A Logistic Regression Model for The Prediction of HBV-Related Cirrhosis

Background: Cirrhosis is one of the most severe complications at the late stage of chronic HBV infection. The liver biopsy is the gold standard for the diagnosis of liver cirrhosis. However, a liver biopsy is associated with the risk of severe complications and a high cost. It is therefore necessary to nd several biomarkers for the diagnosis of HBV-related cirrhosis. Methods: The research was proceeded to evaluate the diagnostic value of hematological parameters to nd the surrogate markers in HBV-related cirrhosis. The research was proceeded on the training set, which was recruited from Zhongnan Hospital, including 102 HBV-related cirrhosis and 102 healthy individuals. The levels of selected hematological parameters were analyzed. The receiver operating characteristic curves were generated to evaluate the diagnostic effectiveness of these parameters. A logistic regression model was built and validated using four validation sets consisting of 261 patients. Results: The result show that the level of RDW, MPV, MPV/PC ratio, PLR and NLR were all signicantly higher in HBV-related cirrhosis patients compared to healthy individuals. Most of these parameters owned a moderate AUC in HBV-related cirrhosis patients. However, their diagnostic sensitivities or specicities were unsatisfactory. Therefore, a logistic regression model was built by combining these hematological parameters. The model showed great diagnostic value with the AUC of 0.987, sensitivity of 96.1% and specicity of 95.1%. Besides, the other four validation sets were generated to validate the logistic regression model and all showed good AUC with moderate specicities and sensitivities. Conclusions: The data indicate that the model might be substantially useful for the diagnosis of HBV-related cirrhosis.

The diagnosis of liver cirrhosis is traditionally based on the patients' manifestations, laboratory assays and imaging tests. However, these diagnostic methods have their limitations. Although the liver biopsy is the gold standard for cirrhosis diagnosis, it is invasive, di cult, expensive, and sometimes accompanied by signi cant morbidity [8,9] . It is therefore not feasible for all patients. It is necessary to nd biomarkers which can distinguish HBV-related cirrhosis in a noninvasive, accurate, and simple manner. Former studies have suggested numerous biochemical molecules such as aspartate aminotransferase , alanine aminotransferase and gamma globulin for cirrhosis or liver brosis detection [10][11][12][13] .However, most of these proteins were investigated in patients with chronic hepatitis C .
It is reported that chronic in ammation is associated with persistent hepatic injury and concurrent tissue regeneration which leads to sequential development of brosis, cirrhosis and eventually HCC [11] .In addition, about one fourth of mild chronic hepatitis patients are affected by cirrhosis within 1 to 13 years of hepatitis onset [14] .
Considering the role of in ammatory responses in cirrhosis development, we designed a research to evaluate diagnostic value of hematological parameters in HBV-related cirrhosis patients compared to healthy people. We focused on white blood cell count (WBC), red blood cell distribu tion width (RDW), mean platelet volume (MPV), MPV/PC ratio, platelet count/lymphocytes ratio (PLR) and number of neutrophils/lympho cytes ratio (NLR). The corresponding ROC curves were used to evaluate diagnostic value. At last, a model was established for the prediction of HBV-related cirrhosis and was validated in four different validation sets from four different hospitals.

Training set
We investigated 102 patients with HBV-related cirrhosis and 102 healthy individuals at Zhongnan Hospital from November 2016 to March 2018. The retrospectively study was under approval of Medical Ethics Committee, Zhongnan Hospital of Wuhan University (201707), and written informed consent was obtained from all participants. Their demographic and blood test results were reviewed in the hospital medical database.

Logistic regression models
A formula for predicting HBV-related cirrhosis was built based on the data in the Training set.-The standard logistic regression formula is: Logit (P) = β0 + β1X1 + βX2 +……+ βnXn.
Regarding Logit(P)=ln[p/(1 − p)], "p" is the estimated probability of HBV-related cirrhosis, "β0" is a constant ,"β" is the in uence coe cient, "n" is the number of in uence factors and "X" is the in uence factors.

Validation sets
Four validation sets were recruited from four centers (Zhongnan Hospital of Wuhan University ;Tongji Hospital, Tongji Medical College of Huazhong University Science and Technology; Union Hospital, Tongji Medical College of Huazhong Science and Technology University; Renmin Hospital of Wuhan University) and were used to assess the performance of the model. They included 261 HBV-related cirrhosis patients and 288 healthy people. 70 HBV-related cirrhosis patients and 80 healthy people, 35 HBV-related cirrhosis patients and 45 healthy people, 31 HBV-related cirrhosis patients and 38 healthy people, 125 HBV-related cirrhosis patients and 125 healthy people were recruited in these sets, respectively.

Statistical analysis
Statistical analysis was performed using SPSS version 22.0 (SPSS, Chicago, IL, USA) or Prism6 (GraphPad software, La Jolla, CA). Data were presented as the mean ± standard deviation (SD). The Shapiro-Wilk test was used to check the normality of the distribution. Normally distributed numeric variables were evaluated by Student's t-test or one-way analyses of variance (ANOVA). Non-normally distributed variables were analyzed by the Mann-Whitney test or nonparametric test and Chi-square test was used to analyze the categorical variables. A difference was considered statistically signi cant when P <0.05. The area under the ROC curve was measured to evaluate the diagnostic value of each hematological pa rameter.

Results
Demographic parameters of the training set 129 patients with cirrhosis were recruited in this -research. The ow chart of the research was showed in Figure 1. After exclusion of 16 patients with alcoholic cirrhosis and 11 patients with chronic hepatitis C infection, 102 patients with HBV-related cirrhosis and 102 age-matched healthy people were enrolled. The healthy people had no medical record of tumor and matched the HBV-related cirrhosis patients in gender (p=0.389), age (p=0.572), height (p=0.646), weight (p=0.190) and smoking (p=0.751) (Table S1).
Hematological parameters of the training set We focused on the expression level of WBC, RDW, MPV, MPV/PC ratio, PLR, and NLR in cirrhosis patients. As presented in Table 1 Table S2.

The correlation between clinical parameters and hematological parameters
Chronic in ammation is associated with persistent hepatic injury and concurrent tissue regeneration, leading to sequential development of brosis, cirrhosis and eventually Hepatocellular carcinoma. We analyzed the correlation between clinical parameters and hematological parameters to nd out the role of these parameters in the progression and metastasis of HBV-related cirrhosis patients. The result showed MPV/PC ratio and PLR were signi cantly correlated with the Child-Pugh score while other parameters not ( Figure 2B to 2F). In addition, all these hematological parameters RDW, MPV, MPV/PC ratio, PLR and NLR were not correlated with smoking or gender ( Table 2).

The logistic regression model for HBV-related cirrhosis
The parameters that were signi cantly changed in the HBV-related cirrhosis patients were then used in the multivariate logistic regression model. RDW, MPV, MPV/PC ratio, PLR and NLR were all considered as independent variables (Table 1)  The estimated probability of 261 HBV-related cirrhosis patients and 228 healthy volunteers were calculated by using the formula Logit (P). In the cohort of Zhongnan Hospital, the probability of 60 (out of 70) HBV-related cirrhosis patients were less than 0.774, and the probability of 70 (out of 80) healthy volunteers were more than 0.774 ( Figure 3A). The AUC of the model for HBV-related cirrhosis was 0.866, with sensitivity of 85.7% and speci city of 87.5%, respectively. In the cohort of Tongji Hospital, the probability of 28 (out of 35) HBV-related cirrhosis patients were less than 0.774, and the probability of 42 (out of 45) healthy volunteers were more than 0.774 ( Figure 3B). The AUC of the model for HBV-related cirrhosis was 0.880, with sensitivity of 80.0% and speci city of 93.3%, respectively. In the cohort of Union Hospital, the probability of 24 (out of 31) HBV-related cirrhosis patients were less than 0.774, and the probability 33 (out of 39) healthy volunteers were more than 0.774 ( Figure 3C). The AUC of the model for HBV-related cirrhosis was 0.813, with sensitivity of 77.4% and speci city of 84.6%, respectively .In the cohort of Renmin Hospital, the probability 110 (out of 125) HBV-related cirrhosis patients were less than 0.774, and the probability 113 (out of 125) healthy volunteers were more than 0.774 ( Figure 3D). The AUC of the model for HBV-related cirrhosis was 0.892, with sensitivity of Discussion Early diagnosis of cirrhosis is important for reducing the complications in patients with chronic HBV infection [15,16] .The liver biopsy is the standard test for distinguishing different liver diseases such as cirrhosis [15] but this test is often associated with high risks of other severe complications, as well as patient discomfort, and costly expense. Therefore, identi cation a reliable and non-invasive cirrhosis diagnosis method is in high demand by physicians and surgeons.
In the present research, we attempted to build a novel affordable and effective model to predict HBV-related cirrhosis using hematological parameters. The blood test, which is routinely done to the chronic HBV infection patients , has essential implications for the natural history of chronic HBV infection [17] . We evaluated the diagnostic value of hematological parameters including WBC, RDW, MPV, MPV/PC ratio, PLR and NLR. Our results indicate that the expression level of RDW, MPV, MPV/PC ratio, PLR and NLR were signi cantly increased in HBV-related cirrhosis patients. Most of them were indicative of HBV-related cirrhosis. Among them, RDW owned the best diagnostic value (AUC=0.970) for HBV-related cirrhosis. However, no signi cant correlation was found between RDW and the Child-Pugh score. RDW, which is used in the differential diagnosis of anemia, is a measure of the range of variation of red blood cell volume.
Previous studies have reported that high RDW level was related to the high mortality risk of in in patients with various disorders [18][19][20] .In our study, we found that RDW was profoundly higher in HBV-related cirrhosis patients compared to healthy people. Our data is consistent with the previous report [21] .The reasons of the elevated RDW might be vitamin B12 or iron de ciency. Interestingly, the AUC of MPV/PC ratio was lower than RDW, but MPV/PC ratio had the highest speci city for HBV-related cirrhosis, in addition, MPV/PC ratio and PLR were signi cantly correlated with the Child-Pugh score, while RDW not. Therefore, it would be better that combining multiple parameters to detect HBV-related cirrhosis. We built the model which combining multiple hematological parameters including RDW, MPV, MPV/PC ratio, PLR and NLR. It had better diagnostic value than any single hematological parameter. Furthermore, we validated the logistic regression model in four different validation sets. We recruited HBV-related cirrhosis patients and healthy volunteers from four different hospitals to constitute different validation sets to avoid the selection bias. The model showed good diagnostic value in all validation sets, indicating that it is effective in predicting HBV-related cirrhosis patients. Previous studies have reported the important role of single biochemical indicators or hematological parameters in cirrhosis diagnosis. Kayadibi [22] showed that cirrhosis might be accurately predicted through measuring platelet count, ALT and AST. Koda M [23] also found that AST to platelet ratio could be a surrogate marker for cirrhosis detection. However, most of these indices were tested in HCV-related cirrhosis patients. In addition, the effectiveness of combinatory in ammatory index in the diagnosis of HBV-related cirrhosis is not well studied. In our research, the model we built showed a better predictive ability than any single in ammatory index. Therefore, this model could be a promising tool for the diagnosis of HBV-related cirrhosis.

Conclusion
This new logistic regression model we built might improve the diagnosis of HBV-related cirrhosis.  Tables   Table1 Hematological parameters analysis of Training set   Parameters HBV-related cirrhosis Healthy controls P Hematological parameters are expressed as mean ± SD; WBC: White blood cell, PC: platelet count, MPV: mean platelet volume, MPV: mean platelet volume, RDW: red blood cell distribution width, MPV/PC ratio: mean platelet volume to platelet count ratio, NLR: neutrophil to lymphocyte ratio, PLR: platelet to lymphocyte ratio;  Figure 1 The ow chart of the retrospective study.

Figure 1
The ow chart of the retrospective study.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. TableS1andS2.docx TableS1andS2.docx