019 Pneumonia in Wuhan, China. JAMA Intern Med 180, 934-782 \n943, doi:10.1001/jamainternmed.2020.0994 (2020). 783 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 44 of all 74 \n65 Yuan, M., Yin, W., Tao, Z., Tan, W. & Hu, Y. Association of radiologic findings with mortality of 784 \npatients infected with 2019 novel coronavirus in Wuhan, China. PLoS One 15, e0230548, 785 \ndoi:10.1371/journal.pone.0230548 (2020). 786 \n66 Zhou, F. et al. Clinical course and risk factors for mortality of adult inpatients with COVID-19 in 787 \nWuhan, China: a retrospective cohort study. Lancet 395, 1054-1062, doi:10.1016/S0140-788 \n6736(20)30566-3 (2020). 789 \n67 Bhatraju, P. K. et al. Covid-19 in Critically Ill Patients in the Seattle Region - Case Series. N Engl J 790 \nMed 382, 2012-2022, doi:10.1056/NEJMoa2004500 (2020). 791 \n68 CDC COVID-19 Response Team. Preliminary Estimates of the Prevalence of Selected Underlying 792 \nHealth Conditions Among Patients with Coronavirus Disease 2019 - United States, February 12-793 \nMarch 28, 2020. MMWR Morb Mortal Wkly Rep 69, 382-386, doi:10.15585/mmwr.mm6913e2 794 \n(2020). 795 \n69 CDC COVID-19 Response Team. Severe Outcomes Among Patients with Coronavirus Disease 796 \n2019 (COVID-19) - United States, February 12-March 16, 2020. MMWR Morb Mortal Wkly Rep 797 \n69, 343-346, doi:10.15585/mmwr.mm6912e2 (2020). 798 \n70 Chen, J. et al. Clinical progression of patients with COVID-19 in Shanghai, China. J Infect 80, e1-799 \ne6, doi:10.1016/j.jinf.2020.03.004 (2020). 800 \n71 Chen, T. et al. Clinical characteristics of 113 deceased patients with coronavirus disease 2019: 801 \nretrospective study. BMJ 368, m1091, doi:10.1136/bmj.m1091 (2020). 802 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 45 of all 74 \n72 Cheng, Y. et al. Kidney disease is associated with in-hospital death of patients with COVID-19. 803 \nKidney Int 97, 829-838, doi:10.1016/j.kint.2020.03.005 (2020). 804 \n73 Huang, C. et al. Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China. 805 \nLancet 395, 497-506, doi:10.1016/S0140-6736(20)30183-5 (2020). 806 \n74 Lian, J. et al. Analysis of Epidemiological and Clinical Features in Older Patients With Coronavirus 807 \nDisease 2019 (COVID-19) Outside Wuhan. Clin Infect Dis 71, 740-747, doi:10.1093/cid/ciaa242 808 \n(2020). 809 \n75 Liang, W. et al. Cancer patients in SARS-CoV-2 infection: a nationwide analysis in China. Lancet 810 \nOncol 21, 335-337, doi:10.1016/S1470-2045(20)30096-6 (2020). 811 \n76 Onder, G., Rezza, G. & Brusaferro, S. Case-Fatality Rate and Characteristics of Patients Dying in 812 \nRelation to COVID-19 in Italy. JAMA 323, 1775-1776, doi:10.1001/jama.2020.4683 (2020). 813 \n77 Ruan, Q., Yang, K., Wang, W., Jiang, L. & Song, J. Clinical predictors of mortality due to COVID-814 \n19 based on an analysis of data of 150 patients from Wuhan, China. Intensive Care Med 46, 846-815 \n848, doi:10.1007/s00134-020-05991-x (2020). 816 \n78 Shi, S. et al. Association of Cardiac Injury With Mortality in Hospitalized Patients With COVID-19 817 \nin Wuhan, China. JAMA Cardiol 5, 802-810, doi:10.1001/jamacardio.2020.0950 (2020). 818 \n79 Tang, N., Li, D., Wang, X. & Sun, Z. Abnormal coagulation parameters are associated with poor 819 \nprognosis in patients with novel coronavirus pneumonia. J Thromb Haemost 18, 844-847, 820 \ndoi:10.1111/jth.14768 (2020). 821 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 46 of all 74 \n80 The Novel Coronavirus Pneumonia Emergency Response Epidemiology Team. The 822 \nEpidemiological Characteristics of an Outbreak of 2019 Novel Coronavirus Diseases (COVID-19) 823 \n— China, 2020. China CDC Weekly 2, 113-122, doi:https://doi.org/10.46234/ccdcw2020.032 824 \n(2020). 825 \n81 Yang, X. et al. Clinical course and outcomes of critically ill patients with SARS-CoV-2 pneumonia 826 \nin Wuhan, China: a single-centered, retrospective, observational study. Lancet Respir Med 8, 475-827 \n481, doi:10.1016/S2213-2600(20)30079-5 (2020). 828 \n82 Zhang, L. et al. Clinical characteristics of COVID-19-infected cancer patients: a retrospective case 829 \nstudy in three hospitals within Wuhan, China. Ann Oncol 31, 894-901, 830 \ndoi:10.1016/j.annonc.2020.03.296 (2020). 831 \n83 Reyes, N. L., Beckman, M. G. & Abe, K. in CDC Yellow Book 2020  Health Information for 832 \nInternational Travel   (eds Centers for Disease Control and Prevention (CDC), G. W. Brunette, & 833 \nJ. B. Nemhauser) Ch. 8, (Oxford University Press, 2019). 834 \n84 Kushner, A., West, W. P. & Pillarisetty, L. S.      (2021).  835 \n85 Thachil, J. et al. ISTH interim guidance on recognition and management of coagulopathy in 836 \nCOVID-19. J Thromb Haemost 18, 1023-1026, doi:10.1111/jth.14810 (2020). 837 \n86 Sugawa, S. Significance of Screening the General Population for Potential Cardiovascular Diseases 838 \nwith a Combination Assay of B-type Natriuretic Peptide and High Sensitive Troponin I. J Med 839 \nDiagn Meth 6 (2017). 840 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 47 of all 74 \n 841 \nAcknowledgements 842 \nOne of the authors, Keiichiro Kimoto, appreciates the kindful encouragement of Hideo Yoshioka, 843 \nMEcon., who is in charge of the Data Strategy Research Institute representative. 844 \n 845 \nCompeting interest declaration 846 \nKeiichiro Kimoto has been in charge of external advisor for Data Strategy Research Institute but 847 \nreserved no financial support for this study. Except for this, the authors have no conflicts of interest and have 848 \nno financial disclosures that should be disclosed. 849 \n 850 \nAuthor contributions 851 \nKeiichiro Kimoto takes responsibility for this research, making study concepts, data analysis, 852 \ninterpretation of analysis results, and drafting the manuscript. Dr. Yamakuchi contributed to interpreting 853 \nanalysis results, manuscript drafting, supervision and administrative role. Dr. Takenouchi contributed to the 854 \nsupervision. Dr. Hashiguchi contributed to the study concept, interpretation of analysis results, manuscript 855 \ndrafting, supervision, and administrative role. 856 \n 857 \nAdditional information 858 \nThis article has supplementary information that contains supplementary discussions. 859 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 48 of all 74 \n 860 \nData availability statement 861 \nWe analyzed clinical data published by other studies (third parties). Used data is identified by 862 \nindicated information of citation (reference numbers and list of references). The corresponding author 863 \nresponds to inquiries in the case of measured values from published figures requested by reviewers or readers. 864 \n 865 \nCode availability statement 866 \nCorrespondence author (KK) can respond to inquiries for the corresponding author's email address 867 \non offering the Python source code and spreadsheet software files for statistical analysis. 868 \n  869 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 49 of all 74 \n 870 \nFigures & figure legends 871 \nFig. 1 872 \n 873 \nFig. 1 | A hyperbolic shape formed by confidence limits. a, A two-way cross-tabulation (contingency table) 874 \nfor calculating an odds ratio (OR). b, Calculation of OR and its 95% confidence interval. c, Histogram of the 875 \ndata following a binomial distribution and a plot of the inverse values of the square roots. d, The mathematical 876 \nformulas for the hyperbolic shape. Note that the OR is not logarithmic, and only the length of the error bar is 877 \nlogarithmic (see the upper left position of panel d). 878 \n  879 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 50 of all 74 \n 880 \nFig. 2 881 \n 882 \nFig. 2 | Re-analysis based on the proposed ideas. a, Data review and meta-regression analysis using the 883 \nsame method as Chandra et al. Ann Intern Med. 2009; 151(3):180-190. Figure 37. We added information from 884 \noriginal studies and our hypothesis to the previously published form, such as latent distribution. The original 885 \nfigure has been shown on the American College of Physicians website, which links to PubMed○R 886 \n(https://pubmed.ncbi.nlm.nih.gov/19581633/). From Chandra D, Parisini E, Mozaffarian D. Meta-analysis: 887 \ntravel and risk for venous thromboembolism. Ann Intern Med. 2009 Aug 4;151(3):180-90. doi: 10.7326/0003-888 \n4819-151-3-200908040-00129. Epub 2009 Jul 6. © 2009 American College of Physicians. Adapted with 889 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 51 of all 74 \npermission. b, grouping the data and hyperbolic shape fitting. c, Onsets of thrombosis after travel reported by 890 \nCannegieter et al25. This figure was re-used and re-drawn from Cannegieter et al. Travel-related venous 891 \nthrombosis: results from a large population-based case-control study (MEGA study). PLoS Med. 2006; 892 \n3(8):e307. Figure 1. https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC1551914/figure/pmed-0030307-893 \ng001/ Copyright © 2006 Cannegieter et al. Creative Commons Attribution License. In 2006, the Creative 894 \nCommons Attribution 2.0 Generic, License was available. https://creativecommons.org/licenses/by/2.0/ d, 895 \nApplying the damped wave function to the data shown in panel c. We decided that the data from Martinelli et 896 \nal.23 and Cannegieter et al.25 should be excluded, and the odds ratio from Parkin et al.24 may decrease (see 897 \nMethods). At 2 hours point, Chandra et al.7 did not use available data (panel a). On the original regression 898 \nline, Chandra et al.7 might conduct a meta-regression analysis reversing the front head and the front side of the 899 \ncross-tabulation. Compering panels c and d helps us understand that using a three-dimensional graph disrupts 900 \nour recognition. 901 \n 902 \n  903 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 52 of all 74 \n 904 \nFig. 3 905 \n 906 \nFig. 3 | Hyperbolic shapes found in the figure reported by Matsushita et al33. a, A figure shows the 907 \nrelationship between the severe and non-severe groups reported by Matsushita et al.33, which shows age 908 \ndifference on the horizontal axis and odds ratio (OR) or hazard ratio of hypertension on the vertical axis. To 909 \nevaluate potential confounding for relative risk by age, Matsushita et al. conducted meta-regression analyses 910 \nbased on the assumption that there was the possibility of confounding by age in the case that the study with a 911 \nlarger age difference has a higher relative risk33. b, Diabetes. c, Cardiovascular disease (CVD). d-f, 912 \nComparisons of error bars, which show 95% confidence interval (C.I.) s. It corresponds to the upper figure. g-913 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 53 of all 74 \ni, Hyperbolic patterns were fitted to the OR and the 95% confidence limit of the OR. In the panel i, a 914 \nhyperbolic shape could not be fitted due to the considerable data variation, likely due to the inconsistency of 915 \nthe term \"CVD\" (see Methods). The numbers marked to each point are the same as the numbers shown in the 916 \noriginal figure. The sources of each data are shown in Methods. This figure was re-used from Matsushita et al. 917 \nGlob Heart. 2020; 15(1):64. Figure 5. 918 \nhttps://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7546112/figure/F5/  919 \nCopyright © 2020 The Authors. Creative Commons Attribution 4.0 International License (CC-BY 4.0) 920 \nhttps://creativecommons.org/licenses/by/4.0/ 921 \n 922 \n  923 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 54 of all 74 \n 924 \nFig. 4 925 \n 926 \nFig. 4 | Parabola shape patterns in the figure by Guo et al35. a, Relationship between high sensitive C-927 \nreactive protein (hsCRP) and cardiac troponin T (TnT) in COVID-19 patients (left) and relationship between 928 \ncardiac troponin T (TnT) and N-terminal pro-brain natriuretic peptide (NT-proBNP) (right). b, Data points 929 \nfrom the right side of the panel a and fitting parabola. c, Three-dimensional data visualisation was constructed 930 \nby mounting the value of hsCRP onto panel b. d, Linear regression analysis on the side surface of the 931 \nparabolic cylinder in panel c. The points were replaced with their average if the values could not be 932 \ndetermined due to overlapping (the points indicated by the left-pointing arrow and the error bar, which are the 933 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 55 of all 74 \naverage and the range of values, respectively). Panel a was re-used from Guo T et al. JAMA Cardiol. 2020; 934 \n5(7):811-818. Figure 1 https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7101506/figure/hoi200026f1/  935 \nCopyright © 2020 Guo T et al. JAMA Cardiology. Creative Commons Attribution License (CC-BY). 936 \nhttps://creativecommons.org/licenses/by/4.0/ 937 \n  938 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 56 of all 74 \n 939 \nExtended data figures & figure legends 940 \nExtended Data Fig. 1 941 \n 942 \n 943 \nExtended Data Fig. 1 | Overall framework of this study. We applied our concept to traveller's thrombosis 944 \nand COVID-19. These were similar in research history (see Supplementary discussion 1: history of traveller's 945 \nthrombosis & Supplementary discussion 2: research situations of COVID-19 related thrombosis). In the case 946 \nof traveller's thrombosis, we analysed a dataset collected by Chandra et al. and Philbrick et al4,7. In the case of 947 \nCOVID-19, we analysed a dataset collected by Matsushita et al7. Flow charts show data accept or reject flows. 948 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 57 of all 74 \nSince duplicating data, Matsushita et al. selected only eight studies data (25 studies included in initial web Figure 949 \n5)33. 950 \n  951 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 58 of all 74 \n 952 \nExtended Data Fig. 2 953 \n 954 \nExtended Data Fig. 2 | Unrecognised cyclic pattern of thrombosis onset after travel25. a, A bar graph 955 \nshowing the relationship between weeks after travel and the number of thrombosis onset in a figure reported 956 \nby Cannegieter et al25. b, Re-expressing as a two-dimensional bar graph avoiding the three-dimensional 957 \nrepresentation. c, Applying a damped wave by non-linear regression analysis. d, Extraction of damped wave 958 \npart by subtracting the monotonic decrease function. e, Dividing into 2 sub-group areas by the envelopes of 959 \nthe damped wave that touch the lower parts of the wave. f, Enlarged and added explanation of the ratio of the 960 \narea. Cannegieter et al.25 used the data up to week eight, and the ratio of subgroup 2 to the total number of 961 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 59 of all 74 \npatients (ratio of S2 to the area of S1 + S2) was 30.0%. In the integration for the infinite interval, it was 30.8%. 962 \nPeak shifts of the wave (peak position of the wave shifted from the original to the other) appeared when 963 \ncomparing panels d and f due to putting by regression curve located in the centre. Panel a was re-used from 964 \nCannegieter et al. PLoS Med. 2006; 3(8):e307. Figure 1. 965 \nhttps://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC1551914/figure/pmed-0030307-g001/  966 \nCopyright © 2006 Cannegieter et al. Creative Commons Attribution License. In 2006, the Creative Commons 967 \nAttribution 2.0 Generic, License (CC BY 2.0) was available. https://creativecommons.org/licenses/by/2.0/ 968 \n 969 \n  970 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 60 of all 74 \n 971 \nExtended Data Fig. 3 972 \n 973 \nExtended Data Fig. 3 | Curve fitting to the dataset reported by Philbrick et al4. a, data stratification by 974 \nPulmonary Embolism (PE) and Deep Vein Thrombosis (DVT). b, Application of S-shaped curve by 975 \nregression analysis to the stratified data. The value in the bracket (panel b) is the point of time converted from 976 \nthe time category (see Methods). Philbrick et al.4 reported the result of a systematic review with a table (list). 977 \nIn contrast, this visualising allows us to extract latent information. 978 \n  979 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 61 of all 74 \n 980 \nExtended Data Fig. 4 981 \n 982 \nExtended Data Fig. 4 | Re-analysis of the data in Table 1 by Clérel & Caillard27. a, A figure made by 983 \nClérel & Caillard27 showed a relationship between travel time and the thrombosis onset in the case of 984 \nstratification by medical history of thrombosis. b, The relationship between time and thrombosis (prepared 985 \nfrom Table 1 reported by Clérel & Caillard27). c, Correlogram (prepared from Table 1 reported by Clérel & 986 \nCaillard27). d, Age distribution by sex (made from Table 1 reported by Clérel & Caillard27). As shown in panel 987 \na, Clérel & Caillard27 summarised all the data for 12 hours or more, but there were two peaks (see panel b). 988 \nJudging from the age distribution (panel d), the number of women patients was more significant than that of 989 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 62 of all 74 \nmen, but there was no difference between the age ranges. In panel c, there was a periodic pattern. Panel a 990 \nreproduced from Clérel & Caillard. Syndrome thrombo-embolique de la station assise prolongée et vols de 991 \nlongue durée: l'expérience du Service Médical d'Urgence d'Aéroports De Paris. Bull Acad Natl Med. 1999; 992 \n183(5):985-997. discussion 997-1001. Figure 3. 993 \nCopyright © 1999 Elsevier Masson SAS. All rights reserved. Académie Nationale de Médecine. 994 \n 995 \n  996 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 63 of all 74 \n 997 \nExtended Data Fig. 5 998 \n 999 \nExtended Data Fig. 5 | Cyclic pattern of thrombosis onset appeared in a figure by Kelman et al28. a, A 1000 \nthrombosis onset distribution reported by Kelman et al28. b, The regression curve is located in the centre of all 1001 \naverage points (the points express the average of thrombosis onset during seven days). c, Curve fitting to the 1002 \nresidual data of the regression curve in panel b. d, Application of damped wave function and adding 1003 \ninterpretation of the results assuming some women started taking oral contraceptives (OC) in the timing of 1004 \ntravel. The observed cyclic pattern was relatively unclear than Cannegieter et al.25 (see Fig. 2). Noteworthy, 1005 \nthe thrombosis onset downed in the days before 90 days, and it seems to be the scheduled withdrawal period 1006 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 64 of all 74 \nof OC use. This figure was re-used and re-drawn from Kelman et al. BMJ. 2003; 327(7423):1072. Figure 1 1007 \nhttps://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC261739/figure/fig1/  1008 \nCopyright © 2003 BMJ Publishing Group Ltd. All rights reserved. The BMJ permission team thankfully 1009 \nconfirm this figure adaptation. Also, we obtained permission to re-use. 1010 \n 1011 \n  1012 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 65 of all 74 \n 1013 \nExtended Data Fig. 6 1014 \n 1015 \nExtended Data Fig. 6 | Thrombosis reported by Clérel & Caillard27 & our novel annotations. a, Clérel & 1016 \nCaillard mentioned that \"their incidence increases during the last years, corresponding to the growth of air 1017 \ntraffic and mainly to the increase of long duration without stop flight.\"27 c, Chronology of various guidelines 1018 \non HRT. In the newly figure (panel b), the increase in thrombosis was associated with the issuance time of 1019 \nguidelines for HRT. HRT was recommended for menopausal women in the 1990s, but its effectiveness was 1020 \nquestioned in the HERS trial (1998)31. Also, the risk was discovered in the WHI trial at the interim analysis 1021 \n(2002)32. It might be the effect of the publication on the HERS study (1998)31 that the increase of thromboses 1022 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 66 of all 74 \nwas relatively small in 1998 despite the publication of two documents recommended in 1997. Panel a was 1023 \nreproduced from Clérel & Caillard. Syndrome thrombo-embolique de la station assise prolongée et vols de 1024 \nlongue durée: l'expérience du Service Médical d'Urgence d'Aéroports De Paris. Bull Acad Natl Med. 1999; 1025 \n183(5):985-997. discussion 997-1001. Figure 1. 1026 \nCopyright © 1999 Elsevier Masson SAS. All rights reserved. Académie Nationale de Médecine. 1027 \n 1028 \n  1029 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 67 of all 74 \n 1030 \nExtended Data Fig. 7 1031 \n 1032 \nExtended Data Fig. 7 | Data cut-off dates in each study cited by Matsushita et al33. The data acquisition 1033 \nperiod in each study was displayed in Gantt chart format. The date display format is year-month-day. The 1034 \ncorrespondence between numbers and authors is as follows: No.2: Cao et al. (Cao, J. et al., Intensive Care 1035 \nMed. 2020;46(5):851-853.)59, No.7: Deng et al. (Deng, Y. et al., Chin Med J (Engl). 2020;133(11):1261-1036 \n1267.)60, No.8: Guan et al. (Guan, W.J. et al., N Engl J Med. 2020;382(18):1708-1720.)61, No.19: Wang D. et 1037 \nal. (Wang, D. et al., JAMA. 2020;323(11):1061-1069.)62, No.20: Wang L. et al. (Wang, L. et al., J Infect. 1038 \n2020;80(6):639-645.)63, No.21: Wu et al. (Wu, C. et al., JAMA Intern Med. 2020;180(7):934-943.)64, No.25: 1039 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 68 of all 74 \nZhou et al. (Zhou, F. et al., Lancet. 2020;395(10229):1054-1062.)66. Abbreviations: ARDS (Acute Respiratory 1040 \nDistress Syndrome), ICU (Intensive Care Unit). The number in parentheses means median age. The number in 1041 \nthe bracket means standard deviation or interquartile range. 1042 \n  1043 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 69 of all 74 \nExtended Data Fig. 8 1044 \n 1045 \nExtended Data Fig. 8 | Bimodal distributions & tiled parabola in COVID-19 patients. a, Guo et al. JAMA 1046 \nCardiol. 2020; 5(7):811-818. Figure 1B 1047 \nhttps://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7101506/figure/hoi200026f1/  1048 \nCopyright © 2020 Guo T et al. JAMA Cardiology. Creative Commons Attribution License (CC-BY). b, 1049 \nMarginal distribution of the scatter plot data. c, Wang et al. Front Cardiovasc Med. 2020; (7): 147. Figure 1 1050 \n(upper, x-axis: troponin I, pg/mL; y-axis: BNP, pg/mL; lower, x-axis: troponin I, pg/mL; y-axis: 1051 \nlymphocyte, %)37. https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7477309/figure/F1/  1052 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 70 of all 74 \nCopyright © 2020 Wang, Zheng, Tong, Wang, Lv, Xi and Liu. CC BY License. d, Caro-Codón et al. Eur J 1053 \nHeart Fail. 2021; 23(3):456-464. Figure 1B (x-axis, LN (troponin I))40. 1054 \nhttps://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC8013330/figure/ejhf2095-fig-0001/  1055 \nCopyright © 2021 European Society of Cardiology. All rights reserved. This Figure can be used for 1056 \nunrestricted research re-use and analysis in any form or by any means with acknowledgement of the original 1057 \nsource as part of the COVID-19 public health emergency, for the duration of the emergency. e, Demir et al. 1058 \nAm J Cardiol. 2021; 147:129-136. Figure 2 (upper: admission; lower: peak measurements; x-axis: troponin T, 1059 \nng/L)41. https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7895690/figure/fig0002/  1060 \nCopyright © 2021 Elsevier Inc. All rights reserved. This figure is granted for unrestricted research re-use and 1061 \nanalyses in any form or by any means with acknowledgement of the original source by Elsevier for as long as 1062 \nthe COVID-19 resource centre remains active. f, Virtual example on regression analysis (see Supplementary 1063 \ndiscussion 5: misuse of linear regression analysis). In panel b (also c, d, and e), the histogram was bimodal 1064 \n(marked \"A\" and \"B\"). The crescent-shape pattern closely resembled the ST-segment elevation myocardial 1065 \ninfarction group pattern that appeared in the study by Budnik et al36. 1066 \n 1067 \n  1068 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 71 of all 74 \n 1069 \nExtended Data Fig. 9 1070 \n 1071 \nExtended Data Fig. 9 | Three subgroup patterns appeared in a figure reported by Guo et al35. a, A 1072 \nscatter plot showing the relationship between cardiac troponin T (TnT) and N-terminal pro-brain natriuretic 1073 \npeptide (NT-proBNP) in a patient with COVID-1935. b, Scatter plot to investigate the relationship between 1074 \nbrain natriuretic peptide (BNP) and cardiac troponin I (cTnl) in healthy subjects reported by Sugawa et al38. c, 1075 \nThe visible points that exceeded the value of 26.2 pg/mL (red line in panel b) were re-plotted with parabola 1076 \n(not accurate regression analysis). d, Visible points in the figure reported by Guo et al.35 with parabolas. e, 1077 \nTransposed panel d for easy comparison. f, Group 1 in the small coordinate system (centre of gravity as the 1078 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 72 of all 74 \norigin of the coordinate system). g, Group 2 in the small coordinate system. h, Group 3 in the small coordinate 1079 \nsystem. In panel f-h, the upper curve is expressed by a quadratic function, in which a coefficient of the 1080 \nquadratic term is equal to a value of the coefficient of the quadratic term for the solid curve multiplied by 3/2. 1081 \nIn the lower curve, a coefficient of the quadratic term of the solid curve multiplied by 2/3. Most data points 1082 \nlocated inside the crescent-shaped region enclosed by the parabolas, but the reason was unclear. Panel a was 1083 \nre-used from Guo T et al. JAMA Cardiol. 2020; 5(7):811-818. Figure 1B 1084 \nhttps://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7101506/figure/hoi200026f1/ Copyright © 2020 Guo T 1085 \net al. JAMA Cardiology. Creative Commons Attribution License (CC-BY). 1086 \nhttps://creativecommons.org/licenses/by/4.0/ Panel b was re-used from Sugawa et al. Sci Rep. 2018; 1087 \n8(1):5120. Figure 1. https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC5865159/figure/Fig1/ Copyright © 1088 \n2018 The Authors. CC-BY 4.0 License 1089 \n 1090 \n  1091 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 73 of all 74 \n 1092 \nExtended Data Fig. 10 1093 \n 1094 \nExtended Data Fig. 10 | A three-dimensional plot reconstructed from the data reported by Guo et al35. 1095 \na, Scatter plot showing the relationship between high sensitive C-reactive protein (hsCRP) and troponin T 1096 \n(TnT) 35. b, Re-drawn scatter plot with a vertical line around hsCRP = 200 mg/mL = 2.0 × 102 mg/mL. c, 1097 \nEnlarged subgroup 3 in the panel d of Extended Data Fig. 9 (data exceeding hsCRP = 200 mg/mL are 1098 \nindicated by red, data not exceeding hsCRP = 200 mg/mL are indicated by blue). d, Enlarged subgroup 3 of 1099 \nthe panel d in Extended Fig. 9 with the foot of the perpendicular from each data point to the parabola. e, The 1100 \nhsCRP value of each patient placed on panel d (shown as a three-dimensional plot). f, The side surface of the 1101 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint \n\n  p. 74 of all 74 \nparabolic cylinder. The point of TnT = 1.31 observed in panel b is not included in panel c, and the point of 1102 \nTnT = 1.71 in panel c is not included in panel b (inconsistent). In panel e, the projection of the data points 1103 \nonto the parabola was used as new points. In panels, e and f, some points of CRP value could not be 1104 \ndetermined because of overlapping, so those points were replaced with the average value (the points indicated 1105 \nby the left-pointing arrows and the error bar, which are the average values and the range of values, 1106 \nrespectively). Panel a was re-used from Guo et al. JAMA Cardiol. 2020; 5(7):811-818. Figure 1. 1107 \nhttps://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7101506/figure/hoi200026f1/ Copyright © 2020 Guo T 1108 \net al. JAMA Cardiology. Creative Commons Attribution License (CC-BY). 1109 \nhttps://creativecommons.org/licenses/by/4.0/ 1110 \n 1111 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}