## 3 Results  
The results of suPAR levels and the distribution (Table 1) in investigated population was Gaussian one (normal distribution). It was confirmed that suPAR level depends on the patient age (cc = 0.31, \(p<0.0001\)) (Figures 1 and 2). The index constructed as suPAR/Age in relation to age has even stronger relation (cc = \(-0.75\), \(p<0.0001\)). The same moderately strong relation is for the index suPAR/Age'2 to age (cc = \(-0.80\), \(p<0.0001\)), and even the numerator of the fraction is more strong: suPAR'2/Age (cc = \(-0.50\), \(p<0.0001\)). \begin{table}
\begin{tabular}{c c c c c} \hline
**IBI Modality Name** & **Average \(\pm\) SD** & **Stnd. Skewness 1** & **Stnd. Kurtosis 2** & **Distribution** \\ \hline suPAR (raw data) & 2.69 \(\pm\) 0.57 ng/mL & 0.796 & 0.501 & Normal \\ suPAR/Age & 1.77 \(\pm\) 0.72 & 5.428 & 0.930 & \\ suPAR/Age’2 & 1.66 \(\pm\) 1.25 & 7.324 & 3.056 & \\ suPAR’2/Age & 2.45 \(\pm\) 1.28 & 7.898 & 8.017 & \\ suPAR’2/lg\_Age & 5.03 \(\pm\) 2.03 3 & 3.928 & 2.619 & \\ SQRT(suPAR’2/lg\_Age) & 2.69 \(\pm\) 0.56 3 & 0.141 & 0.503 & Normal \\ \hline \end{tabular}  
* Standardized skewness within range from \(-2\) up to +2 means normal distribution. 2 Standardized kurtosis within range from \(-2\) up to +2 means normal distribution. 3 Age independent variable (\(p<0.05\)). IBI-index of body inflammation. SD-standard deviation.  
\end{table} 
Table 1: Index of body inflammation calculated in five investigated ways. Summary view for distribution and age dependency. Figure 1: Soluble urokinase-type plasminogen activator receptor (suPAR) level in serum (ng/mL) and calculated body inflammation indeces (no units) separating the measure from patient age influence (average value is marked by red cross, median is marked by vertical line inside the boxes). Note: similarity of SQRT(suPAR’2/lg_Age) to raw data. All calculations performed according Equations (1)–(5). Contrary to above (Figure 1), if the influence of the age (denominator) to the index is weaker, the index becomes independent on patient age (Figure 3): as suPAR^2/lg_Age (cc = 0.05, \(p\) = 0.5046) as well as SQRTsuPAR^2/lg_Age (cc = 0.05, \(p\) = 0.4861). The run of the regression plot is approximately horizontal. Figure 2: Relation of the soluble urokinase-type plasminogen activator receptor (suPAR, ng/mL) and calculated indeces to patient’s age. Simple regression of suPAR raw data and patient age (top, left-hand side). Dash line describes confidence limits at level of 95%. The level of suPAR gradually and significant increases in time (years). The both lowest plots confirm age independence and only lower right-hand belongs normal distribution. Moreover, range of value SQRTsuPAR^2/lg_Age is similar to raw data range. Note: The calculations were based on indeces calculated according to the Equations (1)–(5). There is not normal distribution noted in the first index of this twins. Finally, standardization of body inflammation index (IBI) to form Equation (6):  
\[\text{IBI}=1.223\sqrt[]{\frac{\text{suPAR}^{2}}{\log_{10}\text{Age}}} \tag{6}\]  
makes possible to reach distribution similar to raw suPAR (Figure 4), as well the normal distribution of values of the index, together with simultaneous independence on patient age (bottom right-hand side in Figure 2). Figure 4: Raw suPAR distributions is the same as the Index of Body Inflammation (calculated as \(\text{IBI}_{\text{SQRTsuPAR2}}\)/g.Age) distribution (\(p\) = 0.9110; Kolmogorov-Smirnov test 0.5613). In this way a measure of the inflammatory reaction (IBI) is obtained, independent on the patient’s age, with a normal distribution and a range of values similar to the original serum activity test results. Note: The calculation was based on index derived from the Equation (6). Figure 3: Values of calculated indeces. The search for body inflammation index-to make the suPAR level independent on patient age together with similar representation of variability.