A Greater increase in C5aR1-level at onset and a smaller decrease in IgG-level after recovery in severer COVID-19 patients: A new analysis of existing data with Ishida’s t-test1 and t-test2

It is important to exactly identify the difference in the changes in a receptor C5aR1- 18 levels at onset and Immunoglobulin G (IgG)-levels after recovery between severe ( acute 19 respiratory distress syndrome ) and nonsevere (pneumonia) coronavirus disease 2019 20 patients to reduce the severity of the disease and prevent reinfection with t he causative 21 virus. 2012 literature studies were selected from the PubMed Central® databases with 22 keywords of (((covid-19) AND NOT review) AND C5a / IgG. Three studies 23 showing individual expression levels of C5a/C5aR1 / antibody in the patients before 24 and after the passage of time without significance were selected by assessing the 25 literatures. We extracted dynamics where the slope values of the regression line 26 between the initial ( X ) and changed level ( C ) with passage of time were not zero 27 significantly (p < 0.05) using SAS-JMP-10. We examined the significance of C in the 28 patients with Ishida’s t -test1 and that of the difference in C between the severe and 29 nonsevere patients with Ishida’s t -test2, which used the values on the above regression 30 line as the expected values of C . These tests suggested a greater increase in C5aR1- 31 levels at onset and a smaller decrease in IgG-levels after recovery in severe patients than 32 in nonsevere patients.

However, we found that some of these changes over time (C) were dependent on their 61 initial levels (X) and not suitable for analysis by conventional statistical tests. We 62 developed new statistical tests (Ishida's t-test1 and t-test2) that correctly examine the 63 above changes and then, we analyzed the above changes with Ishida's t-test1 and t-test2 64 to obtain different results from their papers as follows (research funding was not between X and C made by the method of least squares (E-line) (Figure 2 and Extended 77 Figure 1a and 1b) of 39 dynamics and 26 subdynamics (Table 1 and Extended Table 1) 78 described in the three literatures.

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Extraction of dynamics dependent on X. 80 According to the procedure for extraction of dynamics described in Methods and in the 81 latter half of Figure 1, we extracted eighteen dynamics and twelve subdynamics 82 dependent on X (Table 1). C-axis intercept (α), slope value (β), X-axis intercept (γ (= -83 α/β)) of E-line, standard error (SE), standard deviation (SD (=SE√ )), mean of C (Mc),   Generally, measuring of values before and after treatment included RTM (regression to 103 the mean) 11 . Therefore, the above Me should subtract Me of placebo control for the 104 passage of time. However, no placebo control for passage of time was described in all 105 of the three studies 2,6,9 and others (33 studies on C5a/C5aR1 and 1976 studies on 106 antibodies) described in Figure 1. Therefore, we could not get Me free from RTM 11 .

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Analysis of the extracted dynamics with Ishida's test2 108 As we could not get Me free from RTM 11 , we analyzed the difference between Me of 109 particular group k and Me of particular group l (dMe) under the assumption that at least 110 one group is significantly different from RTM 11 , if there is a significant difference 111 between the two groups. 112 We analyzed the difference between dMe, standard deviation (SD2), p-value (p2), effect 113 size (d2) for dMe of the related two dynamics with Ishida's t-test2 (lower of Table 2).

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There was risk of bias due to limitation of databases, RTM 11 by double measurements, 118 limitation of numbers of subjects whose data were able to be estimated from the spots 119 or lines drawn in figures and its estimation errors, and limitation of validity of Ishida's 120 t-test1 and t-test2.

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The E-line crossed the C axis at α. When β ≠ 0 with p < 0.05, this line also crossed the X 123 axis at γ. Thus, the equation for this line was described as E = β(X-γ). A value obtained 124 from this equation in which Xi (X of particular subject i) was put was set as Ei. As  The β for 092 was significantly negative (p = 0.0002) and p1 for Me was 0.00004.

Extended Figures and an Extended
Extended Figure 1a. E-line for 091 -109s. Contents of the dynamics with their source 342 were described in Table 1 or Extended Table 1. Solid and dotted lines indicated that p-343 value of slope of E-line was < 0.05 and ≥ 0.05, respectively.

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Dynamics of IgG levels specific to RBD (titers) from recurrent-positive patients between T7 and T8 (223, n=27) and between T8 and T9 (224, n=23) described in Fig. 4c IgG level by Yang et al. 9 225 226 Dynamics of IgA levels specific to RBD (titers) from recurrent-positive patients between T7 and T8 (225, n=21) and between T8 and T9 (226, n=20) described in Dynamics of all Ig levels specific to RBD (titers) from recurrent-positive patients between T7 and T8 (227, n=27) and between T8 and T9 (228, n=25) described in Fig. 4c all Ig level by Yang et al. 9 Each abbreviation was described in Table 1.