Travel-related Twenty-eight Days Cyclical Thrombosis and Subgroups of COVID-19 Cardiac Biomarker Data: Novel Review Strategy and Meta-analysis Method

132 Using pattern recognition of hyperbolic shape as a key to discoveries in exploratory data analysis, 133 we started research for traveller's Thrombosis and COVID-19, and as a result, our concept of the geometrical 134 viewpoint allowed us to discover many unrecognised patterns. Therefore, approaching data from geometry 135 and exploring data focusing on hyperbolic patterns can be a practical option for researchers. 136 In traveller's thrombosis, we obtained consistent results from two analyses (7.1 hours and 11.8 hours 137 vs 9.2 hours and 12.1 hours) (Fig. 2, b, Extended Data Fig. 3). The discrepancy between the value of 7.1 138 hours and 8.5 hours seems to be explained by the miscalculation found in the data review process (see 139 Methods). Although many researchers have led controversial discussions based on a single curve, our results 140 implied two S-curves. We hypothesised two high-risk periods and two types of high-risk groups, which may 141 have to be considered with the "factor V Leiden paradox"42 (Supplementary discussion 3: two high-risk 142 periods and two types of high-risk groups?). 143 Another noteworthy point is the cyclic patterns (wave) (Fig. 2, c, d) and the raw-risk period just 144 before 90 days in Kelman et al.27 (Extended Data Fig. 5). In Cannegieter et al.24, the cyclic pattern 145 disappeared around 90 days, consistent with that the high-risk period in oral contraceptive (OC) use was the 146 first three months (90 days)42. Also, the above raw-risk period explains extended-use type OC, which has a 147 planned drug withdrawal, such as 84 active days and seven placebo days43-45. In addition, the uptrend in the 148 data by Kelman et al.27 could be explained by depot agent type OC administrated 90 days cycle46. So, our 149 findings imply that the 28 days cycle OC is attributable to the cyclic pattern, and both cycle type and 150 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 9 of all 74 extended-use type OC use is triggered by travel. An opposition may arise considering that both of relative risk 151 reported by Martinelli et al.22 and Cannegieter et al.24 were low (Fig. 2, b), but it seems to be explained by 152 bias derived from using their partner as control (Supplementary discussion 4: OC users and bias by their 153 partner). 154 A halfway cycle (17.9 days) in Kelman et al.28 was explained by a mixture of the 28 days OC cycle 155 and a type of HRT cycle (sequential type; daily estrogen dosing and 10–14 days progestogen)46. Also, another 156 problem is that the wave in Cannegieter et al. was clear (thrombosis onset: March 1999-March 2000)25. 157 However, the wave in Kelman et al. (1981-1999)28 was not clear despite the exposures in Cannegieter et al. 158 (air travel, train, bus, and 48.5% car trip)25 was more complex than Kelman et al. (only air travel)28, was 159 answered by the history of HRT. In Kelman et al.28, there might be both young women taking OC and 160 menopausal women receiving HRT, but only OC users might remain after the HERS study reported risk of 161 HRT (1998)31, which was assisted by the growth of thrombosis onset slowed at the HERS study31 (Extended 162 Data Fig. 6). Also, the above cars might be honeymoon cars. Although it was not decreasing, the result might 163 be caused by some woman's desire for joyful travel to Paris with HRT. 164 Our thought on pharmacoepidemiology in the real world, starting OC or HRT was triggered by 165 travel and decision making of HRT connected to travel, which means that well-planned usage based on risk 166 diversification may allow more safe use of OC and HRT. 167 In appreciation of our ideas to COVID-19, the dataset grouping by Matsushita et al.32 matched the 168 grouping by data cut-off dates (Extended Data Fig. 7), and age structure diverged from middle age to mature 169 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 10 of all 74 and elderly, which was consistent with the hypothesis that COVID-19 spread from the seafood market. 170 Middle-aged people might go into the workforce for manual labour treating fish containers, mature people 171 might want to select IT jobs, and elderly people might stay in the house. 172 Interestingly, our analysis of the data by Guo et al.34 showed three clusters of subgroups, and one of 173 those formed the tilted parabola. Also, the patterns matched the other studies (Fig. 4 a, b, Extended Data Fig. 174 8 & Extended Data Fig. 9)36-41. Considering the study by Budnik et al.36, those subgroups may have different 175 biological mechanisms. 176 Additionally, we found patterns on the side surface of this parabolic cylinder (Fig. 4, c, d, & 177 Extended Data Fig. 10). A paradoxical result on troponin was obtained just before the pandemic48, and 178 Meisel et al. mentioned that the CRP to troponin ratio (CRP/troponin) could serve to differentiate between 179 myopericarditis and acute myocardial ischemia (AMI), although not the study on COVID-19 patients. In 180 COVID-19, Caro-Codón et al. reported interesting behaviour of CRP35. Also, a meta-analysis by Lagunas-181 Rangel reported that the lymphocyte‐to‐C‐reactive protein ratio (LCR) level, which was not a simple 182 measurement value but a ratio, might be related to an inflammatory process47. 183 The above studies might imply complex data structures in 2-dimensional and 3-dimensional scatter 184 plots consisting of biomarker values, and our findings may serve cardiac biomarkers' research field. 185 Supplementary, we explain the misuse of linear regression analysis in the study by Guo et al.35 186 (Supplementary discussion 5: misuse of linear regression analysis). 187 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 11 of all 74 Although many studies on visualization of meta-analysis have been conducted48, our simple idea 188 (hyperbolic pattern) has not been proposed. As named “error”, researchers usually view an error bar 189 negatively. Also, in the wheel's history, an invention of carriages, which was achieved by arranging the 190 wheels in parallel, appeared in ancient times, but the idea of the bicycle, which was innovatively arranging 191 wheels vertically, had not been conceived before the 19th century49,50. Those mental blocks might have made 192 it hard to imagine that vertical error bars provided information on a horizontal axis. 193 Evaluating our ideas, we discovered many oversights which were entirely beyond the initial scope. 194 Appearing overlapped hyperbolic patterns may show poor data review and analysis. Currently, pattern 195 recognition based on Artificial Intelligence (AI) detects cancer sites from images. Considering our discoveries 196 by an analogy that Newton's theory enabled the prediction of a planet's orbit, implementing our idea (a kind of 197 mathematical model or theory) in an AI system might assist another discovery of clinical issues. 198 199 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 12 of all 74 200 Main references 201 1 Van Noorden, R. Journals adopt AI to spot duplicated images in manuscripts. Nature, 202 doi:10.1038/d41586-021-03807-6 (2021). 203 2 Adi, Y., Bayliss, S., Rouse, A. & Taylor, R. S. The association between air travel and deep vein 204 thrombosis: systematic review & meta-analysis. BMC Cardiovasc Disord 4, 7, doi:10.1186/1471-205 2261-4-7 (2004). 206 3 Kuipers, S. et al. Travel and venous thrombosis: a systematic review. J Intern Med 262, 615-634, 207 doi:10.1111/j.1365-2796.2007.01867.x (2007). 208 4 Philbrick, J. T., Shumate, R., Siadaty, M. S. & Becker, D. M. Air travel and venous 209 thromboembolism: a systematic review. J Gen Intern Med 22, 107-114, doi:10.1007/s11606-006-210 0016-0 (2007). 211 5 Spencer, F. A. 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328 1. Numerical experiment 329 Unavoidably, this study conducted a numerical experiment to determine what curve approximates an 330 edge of a confidence limit (Fig. 1, c). 331 Generally, a dose-response relationship often indicates an S-curve. Considering the distribution of a 332 population at thrombosis risk and the cumulative thrombosis onset, each of those is monomodal distribution 333 and the S-shaped curve, respectively. So, we decided to use the sigmoid function, which is generally used in 334 curve fitting to dose-response data, as the formula for the S-curve fitting. 335 Contrastively, the curve expressing the end of a confidence interval (confidence limit) is a sum of 336 the S-shaped curve and U-shaped curve because the width of the confidence interval narrows near the centre 337 of distribution due to many cases around the points. Similarly, the confidence interval widens at the 338 distribution edge due to the small number of cases (see Fig. 1, d). 339 Based on the above consideration, we selected the parabola as a candidate for the U-shaped curve 340 because this curve was mathematically easy to handle (just junior high school level mathematics). So, we 341 examined the validity of using parabola. However, mathematical proof of our conjecture was difficult because 342 normal distribution was continuous probability distribution. So, we used a kind of discrete probability 343 distribution, binomial distribution, to prove our conjecture experimentally because normal distribution could 344 be approximated by binominal distribution. This idea was thinking in reverse of the usual statistical technique. 345 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 20 of all 74 To generate binomial distribution data, we used the "BINOM.DIST" function, which is a function 346 for calculating the probability of binomial distribution in a kind of spreadsheet software, Microsoft Excel○R 347 (Microsoft Corporation, Redmond, Washington, US). 348 349 2. Equations for regression analysis 350 The equations for the S-shaped curve, the upper end of the confidence limit, and the lower end of the 351 confidence limit, those equations are the following (1), (2), and (3), respectively. Note that in the below 352 equations, the coefficient L is generally set as 1. So we used this equation under the condition as L=1 unless 353 there is some reason. 354 355 𝑦 = { 𝐾1 1+e𝐿(𝑥−𝑀) + 𝐾2} (1) 356 𝑦 = { 𝐾1 1+e𝐿(𝑥−𝑀) + 𝐾2} + (𝑎𝑥2 + 𝑏𝑥+ 𝑐) (2) 357 𝑦 = { 𝐾1 1+e𝐿(𝑥−𝑀) + 𝐾2} − (𝑎𝑥2 + 𝑏𝑥+ 𝑐) (3) 358 359 Also, a complete square of the quadratic function that represents the parabola is the following equation (4). 360 361 𝑎𝑥2 + 𝑏𝑥+ 𝑐 = 𝑎 (𝑥 + 𝑏 2𝑎) 2 − 𝑏2−4𝑎𝑐 4𝑎 (4) 362 363 Besides, the point P is the apex of the parabola is the following (5). 364 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 21 of all 74 365 P (− 𝑏 2𝑎 , − 𝑏2−4𝑎𝑐 4𝑎 ) (5) 366 367 The following equations are the formula that expresses the outline of the distribution obtained by differential 368 calculation on the S-shaped curve (6). 369 370 𝑑𝑦 𝑑𝑥 = − 𝐾1𝐿𝑒𝐿(𝑥−𝑀) {𝑒𝐿(𝑥−𝑀)+1} 2 (6) 371 372 3. Analysis tools in this study 373 Reading values from the published figures were performed using the public domain software ImageJ 374 in the public domain (https://imagej.net/Welcome). Regression analysis was performed using Python (Python 375 Software Foundation, Delaware, USA https://www.python.org/psf/records/incorporation/). At this time, 376 Python's functional modules NumPy (NumFOCUS sponsored open-source project, https://numpy.org/), 377 Pandas (NumFOCUS sponsored open-source project, https://pandas.pydata.org/), SciPy (NumFOCUS 378 sponsored open-source project, https://www.scipy.org/) and Matplotlib (NumFOCUS sponsored open-source 379 project, https://matplotlib.org/) were also used. Additionally, a function as "Chart option" of Microsoft 380 Excel○R , which was shown in the "Trendline Options" section contained in "Format Trendline," was used. In 381 the case of symbolic formula manipulation was required, formula manipulation software wxMaxima (Project 382 Maxima maintained by 27 volunteers, https://maxima.sourceforge.io/) was used. 383 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 22 of all 74 384 4. Analysis 1A (dataset: Chandra et al.)7 385 1) Data review to validate eligibility for regression analysis 386 a. The process of data review in this analysis 387 As the first step, we performed data mapping. In the figure of meta-regression analysis reported by 388 Chandra et al.7, it was not described what the data points correspond to the four original papers (Martinelli et 389 al., 2003; Parkin et al., 2006; Cannegieter et al., 2006 and Kuipers et al., 2007)23-26. So, we measured the 390 positions of each point and compared them with the original descriptions in the papers. In the second step, we 391 performed a data review, which was an examination of the accuracy of cited values, and appropriately from 392 the viewpoint of biomedicine. Our re-calculation confirmed the odds ratio (OR), confidence interval of the 393 OR, and adjusted OR. In examining the values, we did not confirm Chandra et al.7 and the four authors23-26 394 because Chandra et al. described that each author did not respond to inquiry7. As a final step, we performed 395 regression analysis using the eligible data for using regression analysis. 396 397 b. Data review 398 The data review showed some problems in the research reported by Cannegieter et al. and Martinelli 399 et al.23,25, and we excluded those data in the regression analysis. Also, there was a point to notice in the data 400 reported by Parkin et al.24 (see Extended Data Fig. 1). 401 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 23 of all 74 In confirming the accuracy of the values, there were no problems with the two studies (Kuipers et al. 402 and Cannegieter et al.)25,26, but there were problems in the other two studies (Martinelli et al. and Parkin et 403 al.)23,24. 404 In Martinelli et al.23, the problem was gender imbalance and unadjusted OR. In addition, although 405 there were no explanations for the odds ratio described in the text cited by Chandra et al7, the above OR was 406 presumed to be an unadjusted value, judging from the context. Comprehensively, judging from both 407 calculation results and the original article, the odds ratio cited by Chandra et al.7 was strongly suspected of 408 being an unadjusted value. 409 In Parkin et al.24, there was a discrepancy between the OR and the described OR calculated by us. 410 Also, it was suspected that cells in the cross table were mistaken (e.g., in the table of Fig. 1a, the cell for 411 control and the cell for total were mistaken). However, the error bar's length was relatively small since the 412 total number of cases was notably smaller than other studies. So, qualitatively, it could only be used to group 413 data to find hyperbolic patterns. 414 In confirming from the viewpoint of the biomedicine side, there were no problems with two studies 415 (Kuipers et al. and Parkin et al.)24,26, but there were problems in the other two studies (Martinelli et al. and 416 Cannegieter et al.)23,25. In Martinelli et al.23, judging from the subtitle, "interaction with thrombophilia and 417 oral contraceptives," oral contraceptive (OC) bias was suspected. Initially, the study aimed to evaluate the 418 interaction between OC use and travel. Considering the above, the OR had to be considered a value that 419 contained a strong bias (see also Supplementary discussion 4: OC users and bias by their partner). In 420 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 24 of all 74 Cannegieter et al.25, the data contained car travel, and the other studies contained only air travel. So exposure 421 factors were different, and there was a problem from the viewpoint of comparability (e.g., air pressure, 422 dehydration, and time difference). Also, Chandra et al.7 showed two types of analysis results, including 423 Cannegieter et al.25 and not. Besides, the cyclic pattern could be explained by OC use was observed (see Fig. 424 2, c & d). Also, Cannegieter et al.25 did not adjust the OR by sex and OC use. So, it was strongly suspected 425 that there was a strong bias derived from the different types of exposure factors and OC. 426 Judging from the above two types of data reviews, we excluded the data reported by two studies 427 (Martinelli et al. and Parkin et al.)23,24. In the data reported by Kuipers et al.26, there was no problem. The 428 data reported by Parkin et al.24 seemed to be used only for the purpose described above. 429 Interestingly, in four studies used in meta-regression analysis by Chandra et al.7, all the first authors' 430 names seem to be women's names ("Suzanne" Cannegieter25, "Saskia" Kuipers26, "Ida" Martinelli23, "Lianne" 431 Parkin24). 432 433 2) Regression Analysis 434 For the data judged as eligible, hyperbolic patterns were visually searched, and each data point was 435 grouped into two groups. Then, a non-linear regression analysis using the formulas above was performed. In 436 the fitting of the U-shaped curve, since there were many unknown coefficients for the number of data (there 437 are seven unknowns, K1, K2, M, a, b, and c. in the equations (2) and (3)), the S-curve was fitted first, and the 438 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 25 of all 74 remaining unknown coefficients (a, b, c) were fitted to the residuals of the S-curve fitting (see equation (2) 439 and (3)). 440 441 3) Additional analysis 442 As described above, the cyclic pattern in the data reported by Cannegieter et al.25 was observed, and 443 we performed additional analysis. To conduct an appropriate non-linear regression analysis, we made an 444 equation by combining two types of equations. The exponential decay equation was usually used to express 445 radioactive decay in physics and clearance in medicine. The other was a trigonometric function (sine function) 446 to express waveforms. The equation is shown in as below equation (7). Also, this scientific model (model 447 formula) was used to estimate the ratio of patients by integral calculation. 448 449 𝑦 = 𝑁1𝑒−𝜆1(𝑡−𝑏) + 𝑁2𝑒−𝜆2(𝑡−𝑏) Asin{𝐵(𝑡 − 𝑏)} (7) 450 451 The data reported as a bar graph was weekly data (see Fig. 2, c and Extended Data Fig. 2). So, the 452 week was converted into the number of days before the analysis, such as; the day getting off the vehicle was 453 set 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 set as days 4 + 7 × two, and the Nth week was set as days 4 + 7 × N. 455 Supplementary, according to the original description by Cannegieter et al.25, 68 patients developed 456 thrombosis in the first week, and "233" patients developed thrombosis within eight weeks after travelling. 457 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 26 of all 74 However, there was a slight discrepancy in the values read from the bar graph. The value in our measurement 458 within eight weeks after travelling was "234", but the effect of only one patient was allowed to be regarded as 459 small (the description of 68 patients was the same.). 460 Cannegieter et al. described the number of patients who travelled with their partners to evaluate the 461 effect of OC (Cannegieter et al., PLoS Med. 2006 Aug;3(8):e307., Table 2)25. We found some mismatches for 462 the number of patients in the table, and the overall discrepancy was only one person by offset, and 463 Cannegieter et al. described that there were derived from missing value25. The mismatch between our 464 measurement and description might be related to the described explanation. 465 466 5. Analysis 1B (dataset: Philbrick et al.)4 467 1) Dataset search and data review 468 a. Dataset search 469 To validate the result of analysis 1A, we searched another dataset from meta-analysis or systematic 470 review on the traveller's thrombosis. To conduct this search, we used PubMed® setting the following search 471

"economy class syndrome [Title] " OR "traveler's [Title] AND thrombosis [Title]" OR "traveler's 472 [Title] AND thromboembolism [Title]" OR "flight [Title] AND thrombosis [Title]" OR "flight [Title] AND 473 thromboembolism [Title]" OR "flight-related [Title] AND thrombosis [Title]" OR "flight-related [Title] AND 474 thromboembolism [Title]" OR "travel [Title] AND thrombosis [Title]" OR "travel [Title] AND 475 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 27 of all 74 thromboembolism [Title]" OR "travel-related [Title] AND thrombosis [Title]" OR "travel-related [Title] AND 476 thromboembolism [Title]" (Filters: Meta-Analysis, Systematic Review). 477 As a result, we obtained the eight articles (da Silva LF et al. J Vasc Bras. 2021 10;20:e20200164; 478 Benhaberou-Brun Perspect Infirm. 2010 7(3):16-7; Chandra et al. Ann Intern Med. 2009 151(3):180-90; 479 Kuipers et al. J Intern Med. 2007 262(6):615-34; Philbrick et al. J Gen Intern Med. 2007 22(1):107-14; Hsieh 480 et 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 Cardiovasc Disord. 2004 19;4:7). 482 Subsequently, we selected articles containing available abstracts on PubMed® online, confirming the 483 contents. As a candidate for our analysis, we selected a systematic review reported by Philbrick et al.4. The 484 study was taken up by the ACP Journal Club of the American College of Physicians5 and another journal 485 club10. So, it seemed to be a highly reputed study. Therefore, we regarded that the dataset contained in the 486 research was suitable for validation. 487 Also, the research contained two lists of tables, one of which was a cohort studies dataset, and the 488 other was the case-control studies. However, the case-control studies had many different exposure factors. So, 489 we decided to use only the cohort studies dataset. 490 491 b. Data review 492 In the data review process, we reviewed the table containing ten cohort studies27,28,51-58 and found 493 seven eligible cohort studies27,51,54-58 for regression analysis. In Gajic et al. and Kelman et al., the only 494 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 28 of all 74 distances were described28,52, and Hughes et al. reported duration data for not per one flight (e.g., mean 39.4 495 h)53, so time data for regression analysis was unavailable. 496 Additionally, although Philbrick et al. described that incidence per million was 0.5 in table 2 of their 497 article4, the number was incorrect because it was based on only 1998. In the original description, Clérel & 498 Caillard mentioned that "According to the number of the passengers landing in the Aeroports de Paris, the 499 incidence during 1998 is 0.5 per million passengers"27. 500 501 2) Regression Analysis 502 For the seven studies, data stratified by Pulmonary Embolism (PE) and Deep Vein Thrombosis 503 (DVT), regression analysis was performed using an S-shaped curve formula (see equation (1)). In the case of 504 curve-fitting on DVT data, we cancelled the setting of coefficient L=1 to increase the degree of freedom of the 505 S-curve (Extended Data Fig. 3, b). To show the error bar in the figure (Extended Data Fig. 3), we did not 506 use the values of confidence limits described in the report by Philbrick et al.4, but values were re-calculated 507 from the number of cases using Wilson's method because data review result described above showed the error 508 of values at the citation. 509 In the seven studies, not OR or relative risk (RR), only the data indicating the incidence rate of 510 thrombosis was available. So, the hyperbolic pattern did not appear in the figure theoretically, and we 511 performed only the S-shaped curve fitting. This mechanism is explanted from the following calculation on a 512 confidence interval of a ratio. 513 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 29 of all 74 The formula for a 95% confidence limit of a ratio using binomial approximation is expressed by the 514 following formula: P is a ratio, and N is the number of trials. 515 516 𝑃 − 1.96 √𝑃(1−𝑃) √𝑁 ≤ 𝑃 ≤ 𝑃 + 1.96 √𝑃(1−𝑃) √𝑁 (8) 517 518 In the above equation, the fraction's numerator is not a constant value and does not depend on only the N, 519 which is associated with a data point's position in a population (see Fig. 1). 520 In this regression analysis, converting time categories to time points was necessary, so we performed 521 this in three directions. The first one was taking the midpoint if the category was not the end of a category 522 sequence (e.g., 10-15 h could be converted to 12.5 h). The second one was taking the midpoint between the 523 time point of 0 and the lower limit of the category if the category was the lower end of a category sequence 524 (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 the value of the midpoint between the time point of 0 and the lower limit of the category sequence if the 526 category 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 Details of conversions are shown below (the original time category is shown in brackets). 528 Belcaro et al. [10-15 h]: 12.5 h (Belcaro, G. et al., Angiology. 2001;52(6):369-74.)51; Clérel et al. 529 [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 h]: 11 h; Lapostolle et al. [ 12 h]: 1.5 h, 4.5 h, 7.5 h, 10.5 h, 13.5 h (12 + 1.5 = 13.5 531 h) (Jacobson, B.F. et al., S Afr Med J. 2003;93(7):522-8.)54; Pérez-Rodríguez et al. [ 8 h]: 3 h, 7 532 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 30 of all 74 h, 11 h (8 + 3 = 11 h) (Pérez-Rodríguez, E. et al., Arch Intern Med. 2003;163(22):2766-70.)56; Schwarz et al. 533 2002 [> 8 h]: 12 h (midpoint of 0-8 h is 4 h and 8 + 4 = 12 hours) (Schwarz, T. et al., Blood Coagul 534 Fibrinolysis. 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 hours) (Schwarz, T. et al., Arch Intern Med. 2003 2003;163(22):2759-64.)58. 536 537 3) Additional analysis 538 a. Regression analysis (data: Kelman et al.28) 539 In the review process, a cyclic pattern was observed. So, we worked on regression analysis. 540 Considering that onset of thrombosis tends to increase again, an equation upward-sloping curve was added to 541 equation (7). The equation is the following (9). 542 543 𝑦 = 𝑁1𝑒−𝜆1(𝑡−𝑏) + 𝑁2𝑒−𝜆2(𝑡−𝑏) Asin{𝐵(𝑡 − 𝑏)} + (𝑎𝑥2 + 𝑏𝑥+ 𝑐) (9) 544 545 b. Analysis by using correlogram (data: Clérel & Caillard27) 546 We considered using the "correlogram" in this study because it was more practical than observing 547 the original data's fluctuation. Periodic fluctuation patterns may be unclear when looking at the original data 548 alone, but potential patterns can be obtained using a correlogram, a data visualization method for analyzing 549 time-series data. Also, as the correlation coefficient plotted on the correlogram, we decided to use Spearman's 550 rank correlation coefficient instead of Pearson's product-moment correlation coefficient, which is easily 551 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 31 of all 74 affected by outliers. Also, we performed a non-linear regression analysis using a mathematical formula (10) 552 that includes two sine functions. 553 554 𝑦 = 𝑛1 sin{𝑎1(𝑥 − 𝑏1)} + 𝑛2 sin{𝑎2(𝑥 − 𝑏2)} (10) 555 556 In correlogram creation, firstly, a combination of data (data X1, data X1) was created by arranging 557 the original time series data (data X1) and a new combination (data X1, data X1') was created by shifting one 558 of them. Secondary, the correlation coefficient (also called the auto-correlation coefficient) between the 559 original time-series data (data X1) and the sifted time-series data (data X1'), except at the ends of two types of 560 time-series data where some correspondence could not be formed. By repeating shifting the time string data 561 and calculating the correlation coefficient, the locus of the correlation coefficient becomes the shape of waves. 562 Firstly (original waves of time strings are overlapped), the correlation coefficient is 1, and the value of the 563 correlation coefficient gradually decreases as the distance of the overlap increases. Finally (the wave is 564 inverted), the correlation coefficient is -1. 565 In this study, since the risk of developing thrombosis is expected to increase as travel time increases 566 by cumulative exposure to environmental risk factors, it was necessary to investigate whether the fluctuations 567 in the number of patients really reflect the periodicity by confirming the fluctuation of the percentage of onset 568 patients to the total number of passengers to examine whether the fluctuation reflects the increase or decrease 569 in the number of passengers. However, this confirmation could not be made because data on the total number 570 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 32 of all 74 of passengers was not available. So, we focused on a method that suppressed the influence of the height of the 571 wave and evaluated only curved shapes. Therefore, we decided to draw a correlogram that reduced wave 572 height by the property of the correlation coefficient, which fluctuates only between -1 and 1. 573 However, Pearson's product-moment correlation coefficient has a weakness: it is easily affected by 574 outliers. Also, as the progress of shifting the one side of the data string against the original data, their 575 correspondence decreases. In other words, the number of data that can be used to calculate the correlation 576 coefficient gradually decreases. This problem may cause considerable variation between the calculated 577 correlation coefficients. Also, the thrombosis onset was recorded in 1-hour increments, and the length of the 578 data was limited to 24 hours (24 data points). Therefore, instead of Pearson's product-moment correlation 579 coefficient, we decided to create a correlogram using Spearman's rank correlation coefficient. 580 581 6. Analysis 2 (dataset: COVID-19)33 582 1) Dataset search and data review 583 c. Dataset search 584 To apply our idea to COVID-19 problems, one of the authors (KK) searched hyperbolic patterns 585 using a search service Google (https://www.google.com/) provided by Google Inc., which allows displaying 586 search results as "images." The search keyword was "COVID-19 AND Meta-analysis". In the case of 587 displaying bubble charts instead of the error bars, the size of the bubble chart (inversely proportional to the 588 length of the error bars) was converted in mind. Consequently, we selected a suspicious study reported by 589 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 33 of all 74 Matsushita et al. (Matsushita, K. et al., Glob Heart. 2020;15(1):64.)33 that included eight research papers in 590 Figure 559-66. 591 592 d. Data review 593 As in the case of Analysis 1, we reviewed to evaluate numerical accuracy and appropriateness from 594 the viewpoints of biomedicine. Since Matsushita et al.33 originally made web Figure 5 and excluded 17 595 studies35,67-82 from avoiding duplication of studies in Wuhan city in the making of Figure 5, we inspected both 596 of studies in Figure 5 (8 studies) and only in web Figure 5 (17 studies). 597 Based on the results shown below, considering the issue of comparability, we excluded the data 598 reported by Yuan et al.65 and Wang L. et al63. Also, we re-calculated age difference using data reported by 599 Guan et al. 61 (see Extended Data Fig. 1). 600 As a side note, the numbers assigned to each point in figure 3 were the same numbers described in 601 the original figure by Matsushita et al.33, and the correspondence relationship is the following (Fig. 3): No.2: 602 Cao 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 Med J (Engl). 2020;133(11):1261-1267.)60, No.8: Guan et al. (Guan, W.J. et al., N Engl J Med. 604 2020;382(18):1708-1720.)61, No.19: Wang D. et al. (Wang, D. et al., JAMA. 2020;323(11):1061-1069.)62, 605 No.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 Intern Med. 2020;180(7):934-943.)64, No.23: Yuan et al. (Yuan, M. et al., PLoS One. 2020;15(3):e0230548)65, 607 No.25: Zhou et al. (Zhou, F. et al., Lancet. 2020;395(10229):1054-1062.)66. 608 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 34 of all 74 609 (i) No.8 Guan et al. (Guan, W.J. et al., N Engl J Med. 2020;382(18):1708-1720.)61 610 We found a matter of consideration in the data reported by Guan et al61. Initially, features of that 611 data differed from the other studies, which contained only cases reported from Wuhan city. In contrast, the 612 data reported by Guan et al.61 contained cases outside of Wuhan city. Also, regarding the situation of the early 613 pandemic, there were concerns about the presence of patients who could not take appropriate medication, 614 especially in non-urban areas. Also, Matsushita et al.33 did not use the data divided into the severe and non-615 severe groups by Guan et al.61 but used the data divided into yes and no by Guan et al.61 using "Presence of 616 Primary Composite End Point", which means entry to the intensive care unit (ICU), use of mechanical 617 ventilation, or death. 618 Since Cao et al. (Wuhan University Zhongnan Hospital in Wuhan; affiliation of Dr Jianlei Cao: 619 Department of Cardiology)59 and Wang et al. (Zhongnan Hospital of Wuhan University in Wuhan; affiliation 620 of Dawei Wang, MD: Department of Critical Care Medicine)62 also used ICU admission as a criterion for 621 severe or non-severe, we examined the rate of severely ill patients and resulted in 21.4% (18/84) and 35.3% 622 (36/102), respectively. However, in the case of using the "Presence of Primary Composite End Point", the 623 percentage was only 6.5% (67/1032). Whereas, in the original categorisation by Guan et al.61, the percentage 624 was 18.7% (173/926). Therefore, we prioritised the original classification of severe or non-severe by Guan et 625 al61. 626 627 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 35 of all 74 (ii) No. 9 Guo et al. (Guo et al. JAMA Cardiol. 2020;5(7):811- 818)35 (only in eFigure5) 628 We read this paper carefully, a report from Wuhan city published in March 2020. Although this 629 document may significantly influence the studies on COVID-19 (according to the JAMA Cardiology website, 630 the article was cited more than 1,500 as of 20th September 2021), we found that misuse of linear regression 631 analysis in Guo et al. on a figure (see Extended Data Fig. 8 & Supplementary discussion 5: misuse of linear 632 regression analysis)35. 633 Additionally, three subgroup patterns appeared in a figure reported by Guo et al., although they did 634 not mention it. Precautionary, we considered whether the subgroups in the Guo et al.35 affected the meta-635 analysis on the web Figure 5. The data in other studies allowed to be expected to have the same subgroups 636 because the patient data described by Guo et al.71 and other studies were reported from China (most of them 637 were in Wuhan City). 638 639 (iii) No. 20 Wang L. et al. (Wang, D. et al., JAMA. 2020;323(11):1061-1069.)63 640 In confirming from the viewpoint of the biomedicine side, it was found that a significant matter of 641 consideration on eligibility, patient population reported by Wang L. et al. was limited to over age 6063. The 642 title was "Coronavirus disease 2019 in elderly patients: Characteristics and prognostic factors based on 4-643 week follow-up", and Matsushita et al. 33 had to pay attention to the word "elderly". 644 645 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 36 of all 74 (iv) No.23 Yuan M. et al. (Yuan M. et al., PLoS One. 2020;15(3):e0230548.)65 646 In confirming the accuracy of values, we found a mixture of values derived from different 647 calculation types in Figure 5: Odds Ratio (OR), hazard ratio, and a value derived from the imputation of 0.5 648 for the zero cells in the cross table. The zero cells appeared in the study reported by Yuan et al65. Yuan M. et 649 al. studied 27 patients who confirmed novel coronavirus infected pneumonia (NCIP) during the early phase of 650 the pandemic to evaluate radiologic characteristics65. In other words, the difficulty of patient enrollment might 651 cause a small sample size, which seemed to be a concern from the viewpoint of comparability (c.f., Guan W. 652 et 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 Deng Y. et al., n=22560). 654 655 (v) The term "Cardiovascular disease (CVD)." 656 There was an inconsistency in the studies on "Cardiovascular disease (CVD)." For example, vascular 657 diseases such as arrhythmia and arteriosclerosis are also classified as CVD, but in the studies reported by 658 Guan et al.61 and Zhou et al.66, the term "Coronary heart disease" was used. Also, "Cardiac disease" was used 659 by Yuan et al.65, "Heart disease" was used by Deng et al.60, and "Cardiovascular disease" was used by Wang L 660 et al63. 661 662 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 37 of all 74 2) Regression analysis 663 Considering the problem of comparability, we re-calculated OR and visually grouped it into two 664 hyperbolic patterns. In the case of S-shaped curve fitting, since there were many unknown coefficients for the 665 number of data (3 unknown coefficients of K1, K2, and M), the regression analysis was performed after setting 666 the zero point value. In the fitting of upper and lower curves, since there were many unknown coefficients 667 (K1, K2, M, a, b, c), we firstly obtained the coefficient of M (see equation (1)) by the curve fitting of the S-668 shaped curve, and then performed curve fitting of parabolas. After substituting M for x value of apex in 669 equation (4) (see equations (4) & (5)), regression analysis was performed on the data in the middle row of 670 Figure 3 (Fig. 3, d-f). Finally, the S-shaped curve and the parabola were merged (Fig. 3, g-i). 671 672 3) Calculation of weighted average 673 In earlier days group, the median age and the number of cases are tabulated by severe and non-674 severe cases as follows. Guan W. et al. (severe n=173 [age: 52] vs non-severe n=926 [age: 45])61, Zhou F. et 675 al. (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 ICU 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 earlier days group (severe n = 347 vs non-severe n = 1282). 678 The weighted average of severe and non-severe in the earlier days group was calculated from these 679 values by the following formulas. In the earlier days group, the weighted average of severe and non-severe 680 were 57.7 and 46.5, respectively. 681 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 38 of all 74 682 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠 𝑖𝑛 𝑒𝑎𝑟𝑙𝑖𝑒𝑟 𝑑𝑎𝑦𝑠 𝑔𝑟𝑜𝑢𝑝 (𝑠𝑒𝑣𝑒𝑟𝑒) = 173 + 54 + 36 + 84 = 𝟑𝟒𝟕 683 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑚𝑒𝑎𝑛 𝑜𝑓 𝑒𝑎𝑟𝑙𝑖𝑒𝑟 𝑑𝑎𝑦𝑠 𝑔𝑟𝑜𝑢𝑝 (𝑠𝑒𝑣𝑒𝑟𝑒) = 173 𝟑𝟒𝟕 × 52 + 54 𝟑𝟒𝟕 × 69 + 36 𝟑𝟒𝟕 × 66 + 84 𝟑𝟒𝟕 × 58.5684 ≅ 57.7 685 686 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠 𝑖𝑛 𝑒𝑎𝑟𝑙𝑖𝑒𝑟 𝑑𝑎𝑦𝑠 𝑔𝑟𝑜𝑢𝑝(𝑛𝑜𝑛 − 𝑠𝑒𝑣𝑒𝑟𝑒) = 926 + 137 + 102 + 117 = 𝟏𝟐𝟖𝟐 687 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑚𝑒𝑎𝑛 𝑜𝑓 𝑒𝑎𝑟𝑙𝑖𝑒𝑟 𝑑𝑎𝑦𝑠 𝑔𝑟𝑜𝑢𝑝 (𝑛𝑜𝑛 − 𝑠𝑒𝑣𝑒𝑟𝑒)688 = 926 𝟏𝟐𝟖𝟐 × 45 + 137 𝟏𝟐𝟖𝟐 × 52 + 102 𝟏𝟐𝟖𝟐 × 51 + 117 𝟏𝟐𝟖𝟐 × 48 ≅ 46.5 689 690 In later days group, the median age and the number of cases are tabulated by severe and non-severe 691 cases 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 [age: 69] vs survival n=116 [age: 48])60, and whole of later days group (severe n = 127 vs non-severe n = 693 200). 694 The weighted average of severe and non-severe in the late date group was calculated from these 695 values by the following formulas. In the late date group, the weighted average of severe and non-severe were 696 68.6 years and 40.9, respectively. 697 698 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠 𝑖𝑛 𝑙𝑎𝑡𝑒 𝑑𝑎𝑡𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑠𝑒𝑣𝑒𝑟𝑒) = 18 + 109 = 𝟏𝟐𝟕 699 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑚𝑒𝑎𝑛 𝑜𝑓 𝑙𝑎𝑡𝑒 𝑑𝑎𝑡𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑠𝑒𝑣𝑒𝑟𝑒) = 18 𝟏𝟐𝟕 × 66 + 109 𝟏𝟐𝟕 × 69 ≅ 68.6 700 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 39 of all 74 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠 𝑖𝑛 𝑙𝑎𝑡𝑒 𝑑𝑎𝑡𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑛𝑜𝑛 − 𝑠𝑒𝑣𝑒𝑟𝑒) = 84 + 116 = 𝟐𝟎𝟎 701 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑚𝑒𝑎𝑛 𝑜𝑓 𝑙𝑎𝑡𝑒 𝑑𝑎𝑡𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑛𝑜𝑛 − 𝑠𝑒𝑣𝑒𝑟𝑒) = 84 𝟐𝟎𝟎 × 31 + 116 𝟐𝟎𝟎 × 48 ≅ 40.9 702 703 4) Additional analysis: Regression analysis on the parabolic cylinder 704 One of the authors (KK) found a way to fit an appropriate curve to the data reported by Guo et al., 705 performing trial and error with his mathematical intuition (Fig. 4). Firstly, he calculated the centre of gravity 706 of the data by each subgroup cluster (centre of gravity: the average of the values on the horizontal axis x and 707 the average of the values on the vertical axis y). Second, he obtained equations of three straight lines passing 708 through the origin and centres of gravity. Thirdly, he obtained the equation of a straight line passing through 709 each centre of gravity and intersecting the straight lines obtained above. Fourthly, he re-set new origin as each 710 centre of gravity and regarded the above two crossed lines as a small cartesian coordinate system. Finally, he 711 applied parabola fitting with Excel○R in each new cartesian coordinate system. In this curve fitting, he used the 712 data of distance between each data point and the straight line obtained secondary, and the data of distance 713 between each data point and the straight line obtained firstly (see "distance from a point to a line" in a high 714 school textbook). 715 716 5) Making example data 717 To explain the misuse of linear regression analysis in Guo et al.35, we made the following data to 718 show the example. It allows being used in R by copying and pasting the following. 719 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 40 of all 74 720 Value_X<-721 c(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 .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 1.68 ,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 ,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 ,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) 726 727 Value_Y<-728 c(2.01742 ,2.02749 ,2.04454 ,2.02009 ,2.03445 ,2.04749 ,2.03641 ,1.99047 ,1.98671 ,2.06711 ,2.09772 ,2.005729 39 ,1.86985 ,2.01679 ,2.12183 ,1.94453 ,1.86497 ,1.87444 ,2.09483 ,1.91073 ,1.69244 ,1.70968 ,1.81376 ,2.0730 4219 ,1.69059 ,1.75939 ,1.95321 ,1.8417 ,1.58169 ,1.75585 ,1.73497 ,1.47847 ,1.9115 ,1.44962 ,1.85063 ,1.3731 2298 ,1.28437 ,1.74621 ,1.27232 ,1.32763 ,1.575 ,1.56609 ,1.5933 ,1.76707 ,1.11264 ,1.06188 ,1.40139 ,0.94732 084 ,1.0756 ,1.38507 ,1.33408 ,1.54375 ,1.60257 ,1.02029 ,0.98612 ,1.79094 ,0.97916 ,0.81212 ,1.1484 ,1.51733 68 ,1.70236 ,1.38945 ,1.69072 ,1.75042 ,1.67571 ,1.38623 ,1.81503 ,1.80665 ,1.41073 ,2.3175 ,2.24852 ,1.75734 95 ,2.81818 ,1.93654 ,2.36998 ,2.0987 ,2.19539 ,2.44747 ,2.57255 ,3.24637 ,2.78881 ,3.51638 ,2.68107 ,2.87735 259 ,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 ,6.89257 ,7.86387 ,7.98237 ,8.64705) 737 738 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 41 of all 74 7. Statement of our intention for data review results 739 To clarify our stance, we mention this statement of intention for results. In this article, we pointed 740 out many overlooking and errors. However, we have no intention to attack previous works because our 741 analysis results owing to their original works, including original research articles, reported valuable data and 742 articles of meta-analysis synthesised valuable datasets. Since just a scientist had better reconfirm the previous 743 studies with no preconception with being grateful to the researchers of those studies, we carefully reviewed 744 the data reported by previous studies. We highly respect previous works, which have the intention to solve 745 medical issues, although some articles contained technical errors. 746 747 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 42 of all 74 748

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Significance of Screening the General Population for Potential Cardiovascular Diseases 838 with a Combination Assay of B-type Natriuretic Peptide and High Sensitive Troponin I. J Med 839 Diagn Meth 6 (2017). 840 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 47 of all 74 841

842 One of the authors, Keiichiro Kimoto, appreciates the kindful encouragement of Hideo Yoshioka, 843 MEcon., who is in charge of the Data Strategy Research Institute representative. 844 845 Competing interest declaration 846 Keiichiro Kimoto has been in charge of external advisor for Data Strategy Research Institute but 847 reserved no financial support for this study. Except for this, the authors have no conflicts of interest and have 848 no financial disclosures that should be disclosed. 849 850 Author contributions 851 Keiichiro Kimoto takes responsibility for this research, making study concepts, data analysis, 852 interpretation of analysis results, and drafting the manuscript. Dr. Yamakuchi contributed to interpreting 853 analysis results, manuscript drafting, supervision and administrative role. Dr. Takenouchi contributed to the 854 supervision. Dr. Hashiguchi contributed to the study concept, interpretation of analysis results, manuscript 855 drafting, supervision, and administrative role. 856 857 Additional information 858 This article has supplementary information that contains supplementary discussions. 859 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 48 of all 74 860 Data availability statement 861 We analyzed clinical data published by other studies (third parties). Used data is identified by 862 indicated information of citation (reference numbers and list of references). The corresponding author 863 responds to inquiries in the case of measured values from published figures requested by reviewers or readers. 864 865 Code availability statement 866 Correspondence author (KK) can respond to inquiries for the corresponding author's email address 867 on offering the Python source code and spreadsheet software files for statistical analysis. 868 869 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 49 of all 74 870 Figures & figure legends 871 Fig. 1 872 873 Fig. 1 | A hyperbolic shape formed by confidence limits. a, A two-way cross-tabulation (contingency table) 874 for calculating an odds ratio (OR). b, Calculation of OR and its 95% confidence interval. c, Histogram of the 875 data following a binomial distribution and a plot of the inverse values of the square roots. d, The mathematical 876 formulas for the hyperbolic shape. Note that the OR is not logarithmic, and only the length of the error bar is 877 logarithmic (see the upper left position of panel d). 878 879 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 50 of all 74 880 Fig. 2 881 882 Fig. 2 | Re-analysis based on the proposed ideas. a, Data review and meta-regression analysis using the 883 same method as Chandra et al. Ann Intern Med. 2009; 151(3):180-190. Figure 37. We added information from 884 original studies and our hypothesis to the previously published form, such as latent distribution. The original 885 figure has been shown on the American College of Physicians website, which links to PubMed○R 886 (https://pubmed.ncbi.nlm.nih.gov/19581633/). From Chandra D, Parisini E, Mozaffarian D. Meta-analysis: 887 travel and risk for venous thromboembolism. Ann Intern Med. 2009 Aug 4;151(3):180-90. doi: 10.7326/0003-888 4819-151-3-200908040-00129. Epub 2009 Jul 6. © 2009 American College of Physicians. Adapted with 889 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 51 of all 74 permission. b, grouping the data and hyperbolic shape fitting. c, Onsets of thrombosis after travel reported by 890 Cannegieter et al25. This figure was re-used and re-drawn from Cannegieter et al. Travel-related venous 891 thrombosis: results from a large population-based case-control study (MEGA study). PLoS Med. 2006; 892 3(8):e307. Figure 1. https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC1551914/figure/pmed-0030307-893 g001/ Copyright © 2006 Cannegieter et al. Creative Commons Attribution License. In 2006, the Creative 894 Commons Attribution 2.0 Generic, License was available. https://creativecommons.org/licenses/by/2.0/ d, 895 Applying the damped wave function to the data shown in panel c. We decided that the data from Martinelli et 896 al.23 and Cannegieter et al.25 should be excluded, and the odds ratio from Parkin et al.24 may decrease (see 897 Methods). At 2 hours point, Chandra et al.7 did not use available data (panel a). On the original regression 898 line, Chandra et al.7 might conduct a meta-regression analysis reversing the front head and the front side of the 899 cross-tabulation. Compering panels c and d helps us understand that using a three-dimensional graph disrupts 900 our recognition. 901 902 903 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 52 of all 74 904 Fig. 3 905 906 Fig. 3 | Hyperbolic shapes found in the figure reported by Matsushita et al33. a, A figure shows the 907 relationship between the severe and non-severe groups reported by Matsushita et al.33, which shows age 908 difference on the horizontal axis and odds ratio (OR) or hazard ratio of hypertension on the vertical axis. To 909 evaluate potential confounding for relative risk by age, Matsushita et al. conducted meta-regression analyses 910 based on the assumption that there was the possibility of confounding by age in the case that the study with a 911 larger age difference has a higher relative risk33. b, Diabetes. c, Cardiovascular disease (CVD). d-f, 912 Comparisons of error bars, which show 95% confidence interval (C.I.) s. It corresponds to the upper figure. g-913 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 53 of all 74 i, Hyperbolic patterns were fitted to the OR and the 95% confidence limit of the OR. In the panel i, a 914 hyperbolic shape could not be fitted due to the considerable data variation, likely due to the inconsistency of 915 the term "CVD" (see Methods). The numbers marked to each point are the same as the numbers shown in the 916 original figure. The sources of each data are shown in Methods. This figure was re-used from Matsushita et al. 917 Glob Heart. 2020; 15(1):64. Figure 5. 918 https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7546112/figure/F5/ 919 Copyright © 2020 The Authors. Creative Commons Attribution 4.0 International License (CC-BY 4.0) 920 https://creativecommons.org/licenses/by/4.0/ 921 922 923 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 54 of all 74 924 Fig. 4 925 926 Fig. 4 | Parabola shape patterns in the figure by Guo et al35. a, Relationship between high sensitive C-927 reactive protein (hsCRP) and cardiac troponin T (TnT) in COVID-19 patients (left) and relationship between 928 cardiac troponin T (TnT) and N-terminal pro-brain natriuretic peptide (NT-proBNP) (right). b, Data points 929 from the right side of the panel a and fitting parabola. c, Three-dimensional data visualisation was constructed 930 by mounting the value of hsCRP onto panel b. d, Linear regression analysis on the side surface of the 931 parabolic cylinder in panel c. The points were replaced with their average if the values could not be 932 determined due to overlapping (the points indicated by the left-pointing arrow and the error bar, which are the 933 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 55 of all 74 average and the range of values, respectively). Panel a was re-used from Guo T et al. JAMA Cardiol. 2020; 934 5(7):811-818. Figure 1 https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7101506/figure/hoi200026f1/ 935 Copyright © 2020 Guo T et al. JAMA Cardiology. Creative Commons Attribution License (CC-BY). 936 https://creativecommons.org/licenses/by/4.0/ 937 938 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 56 of all 74 939 Extended data figures & figure legends 940 Extended Data Fig. 1 941 942 943 Extended Data Fig. 1 | Overall framework of this study. We applied our concept to traveller's thrombosis 944 and COVID-19. These were similar in research history (see Supplementary discussion 1: history of traveller's 945 thrombosis & Supplementary discussion 2: research situations of COVID-19 related thrombosis). In the case 946 of traveller's thrombosis, we analysed a dataset collected by Chandra et al. and Philbrick et al4,7. In the case of 947 COVID-19, we analysed a dataset collected by Matsushita et al7. Flow charts show data accept or reject flows. 948 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 57 of all 74 Since duplicating data, Matsushita et al. selected only eight studies data (25 studies included in initial web Figure 949 5)33. 950 951 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 58 of all 74 952 Extended Data Fig. 2 953 954 Extended Data Fig. 2 | Unrecognised cyclic pattern of thrombosis onset after travel25. a, A bar graph 955 showing the relationship between weeks after travel and the number of thrombosis onset in a figure reported 956 by Cannegieter et al25. b, Re-expressing as a two-dimensional bar graph avoiding the three-dimensional 957 representation. c, Applying a damped wave by non-linear regression analysis. d, Extraction of damped wave 958 part by subtracting the monotonic decrease function. e, Dividing into 2 sub-group areas by the envelopes of 959 the damped wave that touch the lower parts of the wave. f, Enlarged and added explanation of the ratio of the 960 area. Cannegieter et al.25 used the data up to week eight, and the ratio of subgroup 2 to the total number of 961 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 59 of all 74 patients (ratio of S2 to the area of S1 + S2) was 30.0%. In the integration for the infinite interval, it was 30.8%. 962 Peak shifts of the wave (peak position of the wave shifted from the original to the other) appeared when 963 comparing panels d and f due to putting by regression curve located in the centre. Panel a was re-used from 964 Cannegieter et al. PLoS Med. 2006; 3(8):e307. Figure 1. 965 https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC1551914/figure/pmed-0030307-g001/ 966 Copyright © 2006 Cannegieter et al. Creative Commons Attribution License. In 2006, the Creative Commons 967 Attribution 2.0 Generic, License (CC BY 2.0) was available. https://creativecommons.org/licenses/by/2.0/ 968 969 970 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 60 of all 74 971 Extended Data Fig. 3 972 973 Extended Data Fig. 3 | Curve fitting to the dataset reported by Philbrick et al4. a, data stratification by 974 Pulmonary Embolism (PE) and Deep Vein Thrombosis (DVT). b, Application of S-shaped curve by 975 regression analysis to the stratified data. The value in the bracket (panel b) is the point of time converted from 976 the time category (see Methods). Philbrick et al.4 reported the result of a systematic review with a table (list). 977 In contrast, this visualising allows us to extract latent information. 978 979 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 61 of all 74 980 Extended Data Fig. 4 981 982 Extended Data Fig. 4 | Re-analysis of the data in Table 1 by Clérel & Caillard27. a, A figure made by 983 Clérel & Caillard27 showed a relationship between travel time and the thrombosis onset in the case of 984 stratification by medical history of thrombosis. b, The relationship between time and thrombosis (prepared 985 from Table 1 reported by Clérel & Caillard27). c, Correlogram (prepared from Table 1 reported by Clérel & 986 Caillard27). d, Age distribution by sex (made from Table 1 reported by Clérel & Caillard27). As shown in panel 987 a, Clérel & Caillard27 summarised all the data for 12 hours or more, but there were two peaks (see panel b). 988 Judging from the age distribution (panel d), the number of women patients was more significant than that of 989 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 62 of all 74 men, but there was no difference between the age ranges. In panel c, there was a periodic pattern. Panel a 990 reproduced from Clérel & Caillard. Syndrome thrombo-embolique de la station assise prolongée et vols de 991 longue durée: l'expérience du Service Médical d'Urgence d'Aéroports De Paris. Bull Acad Natl Med. 1999; 992 183(5):985-997. discussion 997-1001. Figure 3. 993 Copyright © 1999 Elsevier Masson SAS. All rights reserved. Académie Nationale de Médecine. 994 995 996 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 63 of all 74 997 Extended Data Fig. 5 998 999 Extended Data Fig. 5 | Cyclic pattern of thrombosis onset appeared in a figure by Kelman et al28. a, A 1000 thrombosis onset distribution reported by Kelman et al28. b, The regression curve is located in the centre of all 1001 average points (the points express the average of thrombosis onset during seven days). c, Curve fitting to the 1002 residual data of the regression curve in panel b. d, Application of damped wave function and adding 1003 interpretation of the results assuming some women started taking oral contraceptives (OC) in the timing of 1004 travel. The observed cyclic pattern was relatively unclear than Cannegieter et al.25 (see Fig. 2). Noteworthy, 1005 the thrombosis onset downed in the days before 90 days, and it seems to be the scheduled withdrawal period 1006 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 64 of all 74 of OC use. This figure was re-used and re-drawn from Kelman et al. BMJ. 2003; 327(7423):1072. Figure 1 1007 https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC261739/figure/fig1/ 1008 Copyright © 2003 BMJ Publishing Group Ltd. All rights reserved. The BMJ permission team thankfully 1009 confirm this figure adaptation. Also, we obtained permission to re-use. 1010 1011 1012 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 65 of all 74 1013 Extended Data Fig. 6 1014 1015 Extended Data Fig. 6 | Thrombosis reported by Clérel & Caillard27 & our novel annotations. a, Clérel & 1016 Caillard mentioned that "their incidence increases during the last years, corresponding to the growth of air 1017 traffic and mainly to the increase of long duration without stop flight."27 c, Chronology of various guidelines 1018 on HRT. In the newly figure (panel b), the increase in thrombosis was associated with the issuance time of 1019 guidelines for HRT. HRT was recommended for menopausal women in the 1990s, but its effectiveness was 1020 questioned in the HERS trial (1998)31. Also, the risk was discovered in the WHI trial at the interim analysis 1021 (2002)32. It might be the effect of the publication on the HERS study (1998)31 that the increase of thromboses 1022 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 66 of all 74 was relatively small in 1998 despite the publication of two documents recommended in 1997. Panel a was 1023 reproduced from Clérel & Caillard. Syndrome thrombo-embolique de la station assise prolongée et vols de 1024 longue durée: l'expérience du Service Médical d'Urgence d'Aéroports De Paris. Bull Acad Natl Med. 1999; 1025 183(5):985-997. discussion 997-1001. Figure 1. 1026 Copyright © 1999 Elsevier Masson SAS. All rights reserved. Académie Nationale de Médecine. 1027 1028 1029 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 67 of all 74 1030 Extended Data Fig. 7 1031 1032 Extended Data Fig. 7 | Data cut-off dates in each study cited by Matsushita et al33. The data acquisition 1033 period in each study was displayed in Gantt chart format. The date display format is year-month-day. The 1034 correspondence between numbers and authors is as follows: No.2: Cao et al. (Cao, J. et al., Intensive Care 1035 Med. 2020;46(5):851-853.)59, No.7: Deng et al. (Deng, Y. et al., Chin Med J (Engl). 2020;133(11):1261-1036 1267.)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 al. (Wang, D. et al., JAMA. 2020;323(11):1061-1069.)62, No.20: Wang L. et al. (Wang, L. et al., J Infect. 1038 2020;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 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 68 of all 74 Zhou et al. (Zhou, F. et al., Lancet. 2020;395(10229):1054-1062.)66. Abbreviations: ARDS (Acute Respiratory 1040 Distress Syndrome), ICU (Intensive Care Unit). The number in parentheses means median age. The number in 1041 the bracket means standard deviation or interquartile range. 1042 1043 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 69 of all 74 Extended Data Fig. 8 1044 1045 Extended Data Fig. 8 | Bimodal distributions & tiled parabola in COVID-19 patients. a, Guo et al. JAMA 1046 Cardiol. 2020; 5(7):811-818. Figure 1B 1047 https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7101506/figure/hoi200026f1/ 1048 Copyright © 2020 Guo T et al. JAMA Cardiology. Creative Commons Attribution License (CC-BY). b, 1049 Marginal distribution of the scatter plot data. c, Wang et al. Front Cardiovasc Med. 2020; (7): 147. Figure 1 1050 (upper, x-axis: troponin I, pg/mL; y-axis: BNP, pg/mL; lower, x-axis: troponin I, pg/mL; y-axis: 1051 lymphocyte, %)37. https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7477309/figure/F1/ 1052 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 70 of all 74 Copyright © 2020 Wang, Zheng, Tong, Wang, Lv, Xi and Liu. CC BY License. d, Caro-Codón et al. Eur J 1053 Heart Fail. 2021; 23(3):456-464. Figure 1B (x-axis, LN (troponin I))40. 1054 https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC8013330/figure/ejhf2095-fig-0001/ 1055 Copyright © 2021 European Society of Cardiology. All rights reserved. This Figure can be used for 1056 unrestricted research re-use and analysis in any form or by any means with acknowledgement of the original 1057 source as part of the COVID-19 public health emergency, for the duration of the emergency. e, Demir et al. 1058 Am J Cardiol. 2021; 147:129-136. Figure 2 (upper: admission; lower: peak measurements; x-axis: troponin T, 1059 ng/L)41. https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7895690/figure/fig0002/ 1060 Copyright © 2021 Elsevier Inc. All rights reserved. This figure is granted for unrestricted research re-use and 1061 analyses in any form or by any means with acknowledgement of the original source by Elsevier for as long as 1062 the COVID-19 resource centre remains active. f, Virtual example on regression analysis (see Supplementary 1063

5: misuse of linear regression analysis). In panel b (also c, d, and e), the histogram was bimodal 1064 (marked "A" and "B"). The crescent-shape pattern closely resembled the ST-segment elevation myocardial 1065 infarction group pattern that appeared in the study by Budnik et al36. 1066 1067 1068 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 71 of all 74 1069 Extended Data Fig. 9 1070 1071 Extended Data Fig. 9 | Three subgroup patterns appeared in a figure reported by Guo et al35. a, A 1072 scatter plot showing the relationship between cardiac troponin T (TnT) and N-terminal pro-brain natriuretic 1073 peptide (NT-proBNP) in a patient with COVID-1935. b, Scatter plot to investigate the relationship between 1074 brain natriuretic peptide (BNP) and cardiac troponin I (cTnl) in healthy subjects reported by Sugawa et al38. c, 1075 The visible points that exceeded the value of 26.2 pg/mL (red line in panel b) were re-plotted with parabola 1076 (not accurate regression analysis). d, Visible points in the figure reported by Guo et al.35 with parabolas. e, 1077 Transposed panel d for easy comparison. f, Group 1 in the small coordinate system (centre of gravity as the 1078 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 72 of all 74 origin of the coordinate system). g, Group 2 in the small coordinate system. h, Group 3 in the small coordinate 1079 system. In panel f-h, the upper curve is expressed by a quadratic function, in which a coefficient of the 1080 quadratic term is equal to a value of the coefficient of the quadratic term for the solid curve multiplied by 3/2. 1081 In the lower curve, a coefficient of the quadratic term of the solid curve multiplied by 2/3. Most data points 1082 located inside the crescent-shaped region enclosed by the parabolas, but the reason was unclear. Panel a was 1083 re-used from Guo T et al. JAMA Cardiol. 2020; 5(7):811-818. Figure 1B 1084 https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7101506/figure/hoi200026f1/ Copyright © 2020 Guo T 1085 et al. JAMA Cardiology. Creative Commons Attribution License (CC-BY). 1086 https://creativecommons.org/licenses/by/4.0/ Panel b was re-used from Sugawa et al. Sci Rep. 2018; 1087 8(1):5120. Figure 1. https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC5865159/figure/Fig1/ Copyright © 1088 2018 The Authors. CC-BY 4.0 License 1089 1090 1091 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 73 of all 74 1092 Extended Data Fig. 10 1093 1094 Extended Data Fig. 10 | A three-dimensional plot reconstructed from the data reported by Guo et al35. 1095 a, Scatter plot showing the relationship between high sensitive C-reactive protein (hsCRP) and troponin T 1096 (TnT) 35. b, Re-drawn scatter plot with a vertical line around hsCRP = 200 mg/mL = 2.0 × 102 mg/mL. c, 1097 Enlarged subgroup 3 in the panel d of Extended Data Fig. 9 (data exceeding hsCRP = 200 mg/mL are 1098 indicated by red, data not exceeding hsCRP = 200 mg/mL are indicated by blue). d, Enlarged subgroup 3 of 1099 the panel d in Extended Fig. 9 with the foot of the perpendicular from each data point to the parabola. e, The 1100 hsCRP value of each patient placed on panel d (shown as a three-dimensional plot). f, The side surface of the 1101 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint p. 74 of all 74 parabolic cylinder. The point of TnT = 1.31 observed in panel b is not included in panel c, and the point of 1102 TnT = 1.71 in panel c is not included in panel b (inconsistent). In panel e, the projection of the data points 1103 onto the parabola was used as new points. In panels, e and f, some points of CRP value could not be 1104 determined because of overlapping, so those points were replaced with the average value (the points indicated 1105 by the left-pointing arrows and the error bar, which are the average values and the range of values, 1106 respectively). Panel a was re-used from Guo et al. JAMA Cardiol. 2020; 5(7):811-818. Figure 1. 1107 https://www.ncbi.nlm.nih.gov/labs/pmc/articles/PMC7101506/figure/hoi200026f1/ Copyright © 2020 Guo T 1108 et al. JAMA Cardiology. Creative Commons Attribution License (CC-BY). 1109 https://creativecommons.org/licenses/by/4.0/ 1110 1111 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 7, 2022. ; https://doi.org/10.1101/2022.06.06.22275944doi: medRxiv preprint