Data source
In total, 128 original data were collected from hospital patients with HBV infection (defined as HBsAg, HBeAg, anti-HBe or anti-HBc positive; 76 males; mean age of all patients 57.4 ± 13.6 years) at the Second Affiliated Hospital of Dalian Medical University, China. These patients were newly diagnosed by their physicians and blood samples were collected before they received antiviral treatment. There is seroconversion from an HBeAg-positive phase to an HBeAg-negative, and anti-HBe-positive phase during the natural course of infection [13]. Of 128 such patients, 23, 18 and 87 cases were respectively in HBeAg-positive, HBeAg-negative, and anti-HBe-positive phase.
Laboratory tests
HBV markers (HBsAg, anti-HBs, HBeAg, anti-HBe, and anti-HBc) were measured using a chemiluminescent microparticle immunoassay (Cobas E601 analyzer; F. Hoffmann-La Roche Ltd., Basel, Switzerland) per the manufacturer’s protocols. Anti-HBs levels ≥10 mIU/ml were considered positive. Sample value/cut-off values (S/CO) were used as quantitative indicators for HBsAg, HBeAg, anti-HBe, and anti-HBc. S/CO ≥1.0 was defined as positive for HBsAg and HBeAg. The levels of anti-HBe and anti-HBc in the assays for these molecules are inversely proportional to S/CO; thus, S/CO ratios ≤1.0 were considered anti-HBe and anti-HBc positive.
A real-time fluorescence quantitative PCR system (Roche LightCycler 480II, Roche Ltd., Basel, Switzerland) and commercial diagnostic kits were used for the quantitation of HBV-DNA. The detection values were set at 500 IU/mL and serum samples with >500 IU/mL were considered positive for HBV-DNA.
Establishment of quantitative model
HBsAg (a serological marker of HBV infection, both acute and chronic) and HBeAg (found in the blood when virus is present) were designated as representing the infection phase; the quantitative value for the infection phase was defined as the Antigen index (IAg). Anti-HBs, anti-HBe and anti-HBc antibodies (found after an acute infection or in chronic HBV carriers) were designated as representing the immune response phase; the quantitative value of the immune response phase was defined as the Antibody index (IAb).
IAb was taken as an example to explain the establishment of the model. The quantitative levels of anti-HBs, anti-HBc and anti-HBe antibodies were used to establish a three-dimensional co-ordinate system; the area of the triangle they formed was the quantitative value of infection phase (Fig. 1). The area of the triangle was calculated as:
$$ \mathrm{S}={0.5}^{\ast }\ \sin {60}^{\ast }\ \left(\mathrm{anti}\hbox{-} {\mathrm{HBs}}^{\ast }\ 1/\mathrm{anti}\hbox{-} \mathrm{HBe}+\mathrm{anti}\hbox{-} {\mathrm{HBs}}^{\ast }\ \mathrm{anti}\hbox{-} \mathrm{HBc}+\mathrm{anti}\hbox{-} {\mathrm{HBc}}^{\ast }\ 1/\mathrm{anti}\hbox{-} \mathrm{HBe}\right) $$
Note, anti-HBc and anti-HBe were determined by applying the competition method, for which (1/anti-HBe and 1/anti-HBc) should be substituted.
As 0.5 * sin60 was constant, it could be omitted in analysis.
Because the quantitative value (S) is a large number that is impractical to work with, the square root of S can be substituted as demonstrated below.
$$ IAb=\sqrt{antHBs^{\ast }1/ antiHBe+{antiHBs}^{\ast }1/ antiHBc+1/{antiHBe}^{\ast }1/ antiHBc} $$
The calculation theory for IAg was consistent with that for IAb. The formula for IAg is as follow:
$$ \mathrm{IAg}=\sqrt{{\mathrm{HBsAg}}^{\ast}\mathrm{HBeAg}} $$
Statistical analysis
The IAg and IAb indices were not normally distributed; hence they are stated as quartile values. Difference between groups were analyzed using the Mann–Whitney U-test. The relationship between the IAg and IAb indices was assessed using Spearman correlation. Data were considered statistically significant when the probability of a type I error was ≤0.05. Data were analyzed using SPSS ver. 13.0 software for Windows.