Sparse logistic regression revealed the associations between HBV PreS quasispecies and hepatocellular carcinoma

This study follows the Transparent Reporting of a multivariable prediction model for Individual Prognosis or Diagnosis (TRIPOD) report [30] (Additional file 5: Table S1). HCC patients were enrolled between March 2011 and May 2012 at the Eastern Hepatobiliary Surgery Hospital, Shanghai, China. HBV-related HCC patients fulfilled following criteria: (1) serum hepatitis B virus surface antigen (HBsAg) positive at least 6 months; (2) HBV DNA levels > 1000 IU/ml; (3) HCC characteristic confirmed by operative findings and histopathological examination. The exclusion criteria included hepatitis C virus or human immunodeficiency virus co-infection, a history of liver transplantation, autoimmune liver diseases, metastatic liver cancer, other malignancies, drug-related liver diseases, alcoholic hepatitis and other causes of chronic liver diseases diagnosed before enrollment. CHB patients included fulfilled criteria including: (1) serum HBsAg positive at least 6 months; (2) continuous or repeatedly serum alanine aminotransferase (ALT) elevation (two times above the upper reference range for no other reason than HBV infection) or chronic viral hepatitis characteristic confirmed by liver biopsy; (3) HBV DNA levels > 1000 IU/ml. The exclusion criteria included HCC, the malignancies or other serious disease. This study was approved by The Ethics Committee of the Eastern Hepatobiliary Hospital (EHBHKY2015-01–004). Serum samples were collected from all patients before hepatectomy. Totally, 104 CHB samples and 117 HCC samples were amplified and sequenced successfully, with 63 CHB patients (CHB group) and 46 HBV-related HCC patients (HCC group) in the training set (Shanghai dataset), and 41 CHB and 71 HCC samples in the test set (Shanghai dataset). For the HCC patients, we also collected their clinical examination data.

HBV genomes were extracted from 200 μl of serum samples using the QIAamp DNA Mini kit (QIAGEN GmbH, Hilden, Germany) and eluted in 100 μl of distilled water. The preS region was amplified using Phanta Super-Fidelity DNA Polymerase (Vazyme Biotech, Piscataway, New Jersey, USA) with a pair of primers: 5′-CGCCTCATTYTKYGGGTCA-3′ (forward, nucleotides 2801–2819), and 5′-TCCKGAACTGGAGCCACC-3′ (reverse, nucleotides 62 to 79). PCR amplicons of the preS region were purified with Agencourt AMPure XP beads (Beckman Coulter, Beverly, Massachusetts) and were quantified with the Qubit dsDNA HS assay kit (Invitrogen, Carlsbad, CA, USA). A library of PCR products of the preS region was prepared using the TruSeq DNA PCR-Free sample preparation kit (Illumina, San Diego, CA, USA) and was run on a MiSeq sequencer (Illumina, San Diego, CA, USA) for paired-end sequencing, according to Illumina protocol. Finally, fluorescent signals were analyzed using the MiSeq control software and transferred to sequence data in the FASTQ format.

Quality evaluation of raw reads was performed with the online tool fastqc (http:// www.​bioinformatics.​babraham.​ac.​uk/​projects/​fastqc/​), and the reads having average base calling quality score under 20 were discarded. After quality filtration and adapter removal, paired-end reads were joined with FLASH, v1.2.10 [31]. Merged preS region sequence was genotyped with HBV STAR software as reported previously [32], and corresponding preS regions of 23 reference HBV genomes from the GenBank database were used for genotyping (Accession numbers: X02763, X51970, AF090842, D00329, AB073846, AB602818, X04615, AY123041, AB014381, X65259, M32138, X85254, X75657, AB032431, X69798, AB036910, AF223965, AF160501, AB064310, AF405706, AY090454, AY090457, AY090460). The genotype of each sample was defined as the most frequent one among all 8 types from A to H.

This dataset includes 32 HBV-related HCC patients and 32 CHB patients without HCC (Hong Kong dataset) and patients were enrolled between July 2007 and December 2012 in the Hepatitis and Liver Clinic, Queen Mary Hospital, University of Hong Kong, Hong Kong [16]. Serum samples were collected and sequenced. More details about patients enrollment and HBV sequencing can be found in [16]. Except the Illumina MiSeq platform used in deep sequencing, all the other platforms and tools are different from what we used when generating our data. We got the data from the researchers [16], and used BLAST to map merged reads (fasta format) into HBV reference genome. According to the mapping results, reads with insertions, deletions and turnovers were filtered out. If the normal reads percentage of a sample is less than 20, we removed the sample. Finally, we obtained the data for 26 HCC and 23 CHB patients. The sequence includes 589 nucleotide acids, of which 457 ones are overlapped with the fragment sequenced in our study. We only considered the same 457 positions as those in our dataset for this dataset.

After sequencing the quasispecies, we collected the point mutation data for 457 positions including the positions from 1 to 61 and 2820 to 3215 in and close to the preS region. We counted the frequencies of the nucleotides in each position. To describe the mutation complexity in each position, we transformed the frequency data to Shannon entropy, which is defined as \(H = - \sum\nolimits_{i} {p_{i} } \log p_{i}\), \(\sum\nolimits_{i} {p_{i} } = 1\) where \(i \in \{ A,C,G,T\}\) and p_i is its frequency, \(x\log (x) = 0\) when x = 0. Entropy of all the 457 nucleotide positions of preS region were used as predictors for HCC diagnosis.

We applied Sparse Logistic Regression (SLR) to model the associations between HCC/CHB groups and quasispecies. SLR is to add the term \(\lambda \left\| {\beta_{1} } \right\|\) to the original logistic regression model, where \(\beta\) is the coefficient vector of the variables. This model can simultaneously conduct classification and variable selection. By tuning the parameter \(\lambda\), we can obtain the sparse form of \(\beta\) with the nonzero entries corresponding to the selected variables. The independent variables in our study include the entropy data of the 457 positions, and the response variables denote patients belonging to the CHB or HCC group. We aim to model the associations between the 457 positions and the CHB/HCC group. We applied K-fold cross-validation (CV) to select the parameter \(\lambda\) such that \(\beta\) is the sparsest among those achieving accuracy within one SD of the highest accuracy. Then we applied the fitted model using all training data with selected \(\lambda\) to the test set to see the prediction performance. We directly implemented the function: glmnet() in the R package ‘glmnet’ [16] by setting alpha = 1, which is a parameter to balance the contributions between \(\left\| {\beta_{1} } \right\|\) and \(\left\| {\beta_{2} } \right\|\). With alpha being 1, the \(\left\| {\beta_{2} } \right\|\) term will not contribute to the model, and less variables will be selected with the same classification accuracy. We used four criteria to evaluate the performance of the model in our experiments: accuracy, area under the ROC curve (AUC), sensitivity, and specificity.

For the categorical clinical parameters and those quantitative parameters following non-normal distributions, we applied SLR, as above described. For the parameters following normal distribution, we applied Sparse Partial Least Square regression (SPLS), a method designed to find the combination of all independent variables so as to be most correlated with the response variable. Here, we also imposed l₁ penalty to obtain a sparse solution of the coefficients. We adopted the method proposed in [34] and directly used the R package ‘spls’ [34]. To choose the number of latent components (combinations) κ and the soft threshold η to determine the zero entries of the coefficients, we also used CV to tune the parameters. We first fixed η and varied κ to choose the best κ and then fixed κ to choose the best η.

The baseline information of the CHB and HCC patients (Shanghai dataset) was summarized in Table 1. In both training and test cohort, the HCC patients showed more inferior liver function, older age and lower serum HBV DNA levels.

The nucleotide acid entropy of preS region was calculated and the entropy distribution was shown in Fig. 1A. The median entropy of preS region in CHB patients was 0.0087 (0.0074–0.0092), which is lower than counterpart in HCC patients 0.0090 (0.0076–0.01001). No significant difference was found between entropy of all nucleotide points in preS region (Fig. 1B). When nucleotide points entropy of the preS1 and preS2 were compared respectively, nucleotide points entropy in preS1 region of HCC patients were significantly higher than those in CHB patients. While in preS2 region, the opposite trend was presented between HCC and CHB patients (Fig. 1B). Furthermore, entropy of individual nucleotide positions was compared and the p-value and fold-changes were presented in Fig. 1C. A lot of positions showed significant divergence in entropy between CHB and HCC patients.

Since too many nucleotide positions with divergent entropy exist between CHB and HCC patients, more sophisticated methods should be applied to investigate the associations between nucleotide entropy and HCC development. Thus, we studied the classification of HCC/CHB groups with quasispecies data using SLR [33]. The model was fitted with the training dataset (46 HCC/63 CHB, Shanghai dataset), and was applied to do the prediction in the test sets (71 HCC/41 CHB, Shanghai dataset). To tune the parameter λ that controls the selection of the variables (nucleotide positions), we ran fivefold CV 50 times in the training set. The value of λ started from 0.5² with a proportion of 0.5 to decrease, and the length of λ was set as 15. Figure 2 shows the prediction results for all λ’s. In the training data, when λ is less than 0.5³ (the 2nd point), the four evaluation criteria are all stable, with sensitivity having the greatest SD. In the test set, both accuracy and AUC were stable starting from λ = 0.5³. Here, λ was chosen as 0.5³, and Table 2 shows the classification results. The accuracy and AUC achieved a mean value of 0.861 (SD = 0.032) and 0.883 (SD = 0.043) in the training set and 0.794 and 0.795, respectively, in the test set. The SLR model performed more superior than classic logistic regression model in Table 2. This shows the high associations between HBV quasispecies and HCC development.

The final obtained prediction model using SLR is:where the subscript of each variable means the point mutation positions that were selected. For each sample, after the entropy of each position is calculated, the sample is centralized by subtracting the mean entropy. Then the above formula is applied to compute the probability of being CHB or HCC, with a smaller probability leading to CHB.

Other machine learning methods were also investigated. We compared the above results with those obtained using Support Vector Machine (SVM) [35, 36] and Sparse Support Vector Machine (SSVM) [37]. SVM is a popular classification method in machine learning, which classifies the samples using all the considered variables. Similar to SLR, SSVM is formulated as a hinge loss function with an l₁ penalty term to select the associated variables when doing classification [37]. We implemented SVM using the R package ‘e1071’, and SSVM using R package ‘sparseSVM’ [37], respectively. Using similar procedure as SLR, we trained the model using the training set and applied it to the test set. The prediction results in the test dataset are also shown in Table 2. For SSVM, we also did model calibration using the R package ‘platt’ [38], which implements Platt calibration. Platt calibration is to transform the classification outputs into a probability distribution over classes by fitting a logistic regression model to a classifier’s scores. The performance of SSVM can be improved after calibration. Since SLR outputs the probability for each sample being HCC patient, we directly gave its calibration plot. The prediction results and the reliability diagrams of both SLR and calibrated SSVM were put in Additional file 1: Figure S1 and Additional file 6: Table S2, which shows similar performance. Though the AUC for SVM is higher than that of SLR, it cannot identify the associated variables. The performance of both SSVM and calibrated SSVM is much worse than SLR. Thus, our following analysis for CHB/HCC classification is based on SLR.

To see the differences between the samples of different genotypes, we studied the samples of genotype C and genotype B separately. With the same model training method, we chose λ = 0.5⁸ and λ = 0.5³ for patients of genotype B and genotype C, respectively. The results for different λ’s are shown in Additional file 3: Figure S3, and the results for the chosen λ are listed in Table 4. Compared to results that using all the patients, the specificity increased and the sensitivity decreased for patients of genotype B. Meanwhile, the specificity decreased and the sensitivity increased by several fold for patients of genotype C.

We also performed cross-prediction as a check on prediction performance. We trained the model with genotype C or B patients in the training set and predicted the other genotype patients in the test set. The results were added in Table 4. Accuracy and AUC were both comparable to those within the same genotype, while sensitivity and specificity showed more changes. Thus, for prediction purposes, this finding implies that we might combine all individuals together to produce a larger sample size, as demonstrated by our experiments.

For the HCC patients, we investigated the associations between HBV quasispecies and clinical parameters. For the categorical clinical parameters and those quantitative parameters following non-normal distributions, we applied SLR. For the parameters following normal distribution, we applied SPLS [39]. Owing to the small sample size, we ran tenfold CV 50 times to choose the parameters λ, η, and κ. When we applied the SPLS model, η was set between 0.1 and 0.9 with a step size of 0.1, and κ varied between 2 and 10. If the AUC for the independent test was greater than 0.60, we took the clinical parameter as being associated with HBV quasispecies. Finally, we found that the serum indexes: hepatits B e antigen (HBeAg), HBVDNA, and alkaline phosphatase (ALP) were associated with HBV quasispecies. The classification results for different values of λ and η were showed in Additional file 4: Figure S4. Table 5 shows the classification results for the selected λ and η.

When classifying the HBeAg-positive and -negative patients in the training set, both accuracy and AUC were around 0.9. While the accuracy and AUC in the test set were 0.672 and 0.607, respectively. For the parameter HBVDNA, the accuracy and AUC were around 0.7 for all η’s in the training set. In the test set, the accuracy and AUC decreased to 0.676 and 0.675, respectively. Similarly, for ALP, both accuracy and AUC were stable with all η's around 0.8 and 0.7 in the training set. While the accuracy and AUC were 0.634 and 0.648 in the test set.